To calculate the enthalpy change of adsorption, we can use the van't Hoff equation:H = -R * T * d lnK /dT Where H is the enthalpy change, R is the gas constant 8.314 J/molK , T is the temperature in Kelvin 25C = 298 K , and d lnK /dT is the derivative of the natural logarithm of the equilibrium constant with respect to temperature. However, we are not given any information about how the equilibrium constant changes with temperature, so we cannot directly use this equation.Instead, we can use the equilibrium constant K and the initial pressure of CO P to find the change in Gibbs free energy G for the adsorption process, and then use the relationship between G, H, and entropy change S to find H.The reaction for the adsorption of CO gas on activated carbon can be written as:CO g CO ads The equilibrium constant K for this reaction is given as 1.510^3 L/mol. We can use the relationship between K and G:G = -R * T * ln K Plugging in the values:G = - 8.314 J/molK * 298 K * ln 1.510^3 L/mol G -17200 J/molNow we need to find the entropy change S for the adsorption process. We can use the initial pressure of CO P and the molar density of CO to find the molar volume V of CO:V = 1/V = 1/ 1.25 g/L = 0.8 L/gSince the surface area of activated carbon used is 50 m^2/g, the total surface area A available for adsorption is:A = 50 m^2/g * 1.25 g/L = 62.5 m^2/LAssuming that CO molecules form a monolayer on the activated carbon surface, we can estimate the entropy change S for the adsorption process as the change in translational entropy of CO molecules:S R * ln A/V Plugging in the values:S 8.314 J/molK * ln 62.5 m^2/L / 0.8 L/g S 35 J/molKNow we can use the relationship between G, H, and S:G = H - T * SSolving for H:H = G + T * SH = -17200 J/mol + 298 K * 35 J/molK H -7200 J/molTherefore, the enthalpy change of adsorption for the adsorption of CO gas on activated carbon at 25C is approximately -7200 J/mol.