Question

What is the maximum adsorption capacity of a Langmuir adsorbent if the equilibrium constant (K) is 0.05 L/mmol and the concentration of adsorbate (C) is 0.02 mmol/L at 298 K? The surface area of adsorbent used in the experiment is 0.4 m²/g.

Answer 1

To calculate the maximum adsorption capacity of a Langmuir adsorbent, we need to use the Langmuir isotherm equation: =  KC  /  1 + KC where  is the fractional coverage of the adsorbent surface, K is the equilibrium constant, and C is the concentration of adsorbate.First, we need to find the fractional coverage   : =  0.05 L/mmol * 0.02 mmol/L  /  1 + 0.05 L/mmol * 0.02 mmol/L  = 0.001 /  1 + 0.001  = 0.001 / 1.001  0.001Now, we need to find the maximum adsorption capacity  q_max  using the surface area of the adsorbent  A  and the fractional coverage   :q_max = A * Since the surface area of the adsorbent is given in m/g, we need to convert the concentration of adsorbate  C  to mol/m:0.02 mmol/L *  1 mol/1000 mmol  *  1 L/1000 dm  *  1 dm/1000 cm  *  1 cm/1e-6 m  = 2e-8 mol/mNow, we can find the maximum adsorption capacity  q_max :q_max = 0.4 m/g * 0.001q_max = 0.0004 mol/gSo, the maximum adsorption capacity of the Langmuir adsorbent is 0.0004 mol/g.