Question

For the melting of ice at $25 degree straight C comma$
$straight H subscript 2 straight O left parenthesis straight s right parenthesis space space space rightwards harpoon over leftwards harpoon space space straight H subscript 2 straight O left parenthesis l right parenthesis comma$
the enthalpy of fusion is $6.97 space kJ space mol to the power of negative 1 end exponent$ and entropy of fusion is 25.4 $JK to the power of negative 1 end exponent mol to the power of negative 1 end exponent.$ Calculate the free energy change and predict whether the melting of ice is spontaneous or not at this temperature.

Solution

According to Gibb's Helmoltz equation
$increment straight G space equals space increment straight H space minus space straight T increment straight S space space space space space space space space space space space space space space space... left parenthesis 1 right parenthesis$
$Here space space space space increment straight H space equals space 6.97 space kJ space mol to the power of negative 1 end exponent space equals space 6970 space straight J space mol to the power of negative 1 end exponent space space space space space space space space space space space increment straight S space equals space 25.4 space JK to the power of negative 1 end exponent mol to the power of negative 1 end exponent space space space space space space space space space space space space space space straight T space equals space 25 plus 273 space equals space 298 space straight K$
Substituting the values in (1), we have,
$increment straight G space equals space 6970 space straight J space mol to the power of negative 1 end exponent space space space space space space space equals space minus left parenthesis 298 space straight K right parenthesis space cross times space left parenthesis 25.4 space JK to the power of negative 1 end exponent space mol to the power of negative 1 end exponent right parenthesis space space space space space space space equals space 69700 space mol to the power of negative 1 end exponent space minus space 7569.2 space straight J space mol to the power of negative 1 end exponent space space space space space space space equals space minus 599.2 space straight J space mol to the power of negative 1 end exponent space$

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Thermodynamics

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Define irreversible change.

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