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Thermodynamics

Question
CBSEENCH11008355

Standard entropies X2, Y2 and XY2 are 60, 40 and 50 J K-1 mol-1 respectively for the reaction

1 half space straight X subscript 2 space plus 3 over 2 space straight Y subscript 2 space leftwards harpoon over rightwards harpoon space XY subscript 3 space semicolon space increment straight H space equals space minus space 30 space kJ comma space to space be space at
equilibrium, the temperature should be

  • 750 K

  • 1000 K 

  • 1250 K

  • 500 K 

Solution

A.

750 K

1 half space straight X subscript 2 space plus space 3 over 2 space straight Y subscript 2 space bold a bold space XY subscript 3 space semicolon space increment straight H space equals space minus space 30 space kJ
increment straight S to the power of straight o space equals space straight S subscript left parenthesis XY subscript 3 right parenthesis end subscript superscript straight o space minus space open square brackets 1 half straight S to the power of straight o subscript straight x subscript 2 end subscript plus 3 over 2 space straight S subscript straight Y subscript 2 end subscript superscript straight o close square brackets

equals space 50 space minus space open square brackets 1 half space straight x space 60 space plus space 3 over 2 space straight x space 40 close square brackets
space equals space 50 minus left square bracket 30 plus 60 right square bracket space equals space 50 minus 90
equals negative 40 space JK to the power of minus space mol to the power of negative 1 end exponent
we space know space that
increment straight G to the power of straight o space equals space increment straight H to the power of straight o minus straight T increment straight S to the power of straight o
At space equilibrium comma
increment straight G to the power of straight o space equals 0
increment straight H space equals space straight T increment straight S to the power of straight o
straight T space equals space fraction numerator increment straight H over denominator increment straight S to the power of straight o end fraction space equals space fraction numerator negative 30 space straight x space 10 cubed over denominator negative 40 space straight J space straight K to the power of negative 1 end exponent space mol to the power of negative 1 end exponent space end fraction space equals space 750 space straight K