CHEM 301 - ORGANIC CHEMISTRY I Bond Length and Bond Energy Question Bank Set 3

CHEM 301 - ORGANIC CHEMISTRY

I - Bond Length and Bond Energy

Question Bank - Set 3

Liberty University

Question 1

Question

Calculate the bond length between two oxygen atoms in an ozone molecule (O3)

based on the experimental bond energy of the O=O double bond and the O-O

single bond.

Solution

To calculate the bond length between two oxygen atoms (O3) in an ozone

molecule, we can use the relationship between bond length and bond energy.

Given experimental data:



Bond energy of O=O double bond: 498 kJ/mol



Bond energy of O-O single bond: 146 kJ/mol

Let the bond length of the O=O double bond be d1and the bond length of

the O-O single bond be d2. We can use the following equation:

Total bond energy in ozone molecule = 2×(bond energy of O=O double bond)+(bond energy of O-O single bond)

Step 1: Calculate the total bond energy in an ozone molecule

Total bond energy in ozone molecule = 2 ×498 + 146 = 1142 kJ/mol

Step 2: Determine the total bond length in an ozone molecule using the

experimental bond energies

Total bond energy in ozone molecule = 2 ×D

d1+D

Solving for D:

1142 = 2 ×D

d1+D

Step 3: Substitute the given bond energy values to solve for D

1142 = 2 ×D

498+D

146

Step 4: Solve for D

1142 = 2D

498 +D

146

1142 = 2D×146 + D×498

498 ×146

1142 = 292D+ 498D

72908

1142 ×72908 = 790D

D=1142 ×72908

790

D≈10500 kJ/mol

Therefore, the bond length between two oxygen atoms in an ozone molecule

is approximately 10500 kJ/mol.

Question 2

Question

Predict which bond is stronger - a C-C sigma bond or a C=C pi bond. Justify

your answer with an explanation based on bond length and bond energy.

Solution

To determine which bond is stronger between a C-C sigma bond and a C=C

pi bond, we need to consider the bond length and bond energy of each type of

bond.

Step 1: Bond Length - A single C-C sigma bond is longer than a C=C pi

bond. This is because the sigma bond has more overlap between the atomic

orbitals of the carbon atoms compared to the pi bond, which has less overlap.

- Therefore, the C-C sigma bond has a longer bond length than the C=C pi

bond.

Step 2: Bond Energy - Bond energy is the energy required to break a

bond between two atoms. - Generally, a shorter bond has a higher bond energy

because the atoms are held closer together by stronger forces. - As the C=C pi

bond is shorter than the C-C sigma bond, it has a higher bond energy.

Step 3: Conclusion - The C=C pi bond is stronger than the C-C sigma

bond due to its shorter bond length and higher bond energy. - Therefore, the

C=C pi bond is stronger than the C-C sigma bond in terms of bond strength.

Question 3

Question

For a given molecule X, the carbon-carbon bond length is 1.54 ˚

A and the carbon-

hydrogen bond length is 1.09 ˚

A. The bond energy for the carbon-carbon bond

is 347 kJ/mol and for the carbon-hydrogen bond is 413 kJ/mol. Calculate the

total bond energy needed to break all the carbon-carbon bonds and all the

carbon-hydrogen bonds in one mole of molecule X.

Solution

Step 1: Calculate the total energy needed to break all the carbon-carbon bonds

in one mole of molecule X. Given: Carbon-carbon bond length, dC-C = 1.54 ˚

= 1.54 ×10−10 m Bond energy for carbon-carbon bond, EC-C = 347 kJ/mol =

347 ×103J/mol

The bond energy can be calculated as

E=EC-C

=347 ×103

6.022 ×1023 ≈5.77 ×10−19 J

The total energy needed to break all the carbon-carbon bonds in one mole

of molecule X is given by

Total energy for C-C bonds = EC-C ×Number of C-C bonds in one mole

Since each molecule X contains two carbon atoms connected by a carbon-

carbon bond, there will be NA/2 carbon-carbon bonds in one mole of molecule

Total energy for C-C bonds = 5.77 ×10−19 ×6.022 ×1023

2= 173.1 kJ/mol

Step 2: Calculate the total energy needed to break all the carbon-hydrogen

bonds in one mole of molecule X.

Given: Carbon-hydrogen bond length, dC-H = 1.09 ˚

A=1.09 ×10−10 m

Bond energy for carbon-hydrogen bond, EC-H = 413 kJ/mol = 413 ×103J/mol

The bond energy can be calculated as

E=EC-H

=413 ×103

6.022 ×1023 ≈6.86 ×10−19 J

The total energy needed to break all the carbon-hydrogen bonds in one mole

of molecule X is given by

Total energy for C-H bonds = EC-H ×Number of C-H bonds in one mole

Since each carbon atom in molecule X is connected to three hydrogen atoms

by carbon-hydrogen bonds, there will be 3NAcarbon-hydrogen bonds in one

mole of molecule X.

Total energy for C-H bonds = 6.86 ×10−19 ×3×6.022 ×1023 = 1239.6 kJ/mol

Therefore, the total bond energy needed to break all the carbon-carbon

bonds and all the carbon-hydrogen bonds in one mole of molecule X is 173.1

kJ/mol for carbon-carbon bonds and 1239.6 kJ/mol for carbon-hydrogen bonds,

resulting in a total of 1412.7 kJ/mol.

Question 4

Question

A carbon-carbon double bond consists of a sigma bond and a pi bond. The

carbon-carbon pi bond is formed by the sideways overlap of p orbitals. Given

that the bond length of a carbon-carbon sigma bond is 0.154 nm and the bond

length of a carbon-carbon pi bond is 0.134 nm: Calculate the percentage increase

in bond energy required to break a pi bond relative to breaking a sigma bond.

Solution

Step 1: Calculate the bond energy of each type of bond. The bond energy (E)

of a bond can be calculated using the equation:

E=Energy

Mole

For a carbon-carbon sigma bond:

Eσ=Energyσ

1 mole

For a carbon-carbon pi bond:

Eπ=Energyπ

1 mole

Step 2: Calculate the percentage increase in bond energy. The percentage

increase in bond energy required to break a pi bond relative to breaking a sigma

bond can be calculated using the formula:

Percentage Increase = Eπ−Eσ

Eσ×100%

Now, substituting the given values:

Eσ=Energyσ

1 mole

Eπ=Energyπ

1 mole

Bond Length of sigma bond (σ)=0.154 nm

Bond Length of pi bond (π)=0.134 nm

Percentage Increase = Eπ−Eσ

Eσ×100%

Percentage Increase = Energyπ/1−Energyσ/1

Energyσ/1×100%

Percentage Increase = Energyπ−Energyσ

Energyσ×100%

Percentage Increase = 

Energyπ

1 mole −Energyσ

1 mole 

Energyσ

1 mole 

×100%

Substitute the bond lengths into the bond energy equations and then cal-

culate the percentage increase in bond energy to break a pi bond relative to

breaking a sigma bond.

Question 5

Question

The bond length between two carbon atoms in ethylene (C2H4) is 1.33 ˚

A. The

bond energy of a C-C single bond is 347 kJ/mol and the bond energy of a C=C

double bond is 602 kJ/mol. Calculate the percent ionic character of the C-C

bond in ethylene.

Solution

Step 1: Calculate the actual bond energy of the C-C bond in ethylene. The

actual bond energy is defined as the energy required to break the bond com-

pletely. Since there are two C-C bonds in ethylene, we need to consider both

bonds.

Actual bond energy of the C-C bond = 2 ×347 kJ/mol = 694 kJ/mol

Step 2: Calculate the expected bond energy of two C atoms with a single

bond. This is done by finding the sum of the bond energies of two isolated

carbon atoms.

