The Langmuir adsorption isotherm equation is given by: = K * C / 1 + K * C where is the fractional surface coverage, K is the Langmuir constant, and C is the concentration of adsorbate.In this case, the maximum adsorption capacity occurs when the surface is fully covered, i.e., = 1. We can rearrange the equation to solve for the concentration of adsorbate C when = 1:1 = K * C / 1 + K * C 1 + K * C = K * C1 = K * CC = 1 / KNow, we can plug in the given values for K:C = 1 / 0.05 cm/mg = 20 mg/mLSince the concentration of adsorbate in the solution is 0.1 mg/mL, which is less than the calculated C value of 20 mg/mL, the surface will not be fully covered. Therefore, we need to calculate the fractional surface coverage using the given concentration of adsorbate: = 0.05 cm/mg * 0.1 mg/mL / 1 + 0.05 cm/mg * 0.1 mg/mL = 0.005 / 1.005 0.004975Now, we can calculate the maximum adsorption capacity Q using the fractional surface coverage and the surface area:Q = * Surface Area = 0.004975 * 100 cm 0.4975 cmThe maximum adsorption capacity of the surface at the given temperature is approximately 0.4975 cm.