Question

A certain gas obeys the van der Waals equation with a = 0.58 m6 Pa mol-2 . Its molar volume is found to be 3.5×10-4 m3 mol-1 at 273 K and 5.0 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. The gas constant is gas constant is 8.3145 J/K mole

Answer 1

To calculate the van der Waals constant b, we use the molar volume and the formula nb = V - (molar volume) where n is the number of moles. For the given temperature and pressure, we can calculate the compression factor Z using the van der Waals equation of state.

Step-by-step explanation:

(i) To calculate the van der Waals constant b, we can use the given molar volume. The molar volume (V) can be represented as (V - nb), where n is the number of moles and b is the van der Waals constant. Rearranging the equation, we have nb = V - (molar volume). Substituting the values, we get (number of moles)(b) = (V) - (molar volume). Since one mole of the gas occupies a molar volume of 3.5x10⁻⁴ m³/mol, we can calculate b as (V - (molar volume)) / (number of moles). The number of moles can be obtained by dividing the pressure (5.0 MPa) by the gas constant (8.3145 J/K mol).

(ii) The compression factor (Z) can be calculated using the van der Waals equation of state. The equation is given as (P + (a/V2)) * (V - b) = RT, where P is the pressure, V is the molar volume, a and b is the van der Waals constant, R is the gas constant, and T is the temperature.

Rearranging the equation, we have Z = (P + (a/V₂)) * (V - b) / (RT). Substituting the provided values, to calculate Z.