Question

For which reactions in Exercise 21 is K_p equal to K?

Short answer

For Reaction d),$\text{CuO}\left(\text{s}\right){\text{+H}}_{\text{2}}\left(\text{g}\right)\text{Cu}\left(\text{l}\right){\text{+H}}_{\text{2}}\text{O}\left(\text{g}\right)$K_pis equal to $K_c$ .

Step-by-step solution

The relation between Kp  and  Kc

The relationship between K_p and K can be written as follows:

${\text{K}}_{\text{p}}\text{= K}{\left(\text{RT}\right)}^{\text{∆n}}$ …(1)

Here,

K_p is the equilibrium constant in terms of partial pressures.

K is the equilibrium constant in terms of concentrations.

R is the universal gas constant.

T is the temperature.

is the numerical difference between the coefficients of gaseous products and the coefficients of gaseous reactants.

If$∆\mathrm{n}=0$, then the above equation becomes,

${\text{K}}_{\text{p}}\text{= K}$

This is because the term, ${\left(\text{RT}\right)}^{∆n}$is equal to 1.

Subpart a)

Calculate the value of$∆\mathrm{n}$for the given four reactions as shown below:

For Reaction a:${\text{2NH}}_{\text{3}}\left(\text{g}\right){\text{+CO}}_{\text{2}}\left(\text{g}\right)\rightleftharpoons {\text{N}}_{\text{2}}{\text{CH}}_{\text{4}}\text{O}\left(\text{s}\right){\text{+H}}_{\text{2}}\text{O}\left(\text{g}\right)$

$\begin{array}{rcl}& & ∆\mathrm{n}\text{= 1} \text{-} \left(\text{2 + 1}\right)\\ & & \text{=} \text{-} \text{2}\\ & & \end{array}$

Hence, $K_p$is not equal to $K_p$.

Subpart b)

For Reaction b: ${\text{2NBr}}_{\text{3}}\left(\text{s}\right){\text{N}}_{\text{2}}\left(\text{g}\right){\text{+ 3Br}}_{\text{2}}\left(\text{g}\right)$

localid="1657786559392" $\begin{array}{rcl}∆\mathrm{n}& =& \text{3 + 1} \text{-} 0\\ & & \text{= 4}\\ & & \end{array}$

Hence, $K_p$is not equal to $K_c$.

Subpart c)

For Reaction c: ${\text{2KClO}}_{\text{3}}\left(\text{s}\right)\text{2KCl}\left(\text{s}\right){\text{+ 3O}}_{\text{2}}\left(\text{g}\right)$

$\begin{array}{rcl}& & ∆\mathrm{n}\text{= 3} \text{-} 0\\ & & \text{= 3}\\ & & \end{array}$

Hence, $K_p$ is not equal to $K_c$.

Subpart d)

For Reaction d: $\text{CuO}\left(\text{s}\right){\text{+H}}_{\text{2}}\left(\text{g}\right)\text{Cu}\left(\text{l}\right){\text{+H}}_{\text{2}}\text{O}\left(\text{g}\right)$

$$\begin{gathered} ∆\mathrm{n}=\text{1} \text{-} 1 \\ \text{=} 0 \end{gathered}$$

The value of $∆\mathrm{n}$ for this reaction isequal to zero but not for the other reactions. Hence, Reaction d)has the K_pequal to $K_c$.