2514 Calculating R

DETERMINATION OF THE UNIVERSAL GAS CONSTANT

1.0 INTRODUCTION

A gas is the state of matter that is characterized by having neither a fixed shape nor a fixed volume. Gases exert pressure, are compressible, have low densities and diffuse rapidly when mixed with other gases. On a microscopic level, the molecules (or atoms) in a gas are separated by large distances and are in constant, random motion.

Four measurable properties can be used to describe a gas quantitatively: pressure (P), volume (V), temperature (T) and mole quantity (n). The relationship among these properties is summarized by the Ideal Gas Law:

PV = nRT

Here, P represents as the gas pressure (in atmospheres or torr); V is the gas volume (in liters); n is the number of moles of gas in the sample; T is the gas temperature (in Kelvin). R is a proportionality constant called the Universal Gas Constant, and has a theoretical value of 0.08206 L•atm/K•mol or 62.363 L·torr/mol·K, depending on the units for pressure. Note that the units of R will allow the units of P, V, n and T in the Ideal Gas Law to cancel correctly.

In this lab, students will measure various properties of a sample of hydrogen gas to experimentally determine the value of the Universal Gas Constant, R. The single displacement reaction between magnesium metal and hydrochloric acid will be used to generate the hydrogen gas (with magnesium chloride as a byproduct).

Mg + 2HCl 🡪 H2 + MgCl2

The hydrogen gas will be collected in a eudiometer, a tube closed at one end and marked in milliliter volume units. The gas will be collected in the closed end of the tube over a water bath via the technique of water displacement (see figures shown later in this document).

Students will then obtain the following values for the collected sample of hydrogen gas: (1) Volume, (2) Temperature, (3) Moles, and (4) Pressure. The hydrogen volume will be directly measured from the eudiometer scale. The hydrogen temperature will also be directly measured using a thermometer. However, the mole quantity and pressure of the hydrogen gas must be determined indirectly. The mole quantity of the collected hydrogen can be easily calculated from the measured mass of the magnesium reactant using stoichiometry. But the hydrogen pressure is a little more difficult to obtain. Since hydrogen is collected over a water bath, a small amount of water vapor is mixed with the hydrogen in the eudiometer. The combined pressure of the H2 and H2O gases (after adjustments) will be equal to the external atmospheric pressure:

Patm = Phydrogen + Pwater vapor

Patm (atmospheric pressure) will be measured using a barometer. Pwater vapor (the partial pressure of water vapor) depends on the temperature of the water bath, and can be obtained from the table supplied below. By substituting these values in the above equation, the pressure of hydrogen (Phydrogen) will be determined.

Finally, to determine the value of the Gas Constant (R), the quantities V, T, n and P obtained for the hydrogen gas must simply be substituted into the Ideal Gas Equation. Students can then evaluate their accuracy in this experiment by comparing their experimental result to the true theoretical value of R, and by calculating their percent error.

Temperature (°C)	Pwater vapor (mm Hg or torr)
16	13.5
17	14.5
18	15.5
19	16.5
20	17.5
21	18.7
22	19.3
23	21.1
24	22.4
25	23.8
26	25.2
27	26.7
28	28.3
29	30.0

2.0 SAFETY PRECAUTIONS AND WASTE DISPOSAL

!!Wear your safety goggles!!

Concentrated HCl is corrosive and can burn your skin! If any spills occur, inform your instructor immediately. Wash under running water (sink or shower) and use the neutralizing sodium bicarbonate solution supplied at the sinks if necessary. Confirm that access to an eyewash station is available and know where it is. 6 M HCl is an eye hazard. Also note that hydrogen gas is flammable, so be sure to have no open flames nearby when you perform this experiment.

At the end of the experiment, the HCl solution will be much more dilute. The water, diluted HCl, and MgCl2 mixture may be rinsed down the sink with plenty of water.

3.0 CHEMICALS AND SolutionS

Chemical	Concentration	Approximate amount	Notes
Magnesium (ribbon)	N/A	4 cm
HCl solution	6 M	10 mL	Corrosive!

4.0 GLASSWARE AND APPARATUS

Item	Use	Notes
Copper wire	For holding magnesium ribbon	Return to cart or stockroom (do not dispose!)
Eudiometer	For analysis	50mL or 100mL
Rubber stopper with one hole	For eudiometer
Ruler	For taking measurements
Buret clamp	For supporting eudiometer
Several beakers	For holding laboratory H2O, HCl solution, water bath
Thermometer	For temperature measurement
10 mL graduated cylinder	For measuring HCl solution	Rinse well after use
Funnel	For transferring HCl solution	Rinse well after use
Sandpaper or steel wool	For cleaning magnesium ribbon	Return to cart or stockroom (do not dispose!)

