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Thermodynamics

Question
CBSEENCH11006269

For the reaction:
straight N subscript 2 left parenthesis straight g right parenthesis space plus space 3 straight H subscript 2 left parenthesis straight g right parenthesis space space rightwards arrow space space 2 NH subscript 3 left parenthesis straight g right parenthesis comma
increment straight H equals negative 95.4 space kJ space and space increment straight S space equals space minus 198.3 space kJ divided by straight K.

Calculate the temperature at which it attains equilibrium.


Solution

According to Gibb's Helmoltz equation,
            increment straight G space equals space increment straight H space minus space straight T increment straight S
which it attains equilibrium,
increment straight G space equals space 0
      0 space equals space increment straight H space minus space straight T increment straight S
    or space space increment straight H space equals space straight T increment straight S
therefore space space space space space straight T space equals space fraction numerator increment straight H over denominator increment straight S end fraction space equals space fraction numerator negative 95.4 space kJ over denominator negative 198.3 space kJ space straight K to the power of negative 1 end exponent end fraction space equals space 0.48 space straight K.