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Equilibrium

Question
CBSEENCH11008427

The following equilibrium constants are given:

N2 + 3H2  ⇌ 2NH3; K1

N2 +O2  ⇌ 2NO; K2

H2 + 1/2O2  ⇌ H2O' K3

The equilibrium constants for the oxidation of NH3 by oxygen to give NO is:

  • K2K33 /K1

  • KK2K32 /K1

  • K22K3 /K1

  • K1K2 /K3

Solution

A.

K2K33 /K1

The required equation for the oxidation of NH3 by oxygen to give NO is:
4 NH subscript 3 space plus space 5 straight O subscript 2 space rightwards arrow from 800 to the power of straight o space straight C to Pt space left parenthesis gauze right parenthesis of space 4 space NO space plus space 6 straight H subscript 2 straight O
For space this space space straight K space equals space fraction numerator left square bracket NO right square bracket to the power of 4 left square bracket straight H subscript 2 straight O right square bracket to the power of 6 over denominator left square bracket NH subscript 3 right square bracket to the power of 4 left square bracket straight O subscript 2 right square bracket to the power of 5 end fraction
For space the space equation space left parenthesis straight I right parenthesis space straight K subscript 1 space equals space fraction numerator left square bracket NH subscript 3 right square bracket squared over denominator left square bracket straight N subscript 2 right square bracket left square bracket straight H subscript 2 right square bracket cubed end fraction
For space the space equation space left parenthesis II right parenthesis space straight K subscript 2 space equals space fraction numerator left square bracket NO right square bracket squared over denominator left square bracket straight N subscript 2 right square bracket left square bracket straight O subscript 2 right square bracket end fraction
For space the space equation space left parenthesis III right parenthesis space straight K subscript 3 space equals space fraction numerator left square bracket straight H subscript 2 straight O right square bracket over denominator left square bracket straight H subscript 2 right square bracket left square bracket straight O subscript 2 right square bracket to the power of 1 divided by 2 end exponent end fraction
For space getting space the space straight K space we space must space do
straight K subscript 1 squared space equals space fraction numerator left square bracket NH subscript 3 right square bracket to the power of 4 over denominator left square bracket straight N subscript 2 right square bracket squared left square bracket straight H subscript 2 right square bracket to the power of 6 end fraction comma space straight K subscript 2 squared space equals space fraction numerator left square bracket NO right square bracket to the power of 4 over denominator left square bracket straight N subscript 2 right square bracket squared left square bracket straight O subscript 2 right square bracket squared end fraction
straight K subscript 3 superscript 6 space equals space fraction numerator left square bracket straight H subscript 2 straight O right square bracket to the power of 6 over denominator left square bracket straight H subscript 2 right square bracket to the power of 6 left square bracket straight O subscript 2 right square bracket to the power of begin display style 6 over 2 end style equals 3 end exponent end fraction
straight K space equals space fraction numerator straight K subscript 2 superscript 2 space straight x space straight K subscript 3 superscript 6 over denominator straight K subscript 1 superscript 2 end fraction space substituting space the space value space we space get comma
straight K space equals space fraction numerator left square bracket NO right square bracket to the power of 4 left square bracket straight H subscript 2 straight O right square bracket to the power of 6 over denominator left square bracket NH subscript 3 right square bracket to the power of 4 left square bracket straight O subscript 2 right square bracket to the power of 5 end fraction space so space the space value space of space straight K space in space terms space of space straight K subscript 1 comma space straight K subscript 2 space and space straight K subscript 3 space is space
space straight K thin space equals space fraction numerator straight K subscript 2 straight K subscript 3 superscript 3 over denominator straight K subscript 1 end fraction