To determine the specific surface area of the activated carbon using the BET theory, we first need to convert the given nitrogen adsorption pressures to relative pressures P/P0 . We will assume that the saturation pressure of nitrogen P0 is 760 mmHg.Relative pressures P/P0 :- 6.523/760 = 0.00858- 9.785/760 = 0.01288- 13.092/760 = 0.01722- 19.638/760 = 0.02583- 31.725/760 = 0.04175- 45.200/760 = 0.05947- 61.587/760 = 0.08104- 84.632/760 = 0.11135- 114.684/760 = 0.15090- 147.087/760 = 0.19354Next, we need to obtain the adsorbed gas quantity n at each relative pressure. This information is missing from the given data. Assuming you have the adsorbed gas quantity data, you can then plot the BET plot using the following equation:1/ n P0-P = 1/ n_mC + C-1 / n_mC * P/P0 where n is the adsorbed gas quantity, P0 is the saturation pressure, P is the pressure, n_m is the monolayer capacity, and C is the BET constant.From the linear portion of the BET plot, you can determine the slope S and y-intercept I . Then, calculate the BET constant C and monolayer capacity n_m using the following equations:C = 1 + S/I n_m = 1 / S + I Now, you can calculate the specific surface area A using the following equation:A = n_m * N_A * a / mwhere N_A is Avogadro's number 6.022 x 10^23 mol , a is the area occupied by one nitrogen molecule 0.162 nm , and m is the mass of activated carbon used 0.25 g .Assuming you have the adsorbed gas quantity data, you can follow these steps to calculate the specific surface area of the activated carbon material.