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Thermodynamics

Question
CBSEENCH11006158

The enthalpy change (∆H) 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
is -92.38 kJ at 298 K. what is the increment straight U at 298 K?

Solution

    Here comma space space space increment straight H space equals space minus 92.38 space kJ space equals space 92380 space straight J
space space space space space space space space space space space space space space straight R space equals space 8.314 space JK to the power of negative 1 end exponent space mol to the power of negative 1 end exponent
space space space space space space increment straight n subscript straight g space equals space 2 minus left parenthesis 1 plus 3 right parenthesis space equals space minus 2
space space space space space space space space straight K space equals space 298
we space know space that space increment straight H space equals space increment straight U plus space increment straight n subscript straight g RT
Substituting the values, we have,
     negative 92380 space equals space increment straight U space plus space left parenthesis negative 2 right parenthesis thin space left parenthesis 8.314 right parenthesis thin space left parenthesis 298 right parenthesis
or space space minus 92380 space equals space increment straight U minus 4955

or space space space space space space increment straight U space equals space minus 92380 space plus space 4955
space space space space space space space space space space space space space space space equals negative 87425 space straight J
space space space space space space space space space space space space space space space equals space minus 87.425 space kJ