For the reaction N_{2}\left ( g \right )+O_{2}\left ( g \right )\rightleftharpoons 2NO\left ( g \right ), the equilibrium constant is K_{1}. The equilibrium constant is K_{2} for the reaction

2NO\left ( g \right )+O_{2}\rightleftharpoons 2NO_{2}\left ( g \right )

What is K for the reaction

NO_{2}(g)\rightleftharpoons \frac{1}{2}N_{2}(g)+O_{2}(g)?

  • Option 1)

    1/\left ( 2K_{1}K_{2} \right )

  • Option 2)

    1/\left ( 4K_{1}K_{2} \right )

  • Option 3)

    [1/K_{1}K_{2}]^{\frac{1}{2}}

  • Option 4)

    1/\left ( K_1 K_2 \right )

 

Answers (1)

As we discussed in concept

Law of Chemical equilibrium -

At a given temperature, the product of concentration of the reaction products raised to the respective stoichiometric coefficient in the balanced chemical equation divided by the product of concentration of the reactants raised to their individual stoichiometric coefficients has a constant value.

- wherein

aA+bB\rightleftharpoons cC+dD


K_{c}=\frac{[C]^{c\:[D]^{d}}}{[A]^{a}\:[B]^{b}}

[A],\:[B],\:[C]\:[D]

are equilibrium concentration

 

 N_{2}+O_{2}\:\rightleftharpoons 2NO\:\:\:K_{1}

2NO+O_{2}\:\rightleftharpoons 2NO_{2}\:\:\:K_{2}

NO_{2}\:\rightleftharpoons \frac{1}{2}N_{2}+O_{2}\:\:\:K

K_{1}=\frac{[NO]^{2}}{[N_{2}][O_{2}]}\:,\:K_{2}=\frac{[NO_{2}]^{2}}{[NO]^{2}[O_{2}]}

K=\frac{[N_{2}]^{\frac{1}{2}}.[O_{2}]}{[NO_{2}]}=\sqrt{\frac{[N_{2}][O_{2}]\times [NO]^{2}[O_{2}]}{[NO]^{2}\times [NO_{2}]^{2}}}

K=\sqrt{\frac{1}{K_{1}K_{2}}}

 


Option 1)

1/\left ( 2K_{1}K_{2} \right )

This option is incorrect.

Option 2)

1/\left ( 4K_{1}K_{2} \right )

This option is incorrect.

Option 3)

[1/K_{1}K_{2}]^{\frac{1}{2}}

This option is correct.

Option 4)

1/\left ( K_1 K_2 \right )

This option is incorrect.

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