To calculate the enthalpy change for the adsorption of methane gas on the zeolite catalyst, we need to consider both the work done on the system due to the change in volume and the heat absorbed or released due to the change in temperature.First, let's calculate the work done on the system due to the change in volume. The work done W can be calculated using the formula:W = -P_ext * Vwhere P_ext is the external pressure and V is the change in volume. Since the pressure is not constant, we will use the average pressure during the process:P_avg = P_initial + P_final / 2P_avg = 100 atm + 75 atm / 2P_avg = 87.5 atmNow, we need to convert the pressure to the SI unit Pascals and the volume to the SI unit cubic meters :P_avg = 87.5 atm * 101325 Pa/atm = 8865375 PaV_initial = 10.0 L * 1 m / 1000 L = 0.01 mV_final = 8.00 L * 1 m / 1000 L = 0.008 mV = V_final - V_initial = 0.008 m - 0.01 m = -0.002 mNow, we can calculate the work done:W = -P_avg * V = - -0.002 m * 8865375 Pa = 17730.75 JNext, let's calculate the heat absorbed or released due to the change in temperature. The heat q can be calculated using the formula:q = C_p * Twhere C_p is the heat capacity of the system and T is the change in temperature:T = T_final - T_initial = 288 K - 298 K = -10 Kq = 25 J/K * -10 K = -250 JFinally, we can calculate the enthalpy change H for the adsorption process:H = q + W = -250 J + 17730.75 J = 17480.75 JTherefore, the enthalpy change for the adsorption of 2.50 moles of methane gas on a zeolite catalyst supported by alumina is 17480.75 J.