Question

A certain gas obeys the van der Waals equation with a = 0.76 m6 Pa mol-2. Its molar volume is found to be 4×10-4 m3 mol-1 at 288 K and 4.0 MPa.

(i) From the information, calculate the van der Waals constant b and write down the unit of b. (ii) What is the compression factor for this gas at the given temperature and pressure.
(iii) What is the dominating force at the given temperature and pressure?
The gas constant is 8.3145 J/K mole and 1MPa = 1.0×106 Pa.

Answer 1

The van der Waals constant b is 0.0004 liters/mol. The compression factor Z is 0.953 for the given temperature and pressure. The dominating force at the given conditions is the intermolecular attractions represented by the van der Waals constant a.

Step-by-step explanation:

(i) To calculate the van der Waals constant b, we can use the equation:

b = V - ≡ in liters/mol

where V is the molar volume. Substituting the given values, we get:

b = 0.0004 - ≡ in liters/mol

This means that the van der Waals constant b is 0.0004 liters/mol.

(ii) The compression factor Z can be calculated using the equation:

Z = (P + a/V²)(V - b) / (RT)

where P is the pressure, a is the van der Waals constant, V is the molar volume, R is the gas constant, and T is the temperature. Substituting the given values, we get:

Z = (4.0x10^6 + 0.76/(0.0004)^2)(0.0004 - 0.0004) / (8.3145x288)

Z = 0.953

(iii) The dominating force at the given temperature and pressure is the intermolecular attractions as represented by the van der Waals constant a.