Expected bond energy of two C atoms with a single bond = 2×602 kJ/mol = 1204 kJ/mol

Step 3: Calculate the percent ionic character of the C-C bond in ethylene

using the formula:

Percent Ionic Character = 1−Actual bond energy

Expected bond energy×100%

=1−694

1204×100% = (1 −0.5764) ×100% = 42.36%

Therefore, the percent ionic character of the C-C bond in ethylene is 42.36

Question 6

Question

For the molecule benzene (C6H6), the carbon-carbon bonds have a length of

140 pm and a bond energy of 516 kJ/mol. Calculate the wavelength of the

radiation absorbed when a benzene molecule undergoes the transition from the

ground state to the first excited state due to the stretching of the carbon-carbon

bond. (Assume the molecule behaves like a harmonic oscillator and use the

formula E=hc/λ, where Eis the energy difference between the two states,

his Planck’s constant, cis the speed of light, and λis the wavelength of the

absorbed radiation.)

Solution

Step 1: First, let’s calculate the energy difference between the ground state

and the first excited state due to the stretching of the carbon-carbon bond in

benzene. Given: Bond energy for carbon-carbon bond = 516 kJ/mol 1 kJ/mol

= 6.022 ×1026 Hz

1. Calculate the energy change:

E= Bond energy = 516 kJ/mol = 516 ×103J/mol

E= 516 ×103J/mol ×1 mol

6.022 ×1026 Hz = 8.57 ×10−19 J

Step 2: Now, we can use the formula E=hc/λ to calculate the wavelength

of the absorbed radiation. Given: h= 6.626 ×10−34 J s c= 3.00 ×108m/s

2. Calculate the wavelength:

8.57 ×10−19 J = (6.626 ×10−34 J s) ×(3.00 ×108m/s)/λ

λ= (6.626 ×10−34 J s ×3.00 ×108m/s)/8.57 ×10−19 J

λ≈219.3 nm

Therefore, the wavelength of the absorbed radiation when a benzene molecule

undergoes the transition from the ground state to the first excited state due to

the stretching of the carbon-carbon bond is approximately 219.3 nm.

Question 7

Question

Consider the following molecule:

H−[: 30]C−[: −30] −[: 30]C−[: −30]H

Estimate the approximate bond lengths and classify each bond as a single or

double bond. Assume that the carbon-hydrogen bond length is approximately

1.09 ˚

A. Given that a carbon-carbon single bond has a length of 1.54 ˚

A and a

carbon-carbon double bond has a length of 1.34 ˚

A, determine the total bond

energy for this molecule.

Solution

Step 1: Identify the bonds in the molecule and classify them as single or double

bonds.

The molecule has two types of bonds: carbon-hydrogen (C-H), carbon-

carbon single (C-C), and carbon-carbon double (C=C) bonds. To determine

the type of bonds present, we need to consider the hybridization of the carbon

atoms.

The central carbon atom is sp hybridized due to its linear shape. Therefore,

the central carbon atom forms a triple bond with one adjacent carbon atom and

a single bond with the other.

Thus, the bonds in the molecule are as follows: - Carbon-hydrogen (C-H)

bonds: 6 - Carbon-carbon single (C-C) bonds: 1 - Carbon-carbon double (C=C)

bonds: 1

Step 2: Calculate the bond lengths for each type of bond.

Given bond lengths: - Carbon-hydrogen (C-H) bond length: 1.09 ˚

A - Carbon-

carbon single (C-C) bond length: 1.54 ˚

A - Carbon-carbon double (C=C) bond

length: 1.34 ˚

From the structure of the molecule, we can determine the approximate bond

lengths: - C-H bond length: 1.09 ˚

A - C-C single bond length: 1.54 ˚

A - C-C

double bond length: 1.34 ˚

Step 3: Calculate the total bond energy for the molecule.

The bond energy (E) for each type of bond can be calculated using the

formula:

E=k×1

where kis the bond force constant and dis the bond length. The force

constant for C-H, C-C single, and C-C double bonds can be assumed to be

constant.

Using the given lengths, we can calculate the bond energy for each type of

bond and then sum up the total bond energy for the molecule:

For C-H bonds:

EC-H =k×1

(1.09)2

For C-C single bonds:

EC-C single =k×1

(1.54)2

For C-C double bonds:

EC-C double =k×1

(1.34)2

Total bond energy for the molecule:

Etotal = 6 ×EC-H +EC-C single +EC-C double

Question 8

Question

Calculate the bond length of a C-C single bond in ethane given that the bond

energy is 348 kJ/mol.

Solution

To calculate the bond length of a C-C single bond in ethane, we can use the

relationship between bond energy and bond length. The bond energy can be

converted to energy per bond by dividing it by Avogadro’s number. This energy

per bond can then be converted to length using the conversion factor for energy

to length.

Step 1: Convert the bond energy to energy per bond:

Energy per bond = 348 kJ/mol

6.022 ×1023 molecules/mol

Step 2: Convert the energy per bond to energy per C-C bond in ethane:

Energy per C-C bond in ethane = Energy per bond

Step 3: Convert the energy per C-C bond in ethane to bond length:

Bond length = Energy per C-C bond in ethane

Conversion factor

Given that the conversion factor for energy to length is approximately 1 eV =

1.602×10−19 J, and 1 eV is equivalent to 1.602×10−19 J, so the conversion factor

is 1 J = 1.602 ×1019 m−1.

Step 4: Substitute the values into the formula:

Bond length = Energy per C-C bond in ethane

Conversion factor

Step 5: Calculate the bond length: Substitute the values calculated in Steps

1 - 3 into the formula and solve for the bond length.

Question 9

Question

Explain the relationship between bond length and bond energy in covalent

molecules. Provide examples to illustrate your explanation.

Solution

Step 1: Bond length is the distance between the nuclei of two bonded atoms,

while bond energy is the amount of energy required to break a bond. In general,

there is an inverse relationship between bond length and bond energy: shorter

bond lengths correspond to stronger bonds and higher bond energies.

Step 2: For example, let’s compare the carbon-carbon bonds in ethane (C-

C) and ethyne (CC). The bond length of a carbon-carbon single bond in ethane

is longer than the bond length of a carbon-carbon triple bond in ethyne.

Step 3: Ethane has a C-C single bond with a bond length of approximately

1.54 ˚

A and a bond energy of about 347 kJ/mol. Ethyne has a CC triple bond

with a bond length of approximately 1.20 ˚

A and a bond energy of about 839

kJ/mol.

Step 4: The shorter bond length in ethyne indicates a stronger bond com-

pared to the longer bond in ethane. This is reflected in the much higher bond

energy of the triple bond in ethyne compared to the single bond in ethane.

Step 5: Therefore, the relationship between bond length and bond energy

can be summarized as follows: shorter bond lengths correspond to stronger

bonds with higher bond energies, while longer bond lengths correspond to

weaker bonds with lower bond energies.

Question 10

Question

Calculate the bond energy of a carbon-carbon double bond if it is known that

the bond length is 1.33 ˚

A and the bond energy of a carbon-carbon single bond

is 348 kJ/mol.

Solution

Step 1: Convert the bond length from angstroms to meters. Given that 1 ˚

A =

1×10−10 m, the bond length of 1.33 ˚

A is equivalent to 1.33 ×10−10 m.

Step 2: Calculate the spring constant for the double bond. Using Hooke’s

Law (E= 1/2kx2), where Eis the bond energy, kis the spring constant, and

xis the bond length: k=2E

x2For the single carbon-carbon bond: ksingle =

2×348

(1.33×10−10 )2.

Step 3: Calculate the bond energy of the double bond. For the double bond,

the spring constant is the sum of the individual spring constants of each bond:

kdouble = 2 ×ksingle Edouble =1

2kdouble ×(1.33 ×10−10)2

Step 4: Substitute the values to find the bond energy of the carbon-carbon

double bond. Edouble =1

2×2×2×348

(1.33×10−10 )2×(1.33 ×10−10)2

Question 11

Question

Consider the following molecules and their bond lengths:

Molecule Bond Length (˚

Ethane 1.54

Ethylene 1.33

Acetylene 1.21

Determine the average bond energy (in kJ/mol) of the carbon-carbon bond

in these molecules. Assume that the bond energy is inversely proportional to

the square of the bond length.

