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Chemical Kinetics

Question
CBSEENCH12011437

The equilibrium constants of the following are.

straight N subscript 2 space plus space 3 straight H subscript 2 space rightwards harpoon over leftwards harpoon with space on top space 2 NH subscript 3 space space straight K subscript 1
straight N subscript 2 space plus space straight O subscript 2 space rightwards harpoon over leftwards harpoon with space on top space 2 NO space space space space straight K subscript 2
straight H subscript 2 space plus space 1 half straight O subscript 2 space rightwards arrow with space on top space straight H subscript 2 straight O space straight K subscript 3

The equilibrium constant (K) of the reaction:

2 NH subscript 3 space plus space 5 over 2 straight O subscript 2 space rightwards harpoon over leftwards harpoon with straight K on top space 2 NO space plus space straight H subscript 2 straight O comma space will space be

  • straight K subscript 1 straight K subscript 3 superscript 3 divided by straight K subscript 2
  • straight K subscript 2 straight K subscript 3 superscript 3 space divided by space straight K subscript 1
  • straight K subscript 2 straight K subscript 3 superscript 3 space divided by space straight K
  • straight K subscript 2 straight K subscript 3 space divided by space straight K subscript 1

Solution

B.

straight K subscript 2 straight K subscript 3 superscript 3 space divided by space straight K subscript 1 straight N subscript 2 space plus 3 straight H subscript 2 space rightwards harpoon over leftwards harpoon with space on top space 2 NH subscript 3 space semicolon space straight K subscript 1 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
left parenthesis II right parenthesis space straight N subscript 2 space plus space straight O subscript 2 space rightwards harpoon over leftwards harpoon with space on top space 2 NO space semicolon space straight K subscript 2 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
left parenthesis III right parenthesis space straight H subscript 2 space plus 1 half straight O subscript 2 space rightwards arrow with space on top space straight H subscript 2 straight O semicolon 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
left parenthesis II space plus space 3 space straight x space III minus II right parenthesis space will space space give
2 NH subscript 3 space plus space 5 over 2 straight O subscript 2 space rightwards harpoon over leftwards harpoon with space straight K on top space 2 NO space plus space 3 straight H subscript 2 straight O
therefore space straight K space equals space straight K subscript 2 space straight x space straight K subscript 3 superscript 3 divided by straight K subscript 1