fractional coverage of the surface at two pressure

Question

A certain solid sample adsorbs 0.63 mg of CO when the pressure of the gas is 36.0 kPa and the temperature is 300 K. The mass of gas adsorbed when the pressure is 4.0 kPa and the temperature is 300 K is 0.21 mg. The Langmuir isotherm is known to describe the adsorption. Find the fractional coverage of the surface at the two pressures

Answer 1

P = 36.0 kPa

m = 0.63 mg

P₀ = 4.0 kPa

M = molar mass of CO = 28.01 g/mol

k = Boltzmann constant = 8.617333262145 x 10^-5 eV/K

T = 300 K

θ₁ = (P * m) / (P₀ * M * k * T)

= (36.0 * 0.63) / (4.0 * 28.01 * 10^-3 * 8.617333262145 x 10^-5 * 300)

≈ 0.055

So, the fractional coverage of the surface at a pressure of 36.0 kPa is approximately 0.055.

Now, for the second case:

P = 4.0 kPa

m = 0.21 mg

P₀ = 36.0 kPa

M = molar mass of CO = 28.01 g/mol

k = Boltzmann constant = 8.617333262145 x 10^-5 eV/K

T = 300 K

θ₂ = (P * m) / (P₀ * M * k * T)

= (4.0 * 0.21) / (36.0 * 28.01 * 10^-3 * 8.617333262145 x 10^-5 * 300)

≈ 0.001

So, the fractional coverage of the surface at a pressure of 4.0 kPa is approximately 0.001.