Solution

To find the average bond energy of the carbon-carbon bond in these molecules,

we will first calculate the individual bond energy and then find the average.

Step 1: Calculate the bond energy for each bond.

The relationship between bond energy and bond length is given as E∝1

r2,

where Eis the bond energy and ris the bond length.

For ethane:

Bond Energy = k×1

(1.54)2

For ethylene:

Bond Energy = k×1

(1.33)2

For acetylene:

Bond Energy = k×1

(1.21)2

Step 2: Find the average bond energy.

To find the average bond energy, we calculate the arithmetic mean of the

three bond energies:

Average Bond Energy = Bond Energyethane + Bond Energyethylene + Bond Energyacetylene

Substitute the calculated bond energies for each molecule and then find the

average bond energy in kJ/mol.

Question 12

Question

For the following compounds, rank them in order of increasing C-C bond length:

1. Ethane (C2H6) 2. Ethylene (C2H4) 3. Acetylene (C2H2)

Solution

To rank the compounds in order of increasing C-C bond length, we need to

consider the types of bonds present in each compound.

Step 1: Ethane has a single C-C bond, ethylene has a double C=C bond,

and acetylene has a triple CC bond. The general trend is that as the number

of bonds between two atoms increases, the bond length decreases.

Step 2: Therefore, the compounds in order of increasing C-C bond length

are: 1. Acetylene (C2H2) with a triple CC bond (shortest bond length) 2.

Ethylene (C2H4) with a double C=C bond 3. Ethane (C2H6) with a single C-C

bond (longest bond length)

Question 13

Question

Draw the Lewis structure for sulfur dioxide (SO2) and determine the bond

angle between the sulfur-oxygen bonds. Given that the bond length of the

sulfur-oxygen bond is 1.48 ˚

A and the bond energy is 523 kJ/mol, calculate the

formaldehyde (H2CO) bond angle between the carbon-oxygen bonds assuming

the bond length is 1.43 ˚

Solution

To determine the bond angle in sulfur dioxide (SO2): Step 1: Draw the Lewis

structure for sulfur dioxide (SO2). The Lewis structure for SO2involves a central

sulfur atom single bonded to two oxygen atoms with one double bond between

sulfur and one of the oxygen atoms.

Step 2: Determine the bond angle between the sulfur-oxygen bonds. In SO2,

the structure is trigonal planar with bond angles of approximately 120 degrees

between the sulfur-oxygen bonds.

To calculate the bond angle in formaldehyde (H2CO) using the bond length

and bond energy: Step 3: Calculate the formaldehyde bond angle between the

carbon-oxygen bonds. Given that the bond length between carbon and oxygen

is 1.43 ˚

A and the bond energy is 523 kJ/mol for sulfur dioxide, we can assume

a similar bond energy value for H2CO. The bond energy can be converted to

kilocalories per mole by dividing by 4.184 to give 125 kcal/mol.

Step 4: Use the bond length information to determine the bond angle be-

tween the carbon-oxygen bonds. Using the given bond length of 1.43 ˚

A for

H2CO and the assumption of the bond energy being 125 kcal/mol, we can use

the relationship between bond length and bond angle to estimate the carbon-

oxygen bond angle. Typically, shorter bond lengths indicate stronger bonds and

larger bond angles.

Therefore, based on the bond length of 1.43 ˚

A of the carbon-oxygen bond

in formaldehyde, we expect a slightly larger bond angle compared to the sulfur-

oxygen bond angle of 120 degrees in SO2.

Question 14

Question

The bond length between two carbon atoms in benzene is approximately 139

picometers. Calculate the bond energy of the carbon-carbon bond in benzene

in units of kJ/mol. (Hint: The bond energy is the energy required to break one

mole of bonds.)

Solution

Step 1: We first need to convert the bond length from picometers to meters.

Given: 1 picometer (pm) = 1 ×10−12 meters

Therefore, the bond length in meters is:

139 pm = 139 ×10−12 m=1.39 ×10−10 m

Step 2: Next, we can calculate the force constant (k) using Hooke’s law,

which relates bond energy (E) to bond length (r) and force constant (k) using

the equation:

E=1

2kr2

Since the bond energy is the energy required to break one mole of bonds, we

will need to calculate the bond energy per bond energy unit.

Step 3: Now, we need to calculate the force constant (k) for the carbon-

carbon bond in benzene. The force constant for a bond can be approximated

using the equation:

k=(2.31 ×105J/mol ·m2)

Substitute the known values:

k=(2.31 ×105J/mol ·m2)

(1.39 ×10−10 m)2

k=2.31 ×105

1.93 ×10−20

k= 1.195 ×1025 N/m

Step 4: Finally, we can calculate the bond energy (E) using the calculated

force constant (k) and bond length (r):

E=1

2kr2

E=1

2×1.195 ×1025 N/m ×(1.39 ×10−10 m)2

E=1

2×1.195 ×1025 ×1.93 ×10−20 J

E= 1.146 ×106J/mol

Therefore, the bond energy of the carbon-carbon bond in benzene is 1.146

106J/mol.

Question 15

Question

In a molecule of benzene (C6H6), the average bond length between carbon

atoms is 1.39 ˚

A. Given that the bond energy of a carbon-carbon single bond is

348 kJ/mol and the bond energy of a carbon-carbon double bond is 614 kJ/mol,

calculate the total bond energy in a molecule of benzene.

Solution

Step 1: Determine the total number of carbon-carbon bonds in a molecule of

benzene. Each carbon atom is connected to 3 other carbon atoms in the benzene

ring. Therefore, in a molecule of benzene, there are 6 carbon atoms, resulting

in a total of 6 ×3 = 18 carbon-carbon bonds.

Step 2: Calculate the total bond energy in a molecule of benzene. Since each

carbon-carbon bond in benzene is a combination of a single bond and a double

bond, we can consider it as 1.5 bonds worth of energy. The total bond energy

in a molecule of benzene is then:

18 ×1.5×348 kJ/mol = 9468 kJ/mol

Thus, the total bond energy in a molecule of benzene is 9468 kJ/mol .

Question 16

Question

For the molecules below, rank them in order of increasing bond length:

1. C-C bond in ethane

2. C-C bond in ethylene

3. C-C bond in acetylene

Solution

To rank the C-C bonds in ethane, ethylene, and acetylene by increasing bond

length, we need to consider the bond order of each molecule.

Step 1: In ethane (C2H6), the C-C bond is a single bond, which has a bond

order of 1.

Step 2: In ethylene (C2H4), the C-C bond is a double bond, which has a

bond order of 2.

Step 3: In acetylene (C2H2), the C-C bond is a triple bond, which has a

bond order of 3.

Therefore, the C-C bonds should be ranked in order of increasing bond length

as follows:

1. C-C bond in acetylene (shortest bond length due to triple bond)

2. C-C bond in ethylene (intermediate bond length due to double bond)

3. C-C bond in ethane (longest bond length due to single bond)

Question 17

Question

The carbon-carbon double bond in ethene (C2H4) has a bond length of approx-

imately 1.34 ˚

A and a bond energy of approximately 610 kJ/mol. Calculate the

force constant of this double bond.

Solution

Step 1: Convert the bond length from angstroms to meters.

1˚

A=1×10−10 m

So, the bond length of 1.34 ˚

A is equal to 1.34 ×10−10 m.

Step 2: Convert the bond energy from kJ/mol to joules.

1 kJ/mol = 1000 J/mol

So, the bond energy of 610 kJ/mol is equal to 610 ×1000 J/mol.

