The Langmuir adsorption isotherm is given by the equation: = K * C / 1 + K * C where is the fractional surface coverage, K is the equilibrium constant, and C is the concentration of the adsorbate in solution. In this case, K = 2 x 10^3 M^-1 and C = 5 x 10^-4 M.First, we need to find the fractional surface coverage : = 2 x 10^3 M^-1 * 5 x 10^-4 M / 1 + 2 x 10^3 M^-1 * 5 x 10^-4 M = 1 / 1 + 1 = 1 / 2Now, we need to find the maximum adsorption capacity _max in moles per square meter. The relationship between fractional surface coverage and maximum adsorption capacity is: = * _maxSince we are looking for _max, we can rearrange the equation:_max = / However, we don't have the value for adsorption capacity in the problem. Without this value, we cannot determine the maximum adsorption capacity _max in moles per square meter.