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. answer in atm.

Answer 1

1) For hydrogen, the coefficients for the van der Waals equation:

$a = 0,2476 L^2*bar*mol^{-2} = 0,2473 L^2*atm*mol^{-2}; b = 26,61 cm^3*mol^{-1}.$

$$n = m/M$$

$$n = 25/2 = 12.5 mol$$

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

The calculation is made for 1 atm. Then:

$$(1000 - 12.5*26.61)(p+12.5^20.2473^2/1^2) = 12.5*8.314*293$$

$$667.375(p + 9.579) = 30450.025$$

$$p + 9.579 = 45.627$$

$$p = 35.529 atm$$

2)

$$pV = nRT$$

$$p = nRT/V$$

$$p = 12.5*8.314*293/0.001 = 3045002.5 Pa = 30.05 atm$$