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Chemical Equilibrium Chemistry Class 11th Equilibrium

A(g) ->B(g) + $\frac{1}{2}$ C(g)

In the about reaction, the correct relation between K_p, a and equilibrium pressure (p) is

Option 1 -

$K_{p} = \frac{α^{\frac{1}{2}} 2 p^{\frac{1}{2}}}{{(2 + α)}^{\frac{1}{2}}}$

Option 2 -

$K_{p} = \frac{α^{\frac{1}{2}} 2 p^{\frac{3}{2}}}{{(2 + α)}^{\frac{3}{2}}}$

Option 3 -

$K_{p} = \frac{α^{\frac{1}{2}} 2 p^{\frac{1}{2}}}{{(2 + α)}^{\frac{3}{2}}}$

Option 4 -

$K_{p} = \frac{α^{\frac{3}{2}} p^{\frac{1}{2}}}{{(2 + α)}^{\frac{1}{2}} (1 - α)}$

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Answered by

alok kumar singh | Contributor-Level 10

a week ago

Correct Option - 4

Detailed Solution:

A(g) ->B(g) + $\frac{1}{2}$ (g)

Initial moles n 0 0

Eqb. moles n(1 – a) $\frac{n α}{2}$ n_a

total moles = $n (1 + \frac{α}{2})$

Eqb. pressure $\frac{(1 - α) p}{1 + \frac{α}{2}}$ $\frac{α p}{1 + \frac{α}{2}}$ $\frac{(\frac{α}{2}) p}{1 + \frac{α}{2}}$

$\frac{K_{p} = \frac{α p}{(1 + \frac{α}{2})} \times {[\frac{α p}{(2 + α)}]}^{\frac{1}{2}}}{\frac{(1 + α) p}{1 + \frac{α}{2}}}$

$K_{p} = \frac{α^{\frac{3}{2}} p^{\frac{1}{2}}}{{(2 + α)}^{\frac{1}{2}} (1 - α)}$

...more

A(g) ->B(g) + $\frac{1}{2}$ (g)

Initial moles n 0 0

Eqb. moles n(1 – a) $\frac{n α}{2}$ n_a

total moles = $n (1 + \frac{α}{2})$

Eqb. pressure $\frac{(1 - α) p}{1 + \frac{α}{2}}$ $\frac{α p}{1 + \frac{α}{2}}$ $\frac{(\frac{α}{2}) p}{1 + \frac{α}{2}}$

$\frac{K_{p} = \frac{α p}{(1 + \frac{α}{2})} \times {[\frac{α p}{(2 + α)}]}^{\frac{1}{2}}}{\frac{(1 + α) p}{1 + \frac{α}{2}}}$

$K_{p} = \frac{α^{\frac{3}{2}} p^{\frac{1}{2}}}{{(2 + α)}^{\frac{1}{2}} (1 - α)}$

less

A(g) ->B(g) + <math> <mrow> <mfrac> <mrow> <mn>1</mn> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> </mrow> </math> (g)Initial moles             n                         0             0Eqb. moles               n(1 – a)   <math> <mrow> <mfrac> <mrow> <mi>n</mi> <mi>α</mi> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> </mrow> </math>           na            total moles =   <math> <mrow> <mi>n</mi> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>+</mo> <mfrac> <mrow> <mi>α</mi> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> </mrow> </math> Eqb. pressure   <math> <mrow> <mfrac> <mrow> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>−</mo> <mi>α</mi> </mrow> <mo>)</mo> </mrow> <mi>p</mi> </mrow> <mrow> <mn>1</mn> <mo>+</mo> <mfrac> <mrow> <mi>α</mi> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> </mrow> </mfrac> </mrow> </math> <math> <mrow> <mfrac> <mrow> <mi>α</mi> <mi>p</mi> </mrow> <mrow> <mn>1</mn> <mo>+</mo> <mfrac> <mrow> <mi>α</mi> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> </mrow> </mfrac> </mrow> </math> <math> <mrow> <mfrac> <mrow> <mrow> <mo>(</mo> <mrow> <mfrac> <mrow> <mi>α</mi> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mi>p</mi> </mrow> <mrow> <mn>1</mn> <mo>+</mo> <mfrac> <mrow> <mi>α</mi> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> </mrow> </mfrac> </mrow> </math> <math> <mrow> <mfrac> <mrow> <msub> <mrow> <mi>K</mi> </mrow> <mrow> <mi>p</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <mi>α</mi> <mi>p</mi> </mrow> <mrow> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>+</mo> <mfrac> <mrow> <mi>α</mi> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>×</mo> <msup> <mrow> <mrow> <mo>[</mo> <mrow> <mfrac> <mrow> <mi>α</mi> <mi>p</mi> </mrow> <mrow> <mrow> <mo>(</mo> <mrow> <mn>2</mn> <mo>+</mo> <mi>α</mi> </mrow> <mo>)</mo> </mrow> </mrow> </mfrac> </mrow> <mo>]</mo> </mrow> </mrow> <mrow> <mfrac> <mrow> <mn>1</mn> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> </mrow> </msup> </mrow> <mrow> <mfrac> <mrow> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>+</mo> <mi>α</mi> </mrow> <mo>)</mo> </mrow> <mi>p</mi> </mrow> <mrow> <mn>1</mn> <mo>+</mo> <mfrac> <mrow> <mi>α</mi> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> </mrow> </mfrac> </mrow> </mfrac> </mrow> </math> <math> <mrow> <msub> <mrow> <mi>K</mi> </mrow> <mrow> <mi>p</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <msup> <mrow> <mi>α</mi> </mrow> <mrow> <mfrac bevelled="true"> <mrow> <mn>3</mn> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> </mrow> </msup> <mtext> </mtext> <msup> <mrow> <mi>p</mi> </mrow> <mrow> <mfrac bevelled="true"> <mrow> <mn>1</mn> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> </mrow> </msup> </mrow> <mrow> <msup> <mrow> <mrow> <mo>(</mo> <mrow> <mn>2</mn> <mo>+</mo> <mi>α</mi> </mrow> <mo>)</mo> </mrow> </mrow> <mrow> <mfrac bevelled="true"> <mrow> <mn>1</mn> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> </mrow> </msup> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>−</mo> <mi>α</mi> </mrow> <mo>)</mo> </mrow> </mrow> </mfrac> </mrow> </math>

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A(g) ->B(g) + $\frac{1}{2}$ C(g)

In the about reaction, the correct relation between K_p, a and equilibrium pressure (p) is

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A(g) ->B(g) + 1 2 C(g) In the about reaction, the correct relation between Kp, a and equilibrium pressure (p) is

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A(g) ->B(g) + $\frac{1}{2}$ C(g)

In the about reaction, the correct relation between K_p, a and equilibrium pressure (p) is