A reaction has a standard free-energy change of − 13.50 KJ mol − 1 ( − 3.227 kcal mol − 1 ). Calculate the equilibrium constant for the reaction at 25 degree Celsius

Question

A reaction has a standard free-energy change of    −  13.50       KJ mol          −      1        (  −  3.227       kcal mol          −      1        ). Calculate the equilibrium constant for the reaction at 25 degree Celsius

Dakota Murillo · Accepted Answer

General guidanceConcepts and reasonThis problem is based on the concept of thermodynamics.The thermodynamic potential which is used to calculate maximum reversible work done at constant pressure and temperature is called Gibbs free energy.FundamentalsIn a chemical reaction, the value of reaction quotient when the reaction reach equilibrium is called equilibrium constant.The relation between change in Gibbs free energy   Δ  G and equilibrium constant   (  K  ) is as follow,   Δ  G  =  −  R  T  ln  ⁡  K...… (1)Here, T is temperature and R is gas constant.Convert change in Gibbs free energy in joules per mole as follows:  Δ  G  =  (  −  13.50            k      J              m      o      l        )  (            1000      J              1      k      J        )    =  13500  J     m  o      l          −      1      Convert temperature in kelvin as follows:      T    k    =      T    c    +  273.15Substitute       25    ∘    C for T in above equation as follows:      T    k    =  (  25  +  273.15  )  K    =  298.15  KThe gibbs free energy is in   k  J      /    m  o  l It is converted into   J      /    m  o  l by the use of conversion factor. Temperature is converted into Kelvin by adding 273.15 factor to it.Rearrange equation (1) for K as follows:  ln  ⁡  K  =            −      Δ      G              R      T          K  =  exp  ⁡  (            −      Δ      G              R      T        )Substitute   8.314  J      K          −      1        m  o      l          −      1       for R,   −  13500  J     m  o      l          −      1       for   Δ  G and   298.15  K for T in above equation as follows:  K  =  exp  ⁡  (            −      (      −      13500      J             m      o              l                  −          1                    )              (      8.314      J                     K                  −          1                    m      o              l                  −          1                    )      (      298.15      K      )        )    K  =  231.86The equilibrium constant is 231.86.

A reaction has a standard free-energy change of -13.50 KJ mol^(-1) (-3.227 kcal mol^(-1)). Calculate the equilibrium constant for the reaction at 25 degree Celsius

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