Thermodynamics

Thermodynamics

Question

The following reaction is performed at 298 K
2NO(g) + O2 (g) ⇌ 2NO2 (g)
The standard free energy of formation of NO (g) is 86.6 kJ/mol at 298 K. What is the standard free energy of formation of NO2 (g) at 298 K? (KP = 1.6 x 1012)

  • R (298) In (1.6 x 1012)-86600

  • 86600 + R (298) In (1.6 x 1012)

  • 86600 - In(1.6 x 1012)/R(298)

  • 0.5[2 x 86600-R(298)In (1.6 x 1012)]

Answer

D.

0.5[2 x 86600-R(298)In (1.6 x 1012)]

For the given reaction,
2NO(g) + O2 (g) ⇌ 2NO2 (g)
Given ,
increment straight G subscript straight f superscript straight o left parenthesis NO right parenthesis space equals space 86.6 space kJ divided by mol
increment straight G subscript straight f superscript straight o left parenthesis NO subscript 2 right parenthesis space equals ?
straight K subscript straight p space equals space 1.6 space straight x space 10 to the power of 12
Now, we have,
increment straight G subscript straight f superscript degree space equals space 2 increment straight G subscript straight f left parenthesis NO subscript 2 right parenthesis end subscript superscript straight o space minus space left square bracket 2 increment straight G subscript straight f left parenthesis NO right parenthesis end subscript superscript straight o space plus space increment straight G subscript straight f left parenthesis straight O subscript 2 right parenthesis end subscript superscript straight o right square bracket
equals negative RT space In space straight K subscript straight p space equals space 2 increment straight G subscript straight f superscript straight o subscript left parenthesis NO subscript 2 right parenthesis end subscript space minus left square bracket 2 space straight x 86600 space plus 0 right square bracket
increment straight G subscript straight f superscript straight o subscript left parenthesis NO subscript 2 right parenthesis end subscript space equals space 1 half left square bracket space 2 space straight x space 86600 space minus straight R space straight x space 298 space In space left parenthesis 1.6 space straight x space 10 to the power of 12 right parenthesis right square bracket
increment straight G subscript straight f superscript straight o subscript left parenthesis NO subscript 2 right parenthesis end subscript space equals space 0.5 space left square bracket space space 2 space straight x space 86600 minus space straight R space straight x space left parenthesis 298 right parenthesis In space left parenthesis 1.6 space straight x space 10 to the power of 12 right parenthesis right square bracket

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