# Evaluation of the Gas Law Constant

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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...

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