Ideal Gas Law

1. Measuring the Volume of the Sample

1. Clean the sample carefully and dry it.
2. Fill a high-resolution graduated cylinder with enough distilled water to cover the sample. Note the initial volume
3. Drop the sample into the water and note the volume change. This is the volume of the sample, V.
4. Remove the sample and dry it. Note: alternatively, measured the side length(s) of the sample and calculate its volume using geometry.

2. Load the Sample in the Balance

1. Hang the sample in the magnetic suspension balance.
2. Install the pressure/temperature chamber around the sample.
3. Evacuate the sample environment and refill with hydrogen gas, to 1 bar.
4. Measure the sample weight at 1 bar and room temperature, w_00.

3. Measure Sample Weight as a Function of Pressure at Room Temperature

1. Increase or decrease the pressure in the sample environment to P_i0.
2. Allow the sample environment to equilibrate.
3. Measure the weight of the sample, w_i0.
4. Repeat 3.1-3.3 numerous times.

4. Measure Sample Weight as a Function of Pressure at Various Temperatures

1. Set the temperature to T_j and allow it to equilibrate.
2. Set the pressure of hydrogen gas to 1 bar.
3. Measure the sample weight at 1 bar and T_j, w_0j.
4. Increase or decrease the pressure to P_ij and allow it to equilibrate.
5. Measure the weight of the sample, w_ij.
6. Repeat 4.4-4.5 numerous times.
7. Repeat 4.1-4.6 as desired.

5. Calculate the Ideal Gas Constant

1. Tabulate the measured values {T_j, P_ij, and w_ij} where P_0j is always 1 bar and T₀ is the measured room temperature.
2. Calculate and tabulate the differences Δw_ij and ΔP_ij at each temperature T_j using Equation 6 and Equation 7.
   Δw_ij = w_ij - w_0j (Equation 6)
   Δw_ij = P_ij - P_0j = P_ij - 1 bar (Equation 7)
3. Calculate R_ij for each measurement, and average over all values to determine the ideal gas constant, R. Alternatively, plot the product of ΔP_ij and V as a function of the product of Δw_ij (divided by the molecular weight, MW) and T_j, and perform a linear regression analysis to determine the slope, R. (Equations 8 and 9) For hydrogen, MW = 2.016 g/mol.
   ΔP V = Δn RT (Equation 8)
   (Equation 9)