Question

For oxygen gas, the van der Waals equation of state achieves its best fit for a = 0.14N⋅m4/mol2 and b=3.2×10⁻⁵ m³ /mol. Determine the pressure in 1.7 mol of the gas at 9 ∘C if its volume is 0.50 L , calculated using the van der Waals equation.

Answer 1

The pressure in 1.7 mol of oxygen gas at 9°C and a volume of 0.50 L, calculated using the van der Waals equation, is 46.594 atm.

Step-by-step explanation:

Using the van der Waals equation of state, we can calculate the pressure in 1.7 mol of oxygen gas at 9 °C, with a volume of 0.50 L.

The van der Waals equation of state is given by:

(P + a/V^2)(V - b) = nRT

where P is the pressure, V is the volume, a is a constant representing attractive forces between molecules, b is a constant representing the volume of the molecules, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.

Substituting the given values into the equation:

(P + (0.14N·m^4/mol^2) / (0.50 L)^2)((0.50 L) - (3.2×10^-5 m^3/mol)) = (1.7 mol)(R)(9 + 273.15 K)

Simplifying and solving for P:

P = 46.594 atm