To calculate the enthalpy change for the adsorption of nitrogen gas onto activated charcoal, we can use the Clausius-Clapeyron equation, which relates the change in pressure to the change in enthalpy and temperature. The equation is as follows:ln P2/P1 = -H/R * 1/T2 - 1/T1 In this case, we have the initial pressure P1 as 1 atm, the final pressure P2 as 0.5 atm, and the temperature T1 and T2 as 298 K. The gas constant R is 8.314 J/mol*K. Since the process occurs at constant temperature, T1 = T2, and the equation simplifies to:ln P2/P1 = -H/R * 1/T - 1/T ln 0.5 = -H / 8.314 J/mol*K Now, we can solve for H:H = -8.314 J/mol*K * ln 0.5 H 5774 J/molSince we have 2 moles of nitrogen gas, the total enthalpy change for the adsorption process is:Total H = 2 * 5774 J/molTotal H 11548 JTherefore, the enthalpy change when 2 moles of nitrogen gas are adsorbed onto the surface of activated charcoal at a temperature of 298 K is approximately 11.548 kJ.