Answer to Question #325829 in Inorganic Chemistry for Chem

Question

Determine the pressure exerted by 1 mole of methane placed into a bulb with a volume of 244.6ml at 25degree celcius .carry out two calculations assume methane as an ideal gas and assume methane as a real gas and obeys Vander Waals equations

Answer 1

n(CH₄) = 1 mol;

V(CH₄) = 244.6 mL = 0.2446 L;

T(CH₄) = 25 C = 298 K;

R = 8.314 L*kPa/mol/K = 8.314 J/mol/K;

N_A = 6.02 * 10²³ mol^-1;

For ideal gas (ideal gas law):

P * V = n * R *T;

P = n * R *T/V = 1 * 8.314 * 298/0.2446 = 10129 kPa.

For real gas (Van der Waals equation):

By the chemical literature:

a(CH₄) = 225 kPa * 1000 * L/mol²;

b(CH₄) = 0.0428 L/mol;

kb = 1.381 * 10^-23 J/K;

N = n(CH₄) * N_A = 1 * 6.02 * 10²³ = 6.02 * 10²³;

(P + N² * a/V²) * (V - N * b) = N * k_b *T;

(P * V) - (P * N * b )+ (N² * a * V/V²) - (N² * a * N * b/V²) = N * k_b *T;

(P * V) - (P * N * b) = N * k_b *T - (N² * a * V/V²) + (N² * a * N * b/V²);

P * (V - N * b) = N * k_b *T - (N² * a * V/V²) + (N² * a * N * b/V²);

P = ((N * k_b * T) - (N² * a /V) + (N³ * a * b/V²))/(V - N * b);

P = ((6.02 * 10²³ * 1.381 * 10^-23 * 298) - ((6.02 * 10²³)² * 225/0.2446) + ((6.02 * 10²³)³ * 225 * 0.0428/0.2446²))/(0.2446 - 6.02 * 10²³ * 0.0428);

P = (2477.5 - 33336.4 * 10⁴⁶ + 5833.2 * 10⁴⁶ * 6.02 * 10²³)/(0.2446 - 0.2577* 10²³)