To calculate the enthalpy of adsorption, we can use the Langmuir adsorption isotherm equation and the Clausius-Clapeyron equation. The Langmuir adsorption isotherm equation is: = KP / 1 + KP where is the surface coverage 0.2 monolayers , K is the Langmuir constant, and P is the equilibrium pressure of hydrogen gas 0.5 atm .First, we need to find the Langmuir constant K using the given surface coverage and equilibrium pressure:0.2 = K * 0.5 / 1 + K * 0.5 Solving for K, we get:K = 0.4 / 1 - 0.4 = 0.4 / 0.6 = 2/3Now, we can use the Clausius-Clapeyron equation to relate the enthalpy of adsorption H_ads to the Langmuir constant:ln K = -H_ads / RT + Cwhere R is the gas constant 8.314 J/molK , T is the temperature in Kelvin 25C = 298 K , and C is a constant. We can ignore the constant C since we are only interested in the enthalpy of adsorption.ln 2/3 = -H_ads / 8.314 * 298 Now, we can solve for H_ads:H_ads = -8.314 * 298 * ln 2/3 = 1715.5 J/molHowever, this is the enthalpy of adsorption for the dissociative adsorption process, which involves breaking the H-H bond. We need to account for the heat of dissociation of hydrogen gas 436 kJ/mol to find the enthalpy of adsorption for the overall process:H_ads_total = H_ads + H_dissociationH_ads_total = 1715.5 J/mol + 436,000 J/mol = 437,715.5 J/molTherefore, the enthalpy of adsorption for the adsorption of hydrogen gas onto a nickel surface at 25C is approximately 437.7 kJ/mol.