Step 3: Determine the reduced mass of the C-C double bond. The reduced

mass can be calculated using the formula:

µ=m1·m2

m1+m2

where m1and m2are the masses of the two carbon atoms. The mass of a carbon

atom is approximately 12 atomic mass units (amu).

µ=12 amu ·12 amu

12 amu + 12 amu

µ=144 amu2

24 amu

µ= 6 amu

Step 4: Calculate the force constant using the formula:

k=(2πf)2·µ

4π2

where fis the frequency of the bond vibration. The frequency fcan be calcu-

lated from the bond energy using the formula:

E=hf

where his the Planck’s constant.

Step 5: Calculate the frequency of the bond vibration.

610 ×1000 J/mol = 6.626 ×10−34 J s ·f

f=610 ×1000 J/mol

6.626 ×10−34 J s

f≈9.20 ×1013 Hz

Step 6: Substitute the values into the force constant formula and solve for

k=(2π×9.20 ×1013 Hz)2·6 amu

4π2

k=(2π×9.20 ×1013 Hz)2·6×10−3kg/mol

4π2

k≈1000 N/m

Therefore, the force constant of the carbon-carbon double bond in ethene is

approximately 1000 N/m.

Question 18

Question

The bond length of a C-C bond in benzene is approximately 1.39 ˚

A. The bond

energy of a C-C single bond is 346 kJ/mol. Calculate the expected bond energy

of the C-C bonds in benzene given that it has resonance structures.

Solution

Step 1: Calculate the bond energy of an average C-C bond in benzene. Given

that benzene has resonance structures, each C-C bond in benzene is a combi-

nation of a single and a double bond. Thus, the average bond order of the C-C

bond in benzene is 1.5. The bond energy of a C-C single bond is 346 kJ/mol.

The bond energy of a C-C double bond is greater than that of a single bond,

and typically around 615 kJ/mol. Therefore, the expected bond energy of an

average C-C bond in benzene can be approximated as the average of the bond

energy of a single and a double bond:

346 + 615

2= 480.5 kJ/mol

Step 2: Calculate the total bond energy of all C-C bonds in benzene. Benzene

has a total of 6 C-C bonds. Therefore, the total bond energy of all C-C bonds

in benzene can be calculated as:

6×480.5 = 2883 kJ/mol

Step 3: Answer The expected bond energy of the C-C bonds in benzene,

considering its resonance structures, is 2883 kJ/mol.

Question 19

Question

Calculate the bond length of a carbon-carbon single bond given that the bond

energy is 348 kJ/mol.

Solution

Step 1: Recall that bond length and bond energy are related by Hooke’s Law,

which states that the bond energy is directly proportional to the square of the

bond length.

Step 2: We can express this relationship mathematically as:

E=k·r2

where: - Eis the bond energy (348 kJ/mol), - kis a constant, and - ris the

bond length.

Step 3: Rearranging the equation, we get:

r=rE

Step 4: To find the bond length, we need to determine the value of the

constant k.

Step 5: Bond energy is typically given in kJ/mol, so we need to convert it

to joules per bond.

1 kJ/mol = 1000 J/mol = 1000 J/mol×1 mol

6.022 ×1023 molecules =1000

6.022 ×1023 J/bond

Step 6: Calculating the value of k:

k=348 kJ/mol

6.022 ×1023 bonds/mol =348 ×103

6.022 ×1023 J/bond

Step 7: Substitute the values of Eand kinto the equation:

r=r348 ×103

6.022 ×1023

Step 8: Calculate the bond length rto determine the carbon-carbon single

bond length.

Question 20

Question

The bond length between the carbon atoms in a benzene ring is approximately

1.39 ˚

A. Calculate the bond energy in kJ/mol for the carbon-carbon bond in

benzene.

Solution

Step 1: First, we convert the bond length from angstroms to meters: 1.39 ˚

A =

1.39 ×10−10 m

Step 2: Next, we use the formula for calculating bond energy Eusing the

bond length r:

E=k×r

where kis the force constant for a carbon-carbon single bond, which is approx-

imately 305 N/m.

Step 3: Now, we substitute the values into the formula:

E=305 N/m ×1.39 ×10−10 m

Step 4: Calculate the bond energy in joules:

E=305 ×1.39 ×10−10

Step 5: Next, convert the bond energy from joules to kilojoules (1 J =

1×10−3kJ):

E=305 ×1.39 ×10−10

2×10−3kJ

Step 6: Simplify and calculate the bond energy:

E=305 ×1.39 ×10−10

2×10−3kJ = 2.12 kJ/mol

Therefore, the bond energy for the carbon-carbon bond in benzene is 2.12

kJ/mol.

Question 21

Question

For the molecule CO2, explain the relationship between its bond length and

bond energy. How do these properties influence the overall stability of the

molecule?

Solution

To understand the relationship between bond length, bond energy, and stability

in the molecule CO2, we first need to examine its structure and bonding.

Step 1: Starting with the Lewis structure of CO2, we see that it consists of

one carbon atom double-bonded to two oxygen atoms.

Step 2: The double bonds in CO2consist of one sigma bond and one pi

bond between carbon and each oxygen atom.

Step 3: The presence of the pi bond in the double bond makes it stronger

and shorter than a single bond. Therefore, the carbon-oxygen bonds in CO2

are shorter and stronger than typical carbon-oxygen single bonds.

Step 4: As a result, the bond energy of the carbon-oxygen bonds in CO2

are higher than that of a typical carbon-oxygen single bond. This means that

more energy is required to break the bonds in CO2compared to a single bond.

Step 5: The shorter bond length and higher bond energy in CO2contribute

to its stability as a molecule. The strong carbon-oxygen bonds ensure that the

molecule is held together firmly, making it less likely to react or decompose

easily.

Step 6: In summary, the relationship between bond length, bond energy,

and stability in CO2is such that the shorter and stronger carbon-oxygen bonds

result in a more stable molecule that is less reactive due to the higher energy

required to break these bonds.

Question 22

Question

Calculate the bond energy and the bond length of a carbon-carbon single bond

in ethane (C2H6) given that the enthalpy change for the reaction below is -1560

kJ/mol:

C2H6(g)→2CH3(g)

Solution

Step 1: Write the balanced chemical equation for the reaction and determine

the enthalpy change per mole of C-C single bond broken. Step 2: Calculate the

C-C single bond energy and the bond length using the given enthalpy change

value.

Step 1: First, let’s write out the balanced chemical equation for the reaction

and determine the enthalpy change per mole of C-C single bond broken:

2C2H6(g)→CH3(g)

Since the given enthalpy change is for the formation of two methyl radicals,

the enthalpy change per mole of C-C single bond broken is half of the given

value:

∆H=−1560 kJ/mol

2 mol =−780 kJ/mol

Step 2: To calculate the C-C single bond energy and the bond length, we

use the fact that the bond energy and bond length are inversely related. The

Bond energy can be calculated using the formula:

Bond energy = energy of single C-C bond = −∆H= 780 kJ/mol

The bond energy can also be converted to kilojoules per mol, which is the

typical unit for expressing bond energies.

Now, we can use the calculated bond energy to find the bond length. There

is no direct formula to calculate bond length from bond energy, but we can use

experimental values from literature. For a C-C single bond, the typical bond

energy is around 348 kJ/mol. Substituting this value into the formula, we have:

Energy = Bond energy = k×bond length

Solving for bond length ro:

780 = k×bond length

348

Bond length = 780 ×348

This will give us an estimate of the bond length using the given enthalpy

change.

Question 23

Question

For a certain molecule, the carbon-carbon bond length is measured to be 1.54

A. The experimental bond energy for this molecule is found to be 348 kJ/mol.

Calculate the theoretical bond energy of a carbon-carbon single bond using the

average bond length of 1.54 ˚

A. Assume the bond length is directly proportional

to the bond energy.

Solution

To calculate the theoretical bond energy of a carbon-carbon single bond using

the average bond length of 1.54 ˚

A, we can set up a proportionality relationship

between bond length and bond energy. The experimental bond energy is given

as 348 kJ/mol.

