To calculate the enthalpy of adsorption of methane gas on activated charcoal, we can use the Clausius-Clapeyron equation:H_ads = -R * T * d lnP /d 1/T where H_ads is the enthalpy of adsorption, R is the gas constant 8.314 J/molK , T is the temperature in Kelvin 25C = 298.15 K , P is the saturation pressure of methane 3.78 MPa , and d lnP /d 1/T is the slope of the natural logarithm of the saturation pressure with respect to the inverse of the temperature.However, we don't have enough information to directly calculate d lnP /d 1/T . Instead, we can use the Langmuir adsorption isotherm to relate the amount of methane adsorbed to the saturation pressure:q = q_max * K * P / 1 + K * P where q is the amount of methane adsorbed 5 mmol/g , q_max is the maximum amount of methane that can be adsorbed, K is the Langmuir constant, and P is the saturation pressure 3.78 MPa .We don't have enough information to solve for q_max or K directly, so we cannot calculate the enthalpy of adsorption using the given information. Additional information, such as experimental data or the relationship between the saturation pressure and temperature, would be needed to solve this problem.