Evaluation of the Gas Law Constant

Exercise 7 Illinois Central College CHEMISTRY 130 Laboratory Section: ________

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Name ______________________

Evaluation of the Gas Law Constant
Objectives In this experiment, we will determine the Ideal Gas Constant, R, which relates the number of moles of gas present to its volume, pressure and absolute temperature. Background To see how "R" was derived, we must look at the proportionalities defined by the other fundamental gas laws. For example, Charles' Law showed us that the volume of a gas sample is proportional to its absolute temperature at constant pressure. Thus V ∝ T abs . In addition, Boyle's Law states that the volume of a gas sample is proportional to the inverse of 1 its pressure at constant temperature. That is, V ∝ P . If we include the fact that Avogadro's Law states in effect that the volume of a gas sample is proportional to the number of moles of gas, n, at constant temperature and pressure we have V∝n . Combining these three proportionalities into one produces the following: V∝ nT P

where T is the absolute temperature. Note that any proportionality can be made into an equality if we derive the proper 'proportionality constant'. In this case we will use the symbol "R" to represent this constant. This transforms the above proportionality into the following equality. V = ”R”( nT ) P The value for "R" was empirically derived by using Avogadro's Law which basically states that 1.0 mole of any gas will occupy 22.4 Liters at 0oC (273K) and 1 atmosphere of pressure. This set of four parameters works for all gases, so if we substitute these values into the above equation, we can calculate the proportionality constant that relates each of these parameters to one another. If we rearrange the equation above to solve for "R" we have: R= R=
(1atm)(22.4L) (1mole)(273K) PV nT L−atm = 0.0821 mole−K

This proportionality constant "R" is referred to as the Ideal Gas Constant and relates V,T,P and n for any gas. This experiment is designed to experimentally derive "R" by producing and measuring a quantity of hydrogen gas at a controlled temperature and pressure. These experimental values for the four parameters, P,V,T and n will then be used to calculate "R" and compare your value L−atm obtained to the accepted value of 0.0821 mole−K .

Exercise 7

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The procedure of this experiment is based on the chemical reaction between magnesium metal and hydrochloric acid to produce hydrogen gas. Mg + 2 HCl MgCl2 + H2

Thus, for each mole of magnesium reacted, one mole of hydrogen gas is produced. The volume, pressure, and temperature under which the hydrogen is collected will be measured. From the known quantity of magnesium used and the stoichiometry of the reaction (balanced equation), the number of moles of hydrogen produced can be calculated.

Since the hydrogen is collected in a eudiometer tube over an aqueous solution (see following procedure), the gas pressure in the tube (after the reaction has ceased) is the sum of the hydrogen gas pressure and the vapor pressure of water. In order to obtain the pressure of just the hydrogen gas, the vapor pressure of water, P H 2 O at the temperature of the measurement, must be subtracted from the atmospheric pressure, P atmosphere . (See Table 1.) Thus, the pressure of the hydrogen is given by:

P H 2 = P atmosphere − P H2 O
In case the liquid levels (Step 3.) cannot be equalized after the reaction has ceased, a further correction will be required since the pressure of the gases in the tube (hydrogen and water vapor) will not then be equal to the atmospheric pressure. If this is the case, the difference in levels must be measured as accurately as possible (with a meter stick; note that the graduations on the tube are in milliliters, not millimeters. You must use a meter stick.). This difference, which represents the pressure differential due to the difference in solution levels inside and outside the eudiometer tube, must be converted to mmHg. This can be accomplished by dividing the measured level difference in millimeters by 13.5 (the ratio of the densities of Hg and the aqueous solution). This difference must then be subtracted from the atmospheric pressure. Thus, if the levels cannot be equalized the pressure of hydrogen must be obtained from:
Hydrogen (H2) and water vapor (H2O)

Measure in millimeters with a meterstick

P H 2 = P atmosphere − P H 2 Ovapor − P level difference where P level difference ( mmHg ) =

difference in heights in mm of aqueous solution 13.5

Figure 1. Eudiometer tube setup

Exercise 7

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Temp. oC PH2O,mm Hg Temp. oC PH2O,mm Hg Temp. oC PH2O,mm Hg Temp. oC PH2O,mm Hg 13.0 14.0 15.0 16.0 17.0 18.0 11.2 12 12.8 13.6 14.5 15.5 19.0 20.0 21.0 22.0 23.0 24.0 16.5 17.5 18.7 19.8 21.1 22.4 25.0 26.0 27.0 28.0 29.0 30.0 23.8 25.2 26.7 28.3 30.0 31.8 31.0 32.0 33.0 34.0 35.0 36.0 33.7 35.7 37.7 39.9 42.2 44.6