Step 1: Find the average bond length and bond energy for a

carbon-carbon single bond. Given bond length, l= 1.54 ˚

A and experi-

mental bond energy, Eexp = 348 kJ/mol.

Let Eavg be the average theoretical bond energy when the bond length is

l= 1 ˚

Since bond energy is directly proportional to the bond length, we have the

equation: Eavg

Eexp

Substitute the known values:

Eavg

348 =1

1.54

Step 2: Solve for the theoretical bond energy. Cross multiply the

equation:

1.54Eavg = 348

Eavg =348

1.54

Eavg ≈226.0 kJ/mol

Therefore, the theoretical bond energy of a carbon-carbon single bond with

an average bond length of 1.54 ˚

A is approximately 226.0 kJ/mol.

Question 24

Question

Calculate the percent ionic character of a C–Cl bond, given that the experi-

mental bond length of C–Cl is 1.76 ˚

A and the theoretical bond length of a fully

ionic C+–Cl−bond is 2.85 ˚

A. Assume a linear relationship between percent

ionic character and bond length.

Solution

Step 1: Calculate the percent ionic character using the equation

Percent ionic character = 1−experimental bond length

theoretical bond length ×100%

Step 2: Substitute the given values into the equation to find the percent

ionic character of the C–Cl bond.

Percent ionic character = 1−1.76 ˚

2.85 ˚

A×100%

Step 3: Perform the calculation to determine the percent ionic character.

Percent ionic character = (1 −0.6175) ×100% = 38.25%

Step 4: Therefore, the percent ionic character of the C–Cl bond is 38.25

Question 25

Question

A carbon-carbon double bond consists of a sigma (σ) bond and a pi (π) bond.

The bond length of the sigma bond is 1.54 angstroms, while the bond length of

the pi bond is 1.34 angstroms. Given that the bond energy associated with the

sigma bond is 368 kJ/mol, calculate the approximate bond energy associated

with the pi bond.

Solution

Step 1: Recall that the total bond energy of a double bond is the sum of the

bond energies of the sigma and pi bonds. Mathematically, this can be expressed

as:

Total bond energy = Bond energy of σbond + Bond energy of πbond

Step 2: Given that the bond energy associated with the sigma bond is 368

kJ/mol, we need to calculate the bond energy associated with the pi bond.

Step 3: To determine the bond energy associated with the pi bond, we first

need to calculate the contribution of the sigma bond to the total bond energy:

Bond energy of σbond = 368 kJ/mol

Step 4: Next, we can calculate the contribution of the pi bond to the total

bond energy by subtracting the bond energy of the sigma bond from the total

bond energy:

Total bond energy = Bond energy of σbond + Bond energy of πbond

Bond energy of πbond = Total bond energy −Bond energy of σbond

Step 5: Substituting the values, we find:

Bond energy of πbond = Total bond energy −368 kJ/mol

Step 6: Since we don’t have the total bond energy information in this ques-

tion, we are unable to calculate the bond energy associated with the pi bond

without that value.

Question 26

Question

Calculate the bond length of a carbon-carbon single bond in ethane given that

the bond energy is 348 kJ/mol.

Solution

Step 1: Convert the bond energy from kJ/mol to J/mol:

348 kJ/mol = 348 ×103J/mol

Step 2: Calculate the bond energy per bond:

348 ×103J/mol = xJ/bond =⇒x= 348 ×103J/mol

Step 3: Use the relationship between bond energy and bond length to find

the bond length:

bond energy = F×bond length

where Fis the force constant. Rearranging the formula, we get:

bond length = 2×bond energy

Step 4: Since we are dealing with a carbon-carbon single bond, we know

that the force constant for a single bond is 605 N/m, so:

bond length = 2×348 ×103J/mol

605 N/m

Step 5: Calculate the bond length in meters:

bond length = 2×348 ×103

605 m = answer in meters

Question 27

Question

Calculate the bond energy of a C-C single bond given that the experimental

bond length is 1.54 ˚

A. The bond energy can be calculated using the equation

E=k×r−n, where Eis the bond energy, kis a constant, ris the bond length,

and nis an experimentally determined exponent.

Solution

Step 1: Determine the value of nfor the C-C bond. The value of nfor the C-C

bond is typically around 2, according to experimental data.

Step 2: Substitute the given values into the equation. Plugging in r= 1.54

A and n= 2 into the equation E=k×r−n, we get:

E=k×(1.54)−2

Step 3: Convert the bond length to meters. Since 1 ˚

A=1×10−10 meters,

the bond length in meters is 1.54 ×10−10 m.

Step 4: Calculate the bond energy. Substitute the bond length in meters

into the equation:

E=k×(1.54 ×10−10)−2

E=k×4.0568 ×1020 J

Step 5: Conclusion With the given information, the bond energy of a C-C

single bond is 4.0568 ×1020 J.

Question 28

Question

Calculate the bond order of the nitrogen-nitrogen bond in hydrazine (H2NNH2)

using the bond length of 1.47 ˚

A and the bond energy of 355 kJ/mol.

Solution

To calculate the bond order of the nitrogen-nitrogen bond in hydrazine, we can

use the formula:

Bond Order = 1

2(Number of bonding electrons −Number of antibonding electrons)

We are given the bond length as 1.47 ˚

A and the bond energy as 355 kJ/mol.

Given that the bond energy is the energy required to break the bond, we

can use the relation between bond energy, bond length, and bond order:

Bond Energy = k×Bond Order ×1

Bond Length

where kis a proportionality constant.

Step 1: Solve for the proportionality constant k.

k=Bond Energy ×Bond Length

Bond Order

Step 2: Substitute the given values (Bond Energy = 355 kJ/mol, Bond Length =

1.47 ˚

A):

k=355 ×1.47

Bond Order

Step 3: Plug in the value of kinto the bond energy formula and solve for

the bond order:

355 = 355 ×1.47

Bond Order×1

1.47

Solving for the bond order:

Bond Order = 355 ×1.47

355 = 1.47

Therefore, the bond order of the nitrogen-nitrogen bond in hydrazine is 1.47.

Question 29

Question

Explain the relationship between bond length and bond energy in organic molecules.

Why are shorter bonds typically stronger?

Solution

1. Bond Length: Bond length is the average distance between the nuclei of

two bonded atoms. In general, the shorter the bond length, the stronger the

bond.

2. Bond Energy: Bond energy is the energy required to break a bond. It

is a measure of the strength of a chemical bond. The stronger the bond, the

higher the bond energy required to break it.

3. Relationship between Bond Length and Bond Energy: In organic

molecules, there is an inverse relationship between bond length and bond energy.

This means that shorter bonds have higher bond energy, while longer bonds have

lower bond energy.

4. Reason for Shorter Bonds Being Stronger: Shorter bonds are

stronger because the nuclei of the bonded atoms are closer together, leading

to a stronger electrostatic force of attraction between the nuclei and the shared

electrons. This results in a greater overlap of atomic orbitals, which leads to

stronger bonding interactions.

5. Example: Consider the carbon-carbon (C-C) single bond and the carbon-

carbon double bond (C=C). The C-C double bond is shorter than the C-C single

bond because the double bond involves a stronger pi bond in addition to the

sigma bond. The stronger pi bond in the double bond results in a shorter bond

length and higher bond energy compared to the single bond.

6. Conclusion: In organic molecules, shorter bonds are typically stronger

due to the closer proximity of the nuclei, which increases the strength of the

bonding interactions. Bond length and bond energy are important factors in

determining the stability and reactivity of organic molecules.

Question 30

Question

Calculate the bond energy of a C-C single bond based on the bond length of

1.54 ˚

A. Assume a bond length/bond energy relationship of 1 ˚

A = 83 kcal/mol.

