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Ideal Gas Law Experiment

Objectives • Conduct basic measurements, mathematical calculations and conversions for measurement

of volume, pressure, and temperature; calculate percent error and account for sources of error in an experimental result.

• Conduct laboratory experiments for a redox reaction by using equipment identifiable by name and by following safety procedures.

• Perform chemical calculations using mass, mole and volumes and identify limitations of measuring devices in order to state the uncertainty/significant figures in measurements and calculation results.

• Demonstrate a proficiency in relating the chemistry of gases to everyday phenomena.

Introduction Molecules in gases have very little attraction for one another, because relative to their size,

they are so far apart from each other. For this reason, we can often assume that a gas behaves

“ideally,” meaning that the physical behavior of the gas is independent of the composition of the

gas. If a gas behaves ideally, then its physical properties can be described by the Ideal Gas Equation

(Eq. 1a).

P ∙ V = n ∙ R ∙ T

Equation 1a

Let’s consider why the variables in the ideal gas equation have the relationships expressed

in Equation 1a. The ideal gas equation assumes that there are no attractive forces between gas

molecules. One can picture two billiard balls bouncing off one another in a totally elastic collision.

If these molecules are placed in a balloon the collisions will occur not only with each other but

also with the wall of the balloon, causing the balloon to expand. This expansion can be measured

as a volume (V). More molecules will cause more collisions and thus more expansion. Therefore,

the quantity of molecules or number of moles (n) is directly proportional to the volume, and thus

volume and number of moles appear on opposite sides of the equation.

Another factor to consider is the kinetic energy of these molecules. Kinetic energy is related

to the temperature (T) of the molecules, in that the higher the temperature the greater the kinetic

energy. If the collisions with the wall of the balloon are happening at a very high speed due to high

Ideal Gas Law

kinetic energy, the collisions will be harder and more frequent and thus the wall of the balloon will

be pushed out further (a larger volume) than if the kinetic energy were less. The result is that

volume is also directly proportional to the temperature. This relationship is seen in Equation 1a

with (T) on the right side of the equation and (V) on the left.

Finally, the pressure of the outside environment (atmospheric pressure) needs to be

considered. While the molecules inside the balloon are pushing the balloon out, there are also

molecules in the atmosphere bouncing on the outside of the balloon pushing inward. The greater

the pressure on the outside of the balloon, the smaller the balloon will become which implies that

volume is inversely proportional to the pressure. Note that (P) and (V) are both on the same side

of Equation 1a. The outside atmospheric pressure (P) can be measured with a barometer.

When a gas can be assumed to behave ideally, R is the proportionality constant that relates

the four variables, V, n, T, and P and in this experiment, we will determine its value. Equation 1a can

be rearranged so that the ideal gas constant is on one side of the equation by itself.

R = P ∙ V n ∙ T

Equation 1b

The accepted literature value of the gas constant, R, is 0.0821 !∙#$% %&'∙(

. Note the units for R.

You must use the correct units of the variables in the calculation for R.

Reactive metals undergo reaction with aqueous acids to produce hydrogen gas and the metal

salt. In these reactions, the metals are oxidized (lose their outer shell electrons) to form monatomic

cations while the hydrogen cations (H+) from the acid are reduced (gain electrons) to form

elemental diatomic hydrogen gas (H-H). If the acid is in excess and if the reaction goes to

completion with no side reactions (an assumption we will make), the number of moles of gas

produced can be predicted from the mass of the metal according to the stoichiometric equation for

the reaction. The gas can be collected, and its volume determined under measured conditions of

pressure and temperature. From this information it is possible to determine a value for the gas

constant and temperature. From this information it is possible to determine a value for the gas

constant R.

Ideal Gas Law

The metal you will use is magnesium (Mg). The apparatus you will be using to collect the

hydrogen evolved is called a eudiometer, which looks like a very long graduated test tube. When

it stops expanding, the gas bubble formed in the eudiometer will be trapped between the glass

walls and the water remaining in the tube. Once you submerge the eudiometer in the overgrown

graduated cylinder, called an Equalization Chamber, up to the point where the water level in the

chamber is level with the water level in the eudiometer, the pressure of the gases inside the

eudiometer (Ptotal) will be equal to the external atmospheric pressure, Pbar (measured with a

barometer, present in the laboratory). Since the hydrogen gas is collected over water, the total gas

pressure in the bubble (Ptotal) will be not only from the H2 produced in the chemical reaction but

will be partially due to the pressure of water vapor, Pwater, according to Daltons Law of Partial

Pressures (Eq. 2a).

P$&$#' = P*#+ = P,! + P,!-

Equation 2a

To determine the pressure of the hydrogen gas, PH2, the vapor pressure must be subtracted

from the atmospheric pressure (read from the barometer).

P,! = P*#+ − P,!-

Equation 2b

Ideal Gas Law

Vapor pressure varies with temperature and the pressure from the water vapor can be

obtained from the plot of pressure versus temperature (Figure 1).

