What is the average speed of a molecule F¬2 at 300 C?

3. What is the average speed of a molecule F2 at 300 C?

The average velocity of gas particles is found using the root mean square velocity formula μrms = (3RT/M) ½ where μrms = root mean square velocity in m/sec R = ideal gas constant = 8.3145 (kg·m2/sec2)/K·mol T = absolute temperature in Kelvin M = mass of a mole of the gas in kilograms.

Solution:

Convert temperature to Kelvin (K):

T = 300 +273

T = 573 K

Find molar mass:

Mass of F = 18. 998 g/mol

Since it is diatomic and there are two Flourine molecules,

Molar mass = 2 (18. 998 g/mol)

= 38 g/mol or 38x10-3 kg/mol

Find μrms μrms = (3RT/M) ½ μrms = [3(8.3145 (kg·m2/sec2)/K·mol) (573 K)/38 x 10-3 kg/mol]½ μrms = 613.288 m/seconds (Answer)

4. An unknown mass gas has the formula ClxOy and has a density of 2.875 g/L at 756 mmHg and 11 C. What is the most likely molecular formula of the gas?

Solution:

Recall the ideal gas law equation:

PV = nRT

where P = pressure in atm

V = volume in liter

R = 0.0821 liter·atm/mol·K 

n = number of moles

T = temperature in Kelvin

n = m/MW

where m = mass

MW = molecular weight

so,

PV = m/MW * RT

MW = (m/V) *RT/P

but we know that density (d) = m/V so

MW = d*RT/P

yet we need to convert T in Kelvin and pressure in atm

T = 11 + 273

T = 284 K

P = 756 mmHg (1 atm/ 760 mmHg)

P = 0.995 atm

Substitute these values with R and d to the equation MW = d*RT/P

MW = (2.875 g/L)( 0.0821 L·atm/mol·K )( 284 K)/( 0.995 atm)

MW = 67.372 g/mol

Now recall that,

The molar mass of Cl = 35.45 g/mol and O = 16 g/mol

The total mass of ClxOy = MW = 67.372 g/mol, so the equation out of the masses is

35.45x + 16y = 67.372

We can only do trial and error here since we cannot set-up another equation. But we remember that we can only take integer values for x and y

If we assume x = 2 for example 2(35.45) = 70.9. Oops! This value already exceeds 67.372.

Definitely we can’t make x=0 as it would mean nonexistence of Cl.

If we assume x = 1 35.45<67.372

So x=1 is good.

Now we manipulate 35.45x + 16y = 67.372 and express in terms of y

y = [67.372- 35.45(1)]/16

y = 1.995 (we can round it to 2)

y = 2

Now as a summary we have x=1 and y=2

so ClxOy = Cl1O2 or ClO2

The molecular formula is likely ClO2. (Answer)