Calculate the free energy change of the reaction $straight C left parenthesis graphite right parenthesis space plus space straight O subscript 2 left parenthesis straight g right parenthesis space space space rightwards arrow space space space CO subscript 2 left parenthesis straight g right parenthesis$
$left parenthesis Given space increment straight H space equals space minus 300 space kJ space mol to the power of negative 1 end exponent semicolon space space increment straight S space equals space 3 space JK to the power of negative 1 end exponent space mol to the power of negative 1 end exponent space at space 300 space straight K right parenthesis.$

Solution

According to Gibb's Helmoltz equation,
   $increment straight G space equals space increment straight H space minus space straight T increment straight S space space space space space space space space space space space space space space space space space... left parenthesis 1 right parenthesis$
Here $increment straight H space equals space minus 300 space kJ space mol to the power of negative 1 end exponent$
   $equals space minus 30000 space straight J space mol to the power of negative 1 end exponent$
   $increment straight S space equals space 3 space JK to the power of negative 1 end exponent space mol to the power of negative 1 end exponent space space and space straight T space equals space 300 space straight K$
Substituting the values in (1), we have,
$increment straight G space equals space minus 30000 space straight J space mol to the power of negative 1 end exponent space minus space left parenthesis 300 space straight K right parenthesis space cross times space left parenthesis 3 JK to the power of negative 1 end exponent space mol to the power of negative 1 end exponent right parenthesis space space space space space space space equals space minus 30000 space straight J space mol to the power of negative 1 end exponent space minus 900 space straight J space mol to the power of negative 1 end exponent space space space space space space space equals space minus 30900 space straight J space mol to the power of negative 1 end exponent or space space space space minus 30.9 space kJ$

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Thermodynamics

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