Figure 1. Vapor Pressure of Water over Water versus Temperature

Ideal Gas Law

Procedure 1. Prepare a buret stand with a buret clamp. 2. Obtain a sample of magnesium metal and record the mass, (mass should be between 0.035g

and 0.045g). 3. Envelop the magnesium in a copper wire cage which is attached through the narrow end

of a rubber stopper (Figure 2). The stopper with cage is already prepared for you. The cage does not have to totally cover the magnesium but merely support it without the piece of metal falling out of the cage.

Figure 2. Eudiometer

4. Place the rubber stopper in the eudiometer to check and see if the stopper and the cage will

fit. 5. Remove the stopper. Use a disposable pipette, to dispense 20 mL (± 10%) of the HCl

solution in the eudiometer.

6. Record the volume to the nearest 0.1 mL. 7. Tilt the eudiometer slightly to the side, and slowly and carefully add deionized water to the

eudiometer. You should not disturb the acid that is already in the tube. Add the water until the eudiometer is completely full. These solutions have different densities so you may observe two different layers.

8. Insert the stopper with the wire cage. No reaction should be taking place yet.

Ideal Gas Law

9. Place a finger over the hole in the stopper and invert the eudiometer placing the stoppered end into a 400 mL or 600 mL beaker containing water. The water should be enough to cover the stopper (approx. 200 mL). Do not press the stopper onto the bottom of the beaker because liquid must be allowed to exit the hole in the stopper as the gas forms in the eudiometer tube. Support the eudiometer with a buret clamp during the reaction. The acid should now slowly diffuse down though the inverted tube, and as the acid reaches the metal, bubbles will appear. These bubbles will rise to the top of the tube and collect.

10. Allow the reaction to proceed until all the magnesium is gone and nothing remains but the copper wire cage.

11. Record the volume of gas to 0.1mL. 12. If pieces of magnesium metal remain or perhaps escape, then the experiment needs to be

repeated. If you have produced more hydrogen gas than can be quantified by the eudiometer or if some of the gas escaped, then you need to repeat the experiment.

13. At this point you might note that the volume of solution in the beaker is lower than the volume of solution in the eudiometer which means that the pressure inside the eudiometer is different than the pressure outside the eudiometer. Since we choose to use the barometric pressure (that outside the tube) as a measure of the pressure of the gas inside the tube, we need to get those two pressures equal, which will occur once the level of liquid inside the tube is equal to the level of liquid outside the tube. That is the purpose of the “Equalization Chamber.”

14. When the reaction is complete, place a finger over the hole in the stopper and take the eudiometer to the Equalization Chamber. Submerge it in the Equalization Chamber until the two levels of liquid (outside the eudiometer and inside the eudiometer) are at the same point, and then record the volume of gas collected in the eudiometer to the nearest 0.1mL. This is the value you will use in the calculation of R.

15. Discard the liquid in the eudiometer into the appropriate waste container. 16. Your instructor or TA will show you how to read the barometer so that you can get a value

of barometric pressure to the nearest 0.1 mmHg (millimeters of mercury). You will use the exact conversion definition, 760 mmHg = 1 atmosphere to convert from mmHg to atmosphere. Record the air temperature in the laboratory.

17. Repeat the experiment. You may assume that the barometric pressure and the temperature are constant during the two trials.

Ideal Gas Law

Ideal Gas Law Report Sheet

Name: Partner:

Instructor: Section Code: Date:

Unless otherwise noted, 2 pt. for each answer. Trial 1 Trial 2

Molarity of HCl (M) ___________(1 pt) ___________(1 pt)

Volume of HCl (mL) ___________ ___________

Mass of Mg (gram) ___________ ___________

Volume of gas before Equalization Chamber (mL) ___________(1 pt) ___________(1 pt)

Volume of gas after Equalization Chamber (mL) ___________ ___________

Barometric Pressure (mm Hg) ___________ ___________

Temperature (°C) ___________ ___________

Write the balanced overall equation for the reaction of magnesium and HCl to form H2 gas and a salt (2 pts).

Moles of Mg reacted ___________ ___________

Moles of H2 formed (based on the equation) ___________ ___________

Vapor Pressure of water from curve (mmHg) ___________ ___________

Vapor Pressure of H2 from Dalton’s Law (mmHg) ___________ ___________

Pressure of H2 (atm) ___________ ___________

Volume of H2 (L) ___________ ___________

Temperature (K) ___________ ___________

R (calculated) ___________(6 pts) ___________(6 pts)

Percent error ___________ ___________

R= ___________

Ideal Gas Law

Calculations 1. Show all work for trial one. (12 pts.)

Trial 1

2. The calculation for R depends on the assumption that Mg is the limiting reagent.

Show the calculations that demonstrate that Mg is the limiting reagent for Trial 1.

3. Explain in words how your calculations prove the limiting reagent. (6 pts)

Ideal Gas Law

4. Prior to placing the eudiometer into the Equalization Chamber, is the pressure of the gas inside the tube greater than or less than the pressure outside the tube? Comparing the volume of the gas before and after placing the eudiometer into the Equalization Chamber should help with the explanation. Explain your logic. (4 pts)

5. What experimental measurement most affected the accuracy of the experimental

value of R? Explain. (HINT: Consider the significant figures in your data.) (3 pts)

6. What experimental changes might improve the accuracy of the determined R value?

(3 pts)