Question

The text gives an example reaction for which K = K_P. The text states this is true “because the sum of the coefficients on either side of the balanced equation is identical. . . .” What if you are told that for a reaction K = K_P, but the sum of the coefficients on either side of the balanced equation is not equal? How is this possible?

Short answer

You need to explain how it is possible if K = K_P but the sum of the coefficients on either side of the balanced equation is not equal.

Step-by-step solution

Example reaction

The example reaction from the text is

${\mathrm{H}}_2\left(\mathrm{g}\right)+{\mathrm{F}}_2\left(\mathrm{g}\right)\rightleftharpoons 2\mathrm{HF}\left(\mathrm{g}\right)$

Relation between K and KP for this example reaction

The equilibrium expression, K can be written as

$\mathrm{K}=\frac{{\mathrm{C}}_{\mathrm{HF}}^2}{\left({\mathrm{C}}_{{\mathrm{H}}_2}\right)\left({\mathrm{C}}_{{\mathrm{F}}_2}\right)}$

Unit: $\mathrm{K}=\frac{{(\mathrm{mol}/\mathrm{L})}^2}{(\mathrm{mol}/\mathrm{L})(\mathrm{mol}/\mathrm{L})}$

Hence, K has no unit.

The equilibrium partial pressure, K_P can be written as

${\mathrm{K}}_{\mathrm{P}}=\frac{{\mathrm{P}}_{\mathrm{HF}}^2}{\left({\mathrm{P}}_{{\mathrm{H}}_2}\right)\left({\mathrm{P}}_{{\mathrm{F}}_2}\right)}$

Unit:${\mathrm{K}}_{\mathrm{P}}=\frac{{\left(\mathrm{atm}\right)}^2}{\left(\mathrm{atm}\right)\left(\mathrm{atm}\right)}$

Hence, K_P has no unit.

Again you know that,

${\mathrm{K}}_{\mathrm{P}}=\mathrm{K}{\left(\mathrm{RT}\right)}^{\mathrm{\Delta n}}$

Where,$\mathrm{\Delta n}$= the difference in the sum of the coefficients for the gaseous products and reactants.

For this reaction,$\mathrm{\Delta n}$ = 0

Hence, ${\mathrm{K}}_{\mathrm{P}}=\mathrm{K}$(because both has no unit, therefore they are numerically have same value)

Solution of the problem

According to the question, for a reaction,

${\mathrm{K}}_{\mathrm{P}}=\mathrm{K}$

But,$\mathrm{\Delta n}\ne 0$

But this is not possible because if,$\mathrm{\Delta n}\ne 0$ both K and K_P will have units.

Therefore; ${\mathrm{K}}_{\mathrm{P}}\ne \mathrm{K}$; if the sum of the coefficients on either side of the balanced equation is not equal.