The Langmuir adsorption isotherm equation is given by: = P * K / 1 + P * K where: is the fractional coverage of the adsorbent surface dimensionless P is the equilibrium pressure of the gas in atm, Pa, or any other pressure unit K is the Langmuir constant in the reciprocal of the pressure unit used for P The maximum adsorption capacity of a solid adsorbent for a gas occurs when the surface is fully covered, i.e., when = 1. In this case, the Langmuir equation becomes:1 = P * K / 1 + P * K To find the maximum adsorption capacity, we need to solve for P:P * K = 1P = 1 / KNow, to find the maximum adsorption capacity, we need to know the amount of gas adsorbed per unit mass or volume of the adsorbent. This can be expressed as:q = q_max * where:q is the amount of gas adsorbed in moles or mass units q_max is the maximum adsorption capacity of the solid adsorbent in moles or mass units Since = 1 at maximum adsorption capacity:q_max = qSo, the maximum adsorption capacity of the solid adsorbent for a gas is equal to the amount of gas adsorbed when the surface is fully covered, which can be determined using the equilibrium pressure P = 1 / K and the Langmuir constant K at a certain temperature.