Question

How can standard enthalpy and gibbs free energy of a reaction be used to determine yield at a particular temperature and pressure? The standard enthalpy of formation at 298K is -45.4 kJ/mol and the standard gibbs free energy at 298K is -7.7kJ/mol. The problem requires that the yield of the reaction be determined at 325K and 50 atm. Any help with this would be greatly appreciated.

Answer 1

The following steps should aim at providing a solution to the problem-

A)   Change in temperature   :-

1.Calculate K_eq of the given reaction at 298K , using the given value of G^o applying expression,

....................... G^o = - 2.303 RT log K_eq

2. Calculate K_eq at the desired temperature using Van't Hoff equation-

.......d ln K_eq / dT =    H^o / RT²

......or better , use the the integrated form of the equation as,

.................(ln K₂ / K₁ ) = ( - H^o / R ) [ 1 / T₂ - 1 / T₁ ]

where K₁ is the equilibrium constant at absolute temperature T₁ and K₂ is the equiilibrium constant at absolute temperature T₂

3. Thus , knowing K_eq of the chemical reaction at desired temperature, the concentrations ( in moles / L ) of products can be calculated.

4. So ,finally with concentrations of products and reactants at new equilibrium constant yield can be calculated.

Note -

this should also be in agreement with Le Chatelier's principle.

B) Effect of variation in pressure

a. Calculate K_eq for the reaction at 298 K using relation,

......... G^o   = -2.303 RT log K_eq

b.  

1. The equilibrium constant and hence the yield of products are effected only in case of gaseous reaction by change of pressure as per Le Chatelier's principle.

2 . Any change in pressure over the gaseous system is associated with change in volume also.

3. hence , calculate the volume at desired pressure using relation,

......P1V1 / T1 = P2V2 / T2

4 . and the changed concentrations of reactants and products when applied to the calculated

equilibrium constant at the desired temperature using van't Hoff equation (briefed out above )

5. Based upon the concentrations of products corresponding to a equilibrium constant at different temperature and pressure yield can be calculated .

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Please follow the above steps to calculate the yield , in case of other part of the question , or post this question separately as a fresh question for detailed calculations / answers.

Glad to help.