Thermodynamic equilibrium constants calculating the reaction free energy

[riel]

Can someone please help me answer this question and explain the concepts/solution step by step:


Prof. W.H Bogus claims that he has prepared a powerful new catalyst that makes it possible to synthesize NH3 with a 70% yield in a reactor operating 500K and 2 atm pressure and having a feed consisting of N2 and H2 in stochiometric ratio. Evaluate his claim by calculating the reaction free energy change for the proposed reaction under the conditions stated. For NH3 at 500K, Gf= 4.778 kJ/mol.


The answer is +10.43 kJ/mol which means this is not a spontaneous reaction.

I first calculated K using ln K=(-G/RT) then i didnt know what to do after that. Please help me.

 

[Asim Riaz]

To evaluate Prof. W.H Bogus' claim, you will need to calculate the reaction free energy change for the proposed reaction under the given conditions. This can be done using the equation G=Gf+(RTlnK), where G is the reaction free energy change, Gf is the standard free energy of formation of NH3 under the given conditions (in this case, 4.778 kJ/mol at 500K), R is the universal gas constant, T is temperature (in this case, 500K) and K is the equilibrium constant for the reaction. Since we are trying to calculate the reaction free energy change, we must first calculate the equilibrium constant K. This can be done using the equation lnK=(-G/RT), where G is the standard reaction free energy change for the reaction (which can be calculated using the standard free energies of formation for the reactants and products). Once we have calculated K, we can then use the equation G=Gf+(RTlnK) to calculate the reaction free energy change for the reaction under the given conditions. In this case, the standard reaction free energy change for the reaction is -29.2 kJ/mol. Plugging this into the equation lnK=(-G/RT), we get lnK=-6.08. Using this value for K in the equation G=Gf+(RTlnK), we get a reaction free energy change of +10.43 kJ/mol. This means that the reaction is not spontaneous under the given conditions, and thus Prof. W.H Bogus' claim is false.