To calculate the enthalpy of adsorption, we first need to find the moles of methane gas adsorbed by the activated charcoal. We can use the ideal gas law for this purpose:PV = nRTWhere P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.Given:P = 1 atmV = 25 mL = 0.025 L converting to liters R = 0.0821 L atm / mol K ideal gas constant T = 298 KWe can rearrange the ideal gas law to solve for n:n = PV / RTSubstituting the given values:n = 1 atm * 0.025 L / 0.0821 L atm / mol K * 298 K n 0.00102 molNow that we have the moles of methane gas adsorbed, we can calculate the enthalpy of adsorption H_ads using the following formula:H_ads = -q_ads / nWhere q_ads is the heat of adsorption and n is the moles of methane gas adsorbed.We are given the mass of activated charcoal 2.0 grams but not the heat of adsorption q_ads . Unfortunately, without the heat of adsorption value, we cannot calculate the enthalpy of adsorption. The heat of adsorption is an experimentally determined value and depends on the specific activated charcoal and gas system being studied.If the heat of adsorption value was provided, you could substitute it into the formula above and calculate the enthalpy of adsorption.