5.0 PROCEDURE

1. Setup a ring stand with a buret clamp. Attach the empty eudiometer to the buret clamp with the open-end facing up. (If there is water in the eudiometer, pour it out before attaching it to the clamp.) Label a large beaker “Laboratory H2O” and fill it ¾ full with laboratory H2O.
2. Obtain a strip of Mg ribbon no greater than 0.0400 g and a piece of sandpaper (or steel wool) if you are using the 50-mL eudiometer. If you have the 100-mL eudiometer, obtain a ribbon no greater than 0.0800 g. Take the Mg to your bench and lay it down on a couple of clean paper towels. Use the sandpaper to remove the black oxide on the Mg please take care not to scratch the surface of the workbench. Wipe the Mg with a damp paper towel. Dry Mg completely. Hold the Mg with a paper towel and take the Mg to the balance; precisely record its mass (Data table, page 7).
3. Make a metal loop out of copper wire leaving a tail that will fit through the hole in a rubber stopper that fits into a eudiometer. Take the strip of Mg and place it through the metal loop attached to the rubber stopper so that it is folded in half and the ends are hanging down (Figure 1).
4. Label a 100 mL beaker “6M HCl”. Obtain about 35 mL of 6M HCl from the reagent cart and return to your bench. Note the exact concentration of the HCl (Data table, page 7).
5. Use your 10 mL graduated cylinder to measure approximately 10 mL of the 6M HCl (you do not need exactly 10 mL, but you need to know exactly how much you have) and record the volume of 6M HCl (Data table, page 7). Place the funnel in the eudiometer and pour the 10 mL of HCl into the eudiometer.
6. Remove the eudiometer from the buret clamp. Hold it at a 45° angle. Slowly add the laboratory H2O from the large beaker to the HCl in the eudiometer; try not to mix the HCl and the water as you pour. The goal is to layer the water over the acid. Completely fill the eudiometer with laboratory water; no space or air should remain.
7. Insert the rubber stopper with the magnesium into the opening of the eudiometer- push it all the way in and refill the hole with laboratory water (Figure 1).

8. Place your finger over the hole in the rubber stopper. Invert the tube and place it in the large beaker full of laboratory water. Once the hole is submerged in the water, you can take your finger off it. The reaction will begin shortly.
9. Measure the temperature of the water in the graduated cylinder at the end of the reaction. (Data table, page 7)
10. Gently tap the sides of the eudiometer to dislodge any stuck gas bubbles.
11. Measure the volume of hydrogen gas produced in the eudiometer. Without removing the eudiometer from the water, recover the hole in the rubber stopper with your finger. Carefully take the eudiometer to the large graduated cylinder at the sink. Again, once the hole is submerged in the water, you can take your finger off of it. Raise or lower the eudiometer so that the solution inside is level with the solution in the graduated cylinder. Once this is accomplished, you can read the volume of gas in the eudiometer. (Data table, page 7).

If you cannot get the two water levels equal, simply measure the difference in height in mm between the level of water in the eudiometer and the height in the graduated cylinder. This height can be converted to a pressure and used to correct the total pressure.

P(total) = P(H2)+ P(H2O) + P(water level difference)

P(water level difference) = height/13.59

12. Remove the eudiometer, invert it so that the rubber stopper is facing up, and dispose of the liquid into the sink. Rinse the eudiometer out with a small amount of tap water and final rinse with laboratory water.
13. Repeat the entire procedure two more times for a total of three trials.
14. Determine the barometer pressure and temperature of the room (Data table, page 7). Be mindful to include units.
15. Obtain the data for 3 additional trials by sharing with another group (Data table, page 7). Choose data that is consistent- don’t include points in which there is an obvious error.

Last Name

First Name

Partner Name(s)

Date

6.0 DATA AND CALCULATIONS

	Your group’s data			Another group’s data
	Trial #1	Trial #2	Trial #3	Trial #1	Trial #2	Trial #3
Mass of Mg (g)
Concentration of HCl (M)
Moles Mg
Moles H2 produced
Volume of gas collected (mL)
Temp. of water/gas (°C)
Barometric Pressure (torr)
VP of H20 (torr)
Height difference
Pressure correction (0 if heights same)
Partial pressure of H2 (torr)
R (L•torr/mol• K)
Average R value

1. Calculate the number of moles of Mg from the mass of the magnesium ribbon in each trial, record your data above.

2. Assume that all of the magnesium reacts and that none of the gas escapes during the experiment. Magnesium is the limiting reactant; therefore, the number of moles of hydrogen gas produced (theoretical yield) is determined from the number of moles of magnesium reacted. Use the balanced chemical equation and moles of Mg to calculate the moles of H2 produced in each trial. This is a stoichiometry calculation not an ideal gas law calculation. Record your answers in the data table on page 7.

3. Determine the vapor pressure of water using the temperature of the water/gas measured in step 10 of the procedure and record the vapor pressures in the data table on page 7. The vapor pressure for water at various temperatures is available on page 2.

4. When the reaction was complete, the eudiometer was adjusted so that water in the graduated cylinder was at the same level as the water in the eudiometer. In this case, the atmospheric pressure (PT) is approximately equal to the pressure inside the eudiometer. Dalton’s Law of Partial Pressures can be used to calculate the hydrogen partial pressure (PH2) in units of torr with the atmospheric pressure (PT) and vapor pressure for water (PH2O). Record the calculated partial pressures of H2 in the data table on page 7.

PT = PH2 + PH2O (+ Pwater level)

5. Calculate the value of R. You now have the four variables needed to calculate the Universal Gas Constant, R.

PV = nRT or ,

where n is the number of moles of H2 produced, T is the temperature of the gas in Kelvin (temperature of the water in the graduated cylinder at the end of the reaction), P is the partial pressure of hydrogen in torr, and V is the volume of gas produced in Liters.

7.0 ANALYSIS

Calculate your percent error using the average R as your experimental value and 62.363 L·torr/mol·K as the accepted value of R.

Percentage error= experimental value-accepted valueaccepted value x 100

8.0 POST-LAB QUESTIONS

1. Explain why the vapor pressure of water must be subtracted from the atmospheric pressure to obtain the partial pressure of hydrogen gas.

2. The experiment called for about 0.040 g of Mg and 6M HCl. What volume of 6.0 M HCl is required to react with 0.040 g of Mg? What was the limiting reactant?

3. Using the percent error, discuss the accuracy and precision, respectively, of the experiment.