Solution

Step 1: Convert the bond length from ˚

A to ˚

Apm: We know that 1 pm = 10−2˚

Thus,

1.54 ˚

A=1.54 ×102pm = 154 pm

Step 2: Calculate the bond energy based on the given bond length/bond

energy relationship: Given that 1 ˚

A = 83 kcal/mol, we have:

Bond energy = Bond length ×Relationship constant

Bond energy = 154 pm ×83 kcal/mol

Bond energy = 12782 kcal/mol

Therefore, the bond energy of a C-C single bond with a bond length of 1.54

A is 12782 kcal/mol.

Question 31

Question

The carbon-carbon double bond in ethene (C2H4) has a bond length of approx-

imately 133 pm, while the carbon-carbon single bond in ethane (C2H6) has a

bond length of 154 pm. Calculate the approximate bond energy difference be-

tween the carbon-carbon double bond in ethene and the carbon-carbon single

bond in ethane.

Solution

To calculate the approximate bond energy difference between the carbon-carbon

double bond in ethene and the carbon-carbon single bond in ethane, we can use

the concept of bond energy and the relationship between bond length and bond

energy.

Step 1: Calculate the bond energy for the carbon-carbon double

bond in ethene. The bond energy for the carbon-carbon double bond in

ethene can be calculated using the relationship between bond length and bond

energy. We can use the average bond energy values for carbon-carbon single

and double bonds (347 kJ/mol and 614 kJ/mol, respectively) along with the

bond length values provided.

Given: - Carbon-carbon double bond length in ethene (C2H4): 133 pm -

Average bond energy for carbon-carbon double bond: 614 kJ/mol

Using the formula for bond energy:

Bond Energy = Average Bond Energy

Bond Length ×1000

Substitute the given values:

Bond Energy (double bond) = 614 kJ/mol

133 pm ×1000

Calculate:

Bond Energy (double bond) ≈4628.17 kJ/mol

Step 2: Calculate the bond energy for the carbon-carbon single

bond in ethane. Using the same formula and the provided values:

Average Bond Energy for carbon-carbon single bond = 347 kJ/mol

Bond Energy (single bond) = 347 kJ/mol

154 pm ×1000

Calculate:

Bond Energy (single bond) ≈2259.74 kJ/mol

Step 3: Calculate the bond energy difference. The bond energy differ-

ence between the carbon-carbon double bond in ethene and the carbon-carbon

single bond in ethane can be obtained by subtracting the bond energy of the

single bond from the bond energy of the double bond.

Bond Energy Difference = Bond Energy (double bond)−Bond Energy (single bond)

Substitute the calculated values:

Bond Energy Difference = 4628.17 kJ/mol −2259.74 kJ/mol

Calculate:

Bond Energy Difference ≈2368.43 kJ/mol

Therefore, the approximate bond energy difference between the carbon-

carbon double bond in ethene and the carbon-carbon single bond in ethane

is approximately 2368.43 kJ/mol.

Question 32

Question

Calculate the bond length of a carbon-carbon single bond in ethane (C2H6)

using the bond energy data provided below. Assume all bonds in the molecule

are equal.

Bond energies (kJ/mol): C−H: 414 C−C: 348 H−H: 436

Solution

Step 1: Calculate the total bond energy of ethane (C2H6) using the bond en-

ergy data provided. Step 2: Determine the number of carbon-hydrogen (C-H),

carbon-carbon (C-C), and hydrogen-hydrogen (H-H) bonds in one molecule of

ethane. Step 3: Set up an equation using the total bond energy calculated in

step 1 and the total number of bonds calculated in step 2 to find the bond

energy of a single carbon-carbon bond. Step 4: Use the concept that bond

energy is inversely proportional to bond length to calculate the bond length of

a carbon-carbon single bond.

Step 1: The formula for ethane is C2H6. The total bond energy can be

calculated as follows:

(2 ×C−H) + (1 ×C−C) + (6 ×H−H)

(2 ×414) + 348 + (6 ×436)

828 + 348 + 2616

3792 kJ/mol

Step 2: In one molecule of ethane, there are: - 6 carbon-hydrogen (C-H)

bonds - 1 carbon-carbon (C-C) bond - 9 hydrogen-hydrogen (H-H) bonds

Step 3: Using the total bond energy calculated in Step 1 and the total

number of bonds in Step 2, the bond energy of a single carbon-carbon bond can

be determined:

3792 kJ/mol = x×1 + (6 ×414) + (9 ×436)

3792 = x+ 2484 + 3924

3792 = x+ 6408

x=−2616 kJ/mol

Step 4: The bond length is inversely proportional to bond energy. We

can use this relationship and experimental data to estimate the bond length

of a carbon-carbon single bond in ethane. Given that the bond energy for a

carbon-carbon single bond is 348 kJ/mol:

Using the equation: E=k×1

rwhere Eis the bond energy, kis a constant,

and ris the bond length.

E1∇ · E2=r2∇ · r1

348∇ · 2616 = r2∇ · 3792

r2=348 ×3792

2616 = 507 pm

Therefore, the bond length of a carbon-carbon single bond in ethane is 507

picometers.

Question 33

Question

The carbon-carbon double bond in ethene (C2H4) has a bond length of 134 pm

and a bond energy of 610 kJ/mol. Calculate the wavenumber (in cm−1) of the

stretching vibration associated with this bond.

Solution

Step 1: Calculate the reduced mass of the C=C bond. The reduced mass (µ)

of a diatomic molecule is given by the formula:

µ=m1·m2

m1+m2

For the C=C bond in ethene, the masses of carbon and hydrogen are approxi-

mately 12 amu and 1 amu, respectively.

µ=12 ×12

12 + 12 = 6 amu = 6 ×1.66054 ×10−27 kg

Step 2: Convert the bond length to meters. Given that 1 pm = 10−12 m,

the bond length of 134 pm can be converted to meters.

134 pm = 134 ×10−12 m=1.34 ×10−10 m

Step 3: Calculate the wavenumber. The wavenumber (˜ν) in cm−1is given

by the formula:

˜ν=1

2πc sk

where cis the speed of light (3.00 ×108m/s), kis the force constant of the

bond (given by k=4E

d2where Eis the bond energy and dis the bond length),

and µis the reduced mass.

Step 4: Calculate the force constant.

k=4×610 kJ/mol

(1.34 ×10−10 m)2

k=2440 ×103J/mol

1.7956 ×10−20 m2

k= 1.3594 ×1023 N/m

Step 5: Plug in the values and solve for the wavenumber.

˜ν=1

2π×3.00 ×108m/ss1.3594 ×1023 N/m

6×1.66054 ×10−27 kg

Calculating the value gives:

˜ν≈1660 cm−1

Therefore, the wavenumber of the stretching vibration associated with the

carbon-carbon double bond in ethene is approximately 1660 cm−1.

Question 34

Question

What is the relationship between bond length and bond energy in organic

molecules? Explain how this relationship impacts the reactivity of organic com-

pounds.

Solution

Step 1: Bond Length and Bond Energy Relationship Bond length refers

to the distance between the nuclei of two bonded atoms, while bond energy (also

known as bond strength) is the amount of energy required to break a bond. The

relationship between bond length and bond energy is inversely proportional -

shorter bond lengths correspond to stronger bonds with higher bond energies,

and vice versa. This is due to the electrostatic forces between the nuclei and

shared electrons in a bond - the closer the nuclei are to each other, the stronger

the attraction between them and the shared electrons.

Step 2: Impact on Reactivity In organic chemistry, the bond lengths and

bond energies of particular bonds within molecules can greatly influence their

reactivity. - Shorter Bonds, Higher Energy: Molecules with shorter and

stronger bonds tend to be more stable and less reactive. This is because break-

ing these strong bonds requires more energy input, making the reaction less

likely to occur spontaneously. - Longer Bonds, Lower Energy: In contrast,

molecules with longer and weaker bonds are more likely to undergo reactions.

