Question

1. Use the van der waals equation to calculate the pressure exerted by 1.470 mol of Cl2 in a volune of 5.285 L at a temperature of 280.0 K .

2. Use the ideal gas equation to calculate the pressure exerted by 1.470 mol of Cl2 in a volume of 5.285 L at a temperature of 280.0 K .

Answer 1

1) The van der Waals equation is:

[P + (n²a/V²)](V - nb) = nRT

Where:

• P - pressure,

• V - volume,

• n - number of moles,

• T - temperature,

• R -  ideal gas constant. If the units of P, V, n and T are atm, L, mol and K, respectively, the value of R is 0.0821

• a and b - constants, which are chosen to fit experiment as closely as possible to individual gas molecule.

When the volume, temperature and the number of moles of the gas molecule are known, the pressure can be calculated:

P = [nRT/(V - nb)] - n²a/V²

The Van der Waals constant for Cl₂ are: a= 0.658 J·m³/mol² and b=0.05622 x10³ m³/mol

Then

P = [(1.470 mol)*(0.0821 Latm/molK)(280.0 K)/(5.285 L -(1.470 mol)*(0.05622 x10³ m³/mol))]-(1.470 mol)²(0.658 J·m³/mol²)/( 5.285 L)²

P = 33.79/5.20 - 1.42/27.93

P = 6.50 - 0.051

P = 6.45 atm

2) The ideal gas equation is

PV = nRT

P = nRT/V

P = (1.470 mol)(0.0821 Latm/molK)(280 K) / 5.285L

P = 33.79/5.285

P = 6.39 atm