Question

At high pressures, real gases do not behave ideally. Calculate the pressure exerted by 25.0 g H2 at 20.0°C in a 1.00 L container assuming in Part 1 non-ideal behavior and in Part 2 ideal behavior.
1. Use the van der Waals equation and data in the hint to calculate the pressure exerted.answer in atm
2. Now, calculate the pressure exerted, assuming that the gas behaves as an ideal gas.answe in atm

Answer 1

1) Van der Waals equation:

$$(V - nb)(p+ n^2a^2/V^2) = nRT$$

a and b are constants for the van der Waals equation. These are tabular values that are respectively equal:

$$a = 0,2476 L^2*bar*mol^{-2} ; b = 26,61 cm^3*mol^{-1}.$$

Accordingly, we translate the volume into cm³:

$$1 L = 1000mL = 1000 cm^3$$

The amount of substance for gas is calculated by the formula:

$$n = {m \over M}$$

Then:

$$(V - {m \over M}b)(p+ ({m \over M})^2a^2/V^2) = {m \over M}RT$$

As a result, based on this, we get the answer in the bar:

$$p = 35.46 bar$$

In atm:

$$p = 35.53 atm$$

2) Based on the Mendeleev-Clapeyron equation:

$$p = {{m \over M}RT \over V}$$

$$p = 30.02 atm$$