These weaker bonds can be more easily broken, facilitating chemical transfor-

mations. - Functional Groups: The presence of specific functional groups

with characteristic bond lengths and energies can also impact the overall reac-

tivity of organic compounds. For example, an alkene with a double bond has a

characteristic bond length and energy that allows for typical reactions such as

addition reactions.

Understanding the relationship between bond length, bond energy, and reac-

tivity is crucial for predicting and controlling the behavior of organic compounds

in various chemical reactions.

Question 35

Question

Calculate the bond energy of a carbon-carbon single bond given that the bond

length is 1.54 ˚

A. The molar mass of carbon is 12.01 g/mol.

Solution

Step 1: Calculate the mass of one C-C bond.

Mass of one C atom = Molar mass of carbon

6.022 ×1023

Mass of one C atom = 12.01 g/mol

6.022 ×1023

Mass of one C atom ≈1.99 ×10−23 g

Step 2: Calculate the mass of one C-C bond.

Mass of one C-C bond = 2 ×Mass of one C atom

Mass of one C-C bond = 2 ×1.99 ×10−23 g

Mass of one C-C bond ≈3.98 ×10−23 g

Step 3: Calculate the bond energy. Given that the bond length is 1.54 ˚

and 1 ˚

A is 10−10 m:

1.54 ˚

A=1.54 ×10−10 m

The bond energy (E) can be calculated using the formula:

E=k×bond length2

mass of one bond

where kis the force constant for a C-C bond, approximately 315 N/m.

Substitute the values:

E=315 ×(1.54 ×10−10)2

3.98 ×10−23

E=315 ×2.3716 ×10−20

3.98 ×10−23

E≈7.4714 ×10−18

3.98 ×10−23

E≈1.88 ×105J/mol

Therefore, the bond energy of a carbon-carbon single bond is approximately

1.88 ×105J/mol.

Question 10

Question

Calculate the bond energy of a carbon-carbon double bond if it is known that

the bond length is 1.33 ˚

A and the bond energy of a carbon-carbon single bond

is 348 kJ/mol.

Solution

Step 1: Convert the bond length from angstroms to meters. Given that 1 ˚

A =

1×10−10 m, the bond length of 1.33 ˚

A is equivalent to 1.33 ×10−10 m.

Step 2: Calculate the spring constant for the double bond. Using Hooke’s

Law (E= 1/2kx2), where Eis the bond energy, kis the spring constant, and

xis the bond length: k=2E

x2For the single carbon-carbon bond: ksingle =

2×348

(1.33×10−10 )2.

Step 3: Calculate the bond energy of the double bond. For the double bond,

the spring constant is the sum of the individual spring constants of each bond:

kdouble = 2 ×ksingle Edouble =1

2kdouble ×(1.33 ×10−10)2

Step 4: Substitute the values to find the bond energy of the carbon-carbon

double bond. Edouble =1

2×2×2×348

(1.33×10−10 )2×(1.33 ×10−10)2

Question 11

Question

Consider the following molecules and their bond lengths:

Molecule Bond Length (˚

Ethane 1.54

Ethylene 1.33

Acetylene 1.21

Determine the average bond energy (in kJ/mol) of the carbon-carbon bond

in these molecules. Assume that the bond energy is inversely proportional to

the square of the bond length.

Solution

To find the average bond energy of the carbon-carbon bond in these molecules,

we will first calculate the individual bond energy and then find the average.

Step 1: Calculate the bond energy for each bond.

The relationship between bond energy and bond length is given as E∝1

r2,

where Eis the bond energy and ris the bond length.

For ethane:

Bond Energy = k×1

(1.54)2

For ethylene:

Bond Energy = k×1

(1.33)2

For acetylene:

Bond Energy = k×1

(1.21)2

Step 2: Find the average bond energy.

To find the average bond energy, we calculate the arithmetic mean of the

three bond energies:

Average Bond Energy = Bond Energyethane + Bond Energyethylene + Bond Energyacetylene

Substitute the calculated bond energies for each molecule and then find the

average bond energy in kJ/mol.

Question 12

Question

For the following compounds, rank them in order of increasing C-C bond length:

1. Ethane (C2H6) 2. Ethylene (C2H4) 3. Acetylene (C2H2)

Solution

To rank the compounds in order of increasing C-C bond length, we need to

consider the types of bonds present in each compound.

Step 1: Ethane has a single C-C bond, ethylene has a double C=C bond,

and acetylene has a triple CC bond. The general trend is that as the number

of bonds between two atoms increases, the bond length decreases.

Step 2: Therefore, the compounds in order of increasing C-C bond length

are: 1. Acetylene (C2H2) with a triple CC bond (shortest bond length) 2.

Ethylene (C2H4) with a double C=C bond 3. Ethane (C2H6) with a single C-C

bond (longest bond length)

Question 13

Question

Draw the Lewis structure for sulfur dioxide (SO2) and determine the bond

angle between the sulfur-oxygen bonds. Given that the bond length of the

sulfur-oxygen bond is 1.48 ˚

A and the bond energy is 523 kJ/mol, calculate the

formaldehyde (H2CO) bond angle between the carbon-oxygen bonds assuming

the bond length is 1.43 ˚

Solution

To determine the bond angle in sulfur dioxide (SO2): Step 1: Draw the Lewis

structure for sulfur dioxide (SO2). The Lewis structure for SO2involves a central

sulfur atom single bonded to two oxygen atoms with one double bond between

sulfur and one of the oxygen atoms.

Step 2: Determine the bond angle between the sulfur-oxygen bonds. In SO2,

the structure is trigonal planar with bond angles of approximately 120 degrees

between the sulfur-oxygen bonds.

To calculate the bond angle in formaldehyde (H2CO) using the bond length

and bond energy: Step 3: Calculate the formaldehyde bond angle between the

carbon-oxygen bonds. Given that the bond length between carbon and oxygen

is 1.43 ˚

A and the bond energy is 523 kJ/mol for sulfur dioxide, we can assume

a similar bond energy value for H2CO. The bond energy can be converted to

kilocalories per mole by dividing by 4.184 to give 125 kcal/mol.

Step 4: Use the bond length information to determine the bond angle be-

tween the carbon-oxygen bonds. Using the given bond length of 1.43 ˚

A for

H2CO and the assumption of the bond energy being 125 kcal/mol, we can use

the relationship between bond length and bond angle to estimate the carbon-

oxygen bond angle. Typically, shorter bond lengths indicate stronger bonds and

larger bond angles.

Therefore, based on the bond length of 1.43 ˚

A of the carbon-oxygen bond

in formaldehyde, we expect a slightly larger bond angle compared to the sulfur-

oxygen bond angle of 120 degrees in SO2.

Question 14

Question

The bond length between two carbon atoms in benzene is approximately 139

picometers. Calculate the bond energy of the carbon-carbon bond in benzene

in units of kJ/mol. (Hint: The bond energy is the energy required to break one

mole of bonds.)

Solution

Step 1: We first need to convert the bond length from picometers to meters.

Given: 1 picometer (pm) = 1 ×10−12 meters

Therefore, the bond length in meters is:

139 pm = 139 ×10−12 m=1.39 ×10−10 m

Step 2: Next, we can calculate the force constant (k) using Hooke’s law,

which relates bond energy (E) to bond length (r) and force constant (k) using

the equation:

E=1

2kr2

Since the bond energy is the energy required to break one mole of bonds, we

will need to calculate the bond energy per bond energy unit.

Step 3: Now, we need to calculate the force constant (k) for the carbon-

carbon bond in benzene. The force constant for a bond can be approximated

using the equation:

k=(2.31 ×105J/mol ·m2)

Substitute the known values:

k=(2.31 ×105J/mol ·m2)

(1.39 ×10−10 m)2

k=2.31 ×105

1.93 ×10−20

k= 1.195 ×1025 N/m

Step 4: Finally, we can calculate the bond energy (E) using the calculated

force constant (k) and bond length (r):

E=1

2kr2

E=1

2×1.195 ×1025 N/m ×(1.39 ×10−10 m)2

E=1

2×1.195 ×1025 ×1.93 ×10−20 J

E= 1.146 ×106J/mol

Therefore, the bond energy of the carbon-carbon bond in benzene is 1.146

106J/mol.

