To calculate the enthalpy of adsorption, we can use the Clausius-Clapeyron equation, which relates the change in vapor pressure with temperature for a substance undergoing a phase transition. In this case, the phase transition is the adsorption of nitrogen gas onto the activated charcoal.The Clausius-Clapeyron equation is given by:ln P2/P1 = -H/R * 1/T2 - 1/T1 where P1 and P2 are the initial and final partial pressures of nitrogen gas, H is the enthalpy of adsorption, R is the gas constant 8.314 J/molK , and T1 and T2 are the initial and final temperatures.In this problem, we are given the partial pressure of nitrogen gas P1 as 0.1 atm. Since the gas is being adsorbed onto the activated charcoal, we can assume that the final partial pressure P2 is close to 0 atm. However, we cannot use 0 atm in the equation, as it would lead to an undefined value. Instead, we can use a very small value, such as 0.0001 atm, to represent the final partial pressure.We are also given the initial temperature T1 as 298 K. Since the adsorption process is assumed to be isothermal, the final temperature T2 is also 298 K.Now, we can plug these values into the Clausius-Clapeyron equation:ln 0.0001/0.1 = -H/ 8.314 J/molK * 1/298 K - 1/298 K ln 0.001 = -H/ 8.314 J/molK * 0Since the term 1/298 K - 1/298 K is equal to 0, the equation simplifies to:ln 0.001 = 0This equation tells us that the enthalpy of adsorption H is 0 kJ/mol. However, this result is not physically meaningful, as it implies that there is no energy change associated with the adsorption process. This discrepancy arises because the Clausius-Clapeyron equation assumes a phase transition, whereas adsorption is not a true phase transition.In reality, the enthalpy of adsorption for nitrogen gas on activated charcoal is likely to be similar to the heat of vaporization of nitrogen, which is given as 5.6 kJ/mol. This value represents the energy required to overcome the attractive forces between nitrogen molecules in the gas phase, which is similar to the energy change associated with adsorption onto a solid surface.Therefore, we can estimate the enthalpy of adsorption for this process to be approximately 5.6 kJ/mol.