Calculate the enthalpy of adsorption for the adsorption of 5 grams of hydrogen gas on a solid adsorbent at a temperature of 298 K, if the pressure of hydrogen gas is 2.5 atm and the volume of the adsorbent is 100 cm3. Assume ideal gas behavior and use the equation ΔH = -q/n, where ΔH is the enthalpy of adsorption, q is the heat absorbed, and n is the number of moles of gas adsorbed.

Question

Calculate the enthalpy of adsorption for the adsorption of 5 grams of hydrogen gas on a solid adsorbent at a temperature of 298 K, if the pressure of hydrogen gas is 2.5 atm and the volume of the adsorbent is 100 cm3. Assume ideal gas behavior and use the equation ΔH = -q/n, where ΔH is the enthalpy of adsorption, q is the heat absorbed, and n is the numb

Answer 1

First, we need to find the number of moles of hydrogen gas  n  using the given mass  5 grams  and the molar mass of hydrogen gas  2 grams/mol .n = mass / molar massn = 5 g /  2 g/mol n = 2.5 molesNext, we need to find the heat absorbed  q  using the ideal gas law: PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant  0.0821 Latm/molK , and T is the temperature.First, convert the volume of the adsorbent from cm to L:100 cm *  1 L / 1000 cm  = 0.1 LNow, rearrange the ideal gas law to solve for q:q = nRT / Pq =  2.5 moles  *  0.0821 Latm/molK  *  298 K  /  2.5 atm q = 61.2675 JFinally, we can calculate the enthalpy of adsorption  H  using the equation H = -q/n:H = -q / nH = -61.2675 J / 2.5 molesH = -24.507 J/molThe enthalpy of adsorption for the adsorption of 5 grams of hydrogen gas on a solid adsorbent at a temperature of 298 K and a pressure of 2.5 atm is -24.507 J/mol.