Question 15

Question

In a molecule of benzene (C6H6), the average bond length between carbon

atoms is 1.39 ˚

A. Given that the bond energy of a carbon-carbon single bond is

348 kJ/mol and the bond energy of a carbon-carbon double bond is 614 kJ/mol,

calculate the total bond energy in a molecule of benzene.

Solution

Step 1: Determine the total number of carbon-carbon bonds in a molecule of

benzene. Each carbon atom is connected to 3 other carbon atoms in the benzene

ring. Therefore, in a molecule of benzene, there are 6 carbon atoms, resulting

in a total of 6 ×3 = 18 carbon-carbon bonds.

Step 2: Calculate the total bond energy in a molecule of benzene. Since each

carbon-carbon bond in benzene is a combination of a single bond and a double

bond, we can consider it as 1.5 bonds worth of energy. The total bond energy

in a molecule of benzene is then:

18 ×1.5×348 kJ/mol = 9468 kJ/mol

Thus, the total bond energy in a molecule of benzene is 9468 kJ/mol .

Question 16

Question

For the molecules below, rank them in order of increasing bond length:

1. C-C bond in ethane

2. C-C bond in ethylene

3. C-C bond in acetylene

Solution

To rank the C-C bonds in ethane, ethylene, and acetylene by increasing bond

length, we need to consider the bond order of each molecule.

Step 1: In ethane (C2H6), the C-C bond is a single bond, which has a bond

order of 1.

Step 2: In ethylene (C2H4), the C-C bond is a double bond, which has a

bond order of 2.

Step 3: In acetylene (C2H2), the C-C bond is a triple bond, which has a

bond order of 3.

Therefore, the C-C bonds should be ranked in order of increasing bond length

as follows:

1. C-C bond in acetylene (shortest bond length due to triple bond)

2. C-C bond in ethylene (intermediate bond length due to double bond)

3. C-C bond in ethane (longest bond length due to single bond)

Question 17

Question

The carbon-carbon double bond in ethene (C2H4) has a bond length of approx-

imately 1.34 ˚

A and a bond energy of approximately 610 kJ/mol. Calculate the

force constant of this double bond.

Solution

Step 1: Convert the bond length from angstroms to meters.

1˚

A=1×10−10 m

So, the bond length of 1.34 ˚

A is equal to 1.34 ×10−10 m.

Step 2: Convert the bond energy from kJ/mol to joules.

1 kJ/mol = 1000 J/mol

So, the bond energy of 610 kJ/mol is equal to 610 ×1000 J/mol.

Step 3: Determine the reduced mass of the C-C double bond. The reduced

mass can be calculated using the formula:

µ=m1·m2

m1+m2

where m1and m2are the masses of the two carbon atoms. The mass of a carbon

atom is approximately 12 atomic mass units (amu).

µ=12 amu ·12 amu

12 amu + 12 amu

µ=144 amu2

24 amu

µ= 6 amu

Step 4: Calculate the force constant using the formula:

k=(2πf)2·µ

4π2

where fis the frequency of the bond vibration. The frequency fcan be calcu-

lated from the bond energy using the formula:

E=hf

where his the Planck’s constant.

Step 5: Calculate the frequency of the bond vibration.

610 ×1000 J/mol = 6.626 ×10−34 J s ·f

f=610 ×1000 J/mol

6.626 ×10−34 J s

f≈9.20 ×1013 Hz

Step 6: Substitute the values into the force constant formula and solve for

k=(2π×9.20 ×1013 Hz)2·6 amu

4π2

k=(2π×9.20 ×1013 Hz)2·6×10−3kg/mol

4π2

k≈1000 N/m

Therefore, the force constant of the carbon-carbon double bond in ethene is

approximately 1000 N/m.

Question 18

Question

The bond length of a C-C bond in benzene is approximately 1.39 ˚

A. The bond

energy of a C-C single bond is 346 kJ/mol. Calculate the expected bond energy

of the C-C bonds in benzene given that it has resonance structures.

Solution

Step 1: Calculate the bond energy of an average C-C bond in benzene. Given

that benzene has resonance structures, each C-C bond in benzene is a combi-

nation of a single and a double bond. Thus, the average bond order of the C-C

bond in benzene is 1.5. The bond energy of a C-C single bond is 346 kJ/mol.

The bond energy of a C-C double bond is greater than that of a single bond,

and typically around 615 kJ/mol. Therefore, the expected bond energy of an

average C-C bond in benzene can be approximated as the average of the bond

energy of a single and a double bond:

346 + 615

2= 480.5 kJ/mol

Step 2: Calculate the total bond energy of all C-C bonds in benzene. Benzene

has a total of 6 C-C bonds. Therefore, the total bond energy of all C-C bonds

in benzene can be calculated as:

6×480.5 = 2883 kJ/mol

Step 3: Answer The expected bond energy of the C-C bonds in benzene,

considering its resonance structures, is 2883 kJ/mol.

Question 19

Question

Calculate the bond length of a carbon-carbon single bond given that the bond

energy is 348 kJ/mol.

Solution

Step 1: Recall that bond length and bond energy are related by Hooke’s Law,

which states that the bond energy is directly proportional to the square of the

bond length.

Step 2: We can express this relationship mathematically as:

E=k·r2

where: - Eis the bond energy (348 kJ/mol), - kis a constant, and - ris the

bond length.

Step 3: Rearranging the equation, we get:

r=rE

Step 4: To find the bond length, we need to determine the value of the

constant k.

Step 5: Bond energy is typically given in kJ/mol, so we need to convert it

to joules per bond.

1 kJ/mol = 1000 J/mol = 1000 J/mol×1 mol

6.022 ×1023 molecules =1000

6.022 ×1023 J/bond

Step 6: Calculating the value of k:

k=348 kJ/mol

6.022 ×1023 bonds/mol =348 ×103

6.022 ×1023 J/bond

Step 7: Substitute the values of Eand kinto the equation:

r=r348 ×103

6.022 ×1023

Step 8: Calculate the bond length rto determine the carbon-carbon single

bond length.

Question 20

Question

The bond length between the carbon atoms in a benzene ring is approximately

1.39 ˚

A. Calculate the bond energy in kJ/mol for the carbon-carbon bond in

benzene.

Solution

Step 1: First, we convert the bond length from angstroms to meters: 1.39 ˚

A =

1.39 ×10−10 m

Step 2: Next, we use the formula for calculating bond energy Eusing the

bond length r:

E=k×r

where kis the force constant for a carbon-carbon single bond, which is approx-

imately 305 N/m.

Step 3: Now, we substitute the values into the formula:

E=305 N/m ×1.39 ×10−10 m

Step 4: Calculate the bond energy in joules:

E=305 ×1.39 ×10−10

Step 5: Next, convert the bond energy from joules to kilojoules (1 J =

1×10−3kJ):

E=305 ×1.39 ×10−10

2×10−3kJ

Step 6: Simplify and calculate the bond energy:

E=305 ×1.39 ×10−10

2×10−3kJ = 2.12 kJ/mol

Therefore, the bond energy for the carbon-carbon bond in benzene is 2.12

kJ/mol.

Question 21

Question

For the molecule CO2, explain the relationship between its bond length and

bond energy. How do these properties influence the overall stability of the

molecule?

Solution

To understand the relationship between bond length, bond energy, and stability

in the molecule CO2, we first need to examine its structure and bonding.

Step 1: Starting with the Lewis structure of CO2, we see that it consists of

one carbon atom double-bonded to two oxygen atoms.

Step 2: The double bonds in CO2consist of one sigma bond and one pi

bond between carbon and each oxygen atom.