A chemistry student is studying the adsorption of a gas on a solid surface using the Langmuir adsorption isotherm. The student knows that the maximum adsorption capacity (θ_max) of the surface is 0.5 mol/L and that the equilibrium constant (K) for the process is 0.02 L/mol. The student is asked to calculate the fraction of the surface covered by the adsorbate when the gas pressure is 2 atm at the temperature of the experiment.

Question

A chemistry student is studying the adsorption of a gas on a solid surface using the Langmuir adsorption isotherm. The student knows that the maximum adsorption capacity (θ_max) of the surface is 0.5 mol/L and that the equilibrium constant (K) for the process is 0.02 L/mol. The student is asked to calculate the fraction of the surface covered by the adsorb

Answer 1

To calculate the fraction of the surface covered by the adsorbate   , we can use the Langmuir adsorption isotherm equation: =  KP  /  1 + KP where  is the fraction of the surface covered by the adsorbate, K is the equilibrium constant  0.02 L/mol , and P is the gas pressure  2 atm .First, we need to convert the pressure from atm to mol/L using the ideal gas law equation:PV = nRTAssuming the temperature  T  and the gas constant  R  remain constant, we can write the equation as:P1V1 = P2V2Given that 1 atm = 1 mol/L  assuming R and T are constant , we can convert the pressure: 2 atm  1 L  =  P2  1 L P2 = 2 mol/LNow, we can plug the values into the Langmuir adsorption isotherm equation: =  0.02 L/mol  2 mol/L  /  1 +  0.02 L/mol  2 mol/L   = 0.04 /  1 + 0.04  = 0.04 / 1.04  0.0385The fraction of the surface covered by the adsorbate is approximately 0.0385 or 3.85%.