Table 1. Vapor pressures of water at various temperature Procedure 1. Weigh approximately 35 mg of Mg ribbon on the top-loading balance to the nearest mg. and record this mass on your report sheet. 2. Add approximately 8 mL of concentrated HCl to a eudiometer tube. With your wash bottle, wash down into the tube any acid that might have adhered to the eudiometer walls. Coil the weighed strip of Mg ribbon into the eudiometer tube, approximately 5-10 cm from the open end (Copper wire wrapped around the ribbon helps to keep it in place). Fill the tube with water and invert into a suitable vessel nearly filled with water. Clamp in position (Figure 1.). The Mg may break free from the copper wire. Tilt the tube to ensure that the Mg does not stick to the sides of the tube. 3. The concentrated HCl will gradually diffuse down to the Mg and react with it. After reaction has ceased, measure the difference in levels of the solution inside and outside the tube with a ruler as shown (Figure 1.). Record this value in millimeters of solution. 4. After temperature equilibrium is attained (approximately two minutes), record the temperature of the water in the vessel and the volume of hydrogen gas produced (± 0.01 mL.). Take this temperature value as your gas temperature. 5. Repeat the experiment for a total of four determinations. 6. Calculate the number of moles of magnesium used as a reactant for each trial. number of moles of Mg = mass of Mg ribbon 24.3 g/mole

7. Calculate the corrected pressure for the experiment as described above. (See page 2.) 8. Calculate R from the equation R = PV/nT. 9. Calculate the % relative average deviation in the four measurements of R. 10. From the theoretical value for R and your average value for R, calculate the relative error in R. Relative % error = your value of R - the accepted value the accepted value

× 100

Exercise 7

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Exercise 7 Illinois Central College CHEMISTRY 130 Laboratory Section ________

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Name:________________________

REPORT SHEET
Evaluation of the Ideal Gas Constant
Trial 1 Mass of Mg, g. Number of moles of Mg = moles H2 Initial Eudiometer reading, mL. Final Eudiometer reading, mL. Volume of gas, mL. Volume of gas, Liters Barometric pressure, mm Hg Difference in levels, mm solution Difference in levels, mm Hg Vapor pressure of water, mm Hg Corrected pressure, mm Hg Corrected pressure, atm. Temperature, K "R" , L-atm/mol-K Average "R", L-atm/mol-K Deviation from the average Average deviation %R.A.D. % Relative Error
Sample calculation of "R":

Trial 2

Trial 3

Trial 4

Exercise 7

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Questions 1. What would be the effect (higher, lower or the same) on the calculated value of R of each of the following? Please explain why in each case.

a. Some H2 escapes.

b. Some Mg adheres to the inside eudiometer wall and does not react.

c. The volume of H2 is read when the liquid level in the eudiometer tube is above that in the beaker without making a correction for the level difference.

2. What does your relative average deviation tell you, in general, about your value of R or, for that matter, any set of datum?

3. What does your relative error tell you, in general, about your value of R or, again, any set of datum?

4. What are two of the more important sources of unavoidable error in this experiment? Answer in terms of the design of the experiment and apparatus used.

Exercise 7 Illinois Central College CHEMISTRY 130 Laboratory Section: ________

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Name ______________________ SHOW YOUR WORK

PRELAB: Exp.7

Evaluation of the Ideal Gas Constant

1. Referring to the lab text, if the barometric pressure in the lab is 752 mm Hg at 23oC and the difference in the levels of solution inside and outside the eudiometer tube is 185 mm, calculate the corrected pressure of the hydrogen gas in atmospheres. (Remember to correct for the vapor pressure of water.)

2. If 3.0 moles of nitrogen gas are collected in a 35.0 liter container at 20oC, what would be the pressure exerted on the container, in atmospheres?

3. If a gas collection vessel contains 66.0 grams CO2, 96.0 grams O2 and 4.0 grams of H2 and has a total pressure of 1860 mm Hg, what is the partial pressure of the hydrogen gas?

4. If 22.0 grams of CO2 gas are collected over water at 35oC and a total pressure of 790 mm Hg, what volume of dry CO2 could be obtained.

5. Using Avogadro's hypothesis, derive the numerical value for "R", the Ideal Gas Constant. Use any units you like but be sure to include them in your derivation.

Exercise 7

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