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Thermodynamics

Question
CBSEENCH11006267

From the following values of ∆H and ∆S, decide whether or not these reactions will be spontaneous at 298 K:

Reaction A:
∆H = – 10.5 X 103 J mol–1
∆S = + 31 JK–1 mol–1

Reaction B:
∆H = – 11.7 X 103 J mol–1 ;
∆S = –105 jK–1 mol–1.

Solution

(i) Reaction A:
According to Gibb’s Helmholtz equation,
increment straight G space equals space increment straight H space minus space straight T increment straight S
space space space space equals space minus 10.5 space cross times space 10 cubed straight J space mol to the power of negative 1 end exponent space minus left parenthesis 298 space straight K right parenthesis space cross times space left parenthesis 31 space JK to the power of negative 1 end exponent space mol to the power of negative 1 end exponent right parenthesis
space space space space equals space minus 10500 space straight J space mol to the power of negative 1 end exponent space minus 9238 space straight J space mol to the power of negative 1 end exponent
space space space space equals space minus 19738 space straight J space mol to the power of negative 1 end exponent
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space
Since ∆G is –ve, the reaction A will be spontaneous at 298 K.
(ii) Reaction B:
  increment straight G space equals space increment straight H space minus space straight T increment straight S
space space space space space space space equals space minus 11.7 space cross times space 10 cubed straight J space mol to the power of negative 1 end exponent
space space space space space space space space space space space space space space space space space space space space space space space space space space space minus left parenthesis 298 space straight K right parenthesis space cross times space left parenthesis negative 105 space JK to the power of negative 1 end exponent space mol to the power of negative 1 end exponent right parenthesis
space space space space space space equals negative 11700 space straight J space mol to the power of negative 1 end exponent space plus space 31290 space straight J space mol to the power of negative 1 end exponent
space space space space space space equals space 19590 space straight J space mol to the power of negative 1 end exponent
As ∆G is +ve, the reaction B will not be spontaneous at 298 K.