Here's a precise problem for a chemistry student to solve, based on Thermochemistry and the Enthalpy of Desorption Calculations:Given the following data for the adsorption of hydrogen gas on a metal surface:- Initial pressure of hydrogen gas = 1 atm- Final pressure of hydrogen gas after adsorption = 0.2 atm- Temperature = 298 K- Surface area of the metal = 5 cm^2- Enthalpy of Desorption of hydrogen gas on the metal surface = -40 kJ/molCalculate the enthalpy change (in kJ) for the adsorption of hydrogen gas on the metal surface.

Question

Here's a precise problem for a chemistry student to solve, based on Thermochemistry and the Enthalpy of Desorption Calculations:Given the following data for the adsorption of hydrogen gas on a metal surface:- Initial pressure of hydrogen

Answer 1

To calculate the enthalpy change for the adsorption of hydrogen gas on the metal surface, we first need to determine the amount of hydrogen gas adsorbed. We can do this using the Ideal Gas Law:PV = nRTWhere P is pressure, V is volume, n is the number of moles of gas, R is the ideal gas constant  0.0821 L atm/mol K , and T is temperature.First, we need to find the change in pressure  P  of hydrogen gas:P = Initial pressure - Final pressure = 1 atm - 0.2 atm = 0.8 atmNext, we need to find the volume of hydrogen gas adsorbed. Since we don't have the volume, we can assume that the volume of the gas before and after adsorption is the same. Therefore, we can use the ratio of the initial and final pressures to find the ratio of the initial and final moles of hydrogen gas:n_initial / n_final = P_initial / P_finaln_initial / n_final = 1 atm / 0.2 atm = 5Since the ratio of initial to final moles is 5, the change in moles  n  is:n = n_initial - n_final = 4 * n_finalNow we can use the Ideal Gas Law to find the moles of hydrogen gas adsorbed:PV = nRT 0.8 atm  * V =  4 * n_final  *  0.0821 L atm/mol K  *  298 K We can cancel out the volume  V  since it is the same before and after adsorption:0.8 = 4 * n_final * 0.0821 * 298Now, we can solve for n_final:n_final = 0.8 /  4 * 0.0821 * 298  = 0.00268 molSince n = 4 * n_final, we can find the moles of hydrogen gas adsorbed:n = 4 * 0.00268 mol = 0.01072 molFinally, we can calculate the enthalpy change for the adsorption of hydrogen gas on the metal surface using the Enthalpy of Desorption:H_adsorption = -H_desorption * nH_adsorption = - -40 kJ/mol  * 0.01072 mol = 0.4288 kJThe enthalpy change for the adsorption of hydrogen gas on the metal surface is approximately 0.429 kJ.