The Brunauer-Emmett-Teller BET equation is used to determine the surface area of a porous material like activated carbon. The equation is:V = V_m * C * P / [ 1 - P * 1 + C - 1 * P ]where:V = volume of adsorbed gas in this case, nitrogen at a given pressure PV_m = volume of gas required to form a monolayer on the surfaceC = BET constant k in the problem P = relative pressure P/P0 Since the nitrogen gas is adsorbed at 1 atm pressure P0 , the relative pressure P is 1.Given:V = 10 mLk = 0.25 mL/mP = 1We can rearrange the BET equation to solve for V_m:V_m = V * [ 1 - P * 1 + C - 1 * P ] / C * P V_m = 10 * [ 1 - 1 * 1 + 0.25 - 1 * 1 ] / 0.25 * 1 V_m = 10 * [0 * 1 - 0.75 ] / 0.25Since 1 - P = 0, the equation simplifies to:V_m = 0This result indicates that there is an error in the given data or the conditions provided. It is not possible to have a monolayer volume of 0 mL. Please check the given data and conditions and try again.