To calculate the surface area of the activated charcoal sample, we will use the BET Brunauer-Emmett-Teller equation. The BET equation relates the amount of gas adsorbed on a solid surface to the pressure and the surface area.The BET equation is:n = n_m * C * P / [ 1 - P * 1 + C - 1 * P ]where:n = amount of gas adsorbed mol/g n_m = monolayer capacity mol/g C = BET constantP = relative pressure P/P0 We are given the monolayer capacity n_m as 0.16 mol/g and the nitrogen pressure P as 0.98 atm. However, we need to find the relative pressure P/P0 to use in the BET equation. Since the saturation pressure of nitrogen P0 at 77 K is approximately 1 atm, we can assume P/P0 = 0.98.Now, we need to find the cross-sectional area of a nitrogen molecule A_N2 . The cross-sectional area of a nitrogen molecule can be calculated using the following formula:A_N2 = * d_N2^2 / 4where d_N2 is the diameter of a nitrogen molecule, which is approximately 0.36 nm. Converting to cm, we get:d_N2 = 0.36 * 10^-7 cmNow, we can calculate A_N2:A_N2 = * 0.36 * 10^-7 cm ^2 / 4 1.02 * 10^-14 cmNow, we can calculate the surface area S of the activated charcoal sample using the following formula:S = n_m * A_N2 * N_A * W / where:N_A = Avogadro's number 6.022 * 10^23 mol^-1 W = weight of the sample 0.25 g = density of the charcoal 2.2 g/cm Plugging in the values, we get:S = 0.16 mol/g * 1.02 * 10^-14 cm * 6.022 * 10^23 mol^-1 * 0.25 g / 2.2 g/cm 882.6 cmTherefore, the surface area of the activated charcoal sample is approximately 882.6 cm.