Q17.36P - Chemistry: Molecular Nature Of Matter And Change

Question

At ${\mathbf{100}}^{\mathbf{\circ }}\mathbf{C}\mathbf{,}\mathbf{ }{\mathbf{K}}_{\mathbf{p}}\mathbf{=}\mathbf{60}\mathbf{.}\mathbf{6}$for the reaction 

$\mathbf{2}{\mathbf{NOBr}}_{\mathbf{\left(}\mathbf{g}\mathbf{\right)}}\mathbf{\square }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{2}{\mathbf{NO}}_{\mathbf{\left(}\mathbf{g}\mathbf{\right)}}\mathbf{+}{\mathbf{Br}}_{\mathbf{2}\mathbf{\left(}\mathbf{g}\mathbf{\right)}}$

In a given experiment, 0.10 atm of each component is placed in a container. Is the system at equilibrium? If not, in which direction will the reaction proceed?

Step-by-Step Solution

Answer

The value of ${\mathrm{K}}_{\mathrm{p}}$for the reaction at 373 K is 60.6.

If the value of ${\mathrm{Q}}_{\mathrm{P}}$ is equal to ${\mathrm{K}}_{\mathrm{P}}$, the reaction will be at equilibrium. Here, ${\mathrm{Q}}_{\mathrm{P}}$ is less

than ${\mathrm{K}}_{\mathrm{P}}$.

Thus, the reaction is not at equilibrium. And so, the reaction shifts towards products.

Step 1: Is the system at equilibrium?

Rewrite the reaction as follows:

$2{\mathrm{NOBr}}_{\left(\mathrm{g}\right)}\square 2{\mathrm{NO}}_{\left(\mathrm{g}\right)}+{\mathrm{Br}}_{2\left(\mathrm{g}\right)}$

The expression for the reaction quotient is the ratio of partial pressure of products to partial pressure of reactants, with each partial pressure term raised to a power equal to its stoichiometric coefficient.

The expression for the reaction quotient ${\mathrm{Q}}_{\mathrm{P} }\mathrm{is} ,$

${\mathrm{Q}}_{\mathrm{P}}=\frac{{\mathrm{P}}^2{ }_{\mathrm{NO}}{\mathrm{P}}_{{\mathrm{Br}}_2}}{{\mathrm{P}}^2{ }_{\mathrm{NOBr}}}$

The partial pressure of each gas in the reaction is 0.10 atm. That is

$$\begin{gathered} {\mathrm{P}}_{\mathrm{NO}}={\mathrm{P}}_{{\mathrm{Br}}_2} \\ ={\mathrm{P}}_{\mathrm{NOBr}} \\ =0.10 \mathrm{atm} \end{gathered}$$

The value of  ${\mathrm{K}}_{\mathrm{P}}$  for the reaction at 373 K is 60.6.

If the value of ${\mathrm{Q}}_{\mathrm{P}}$ is equal to ${\mathrm{K}}_{\mathrm{P}}$ , the reaction will be at equilibrium. Here, ${\mathrm{Q}}_{\mathrm{P}}$ is less

than ${\mathrm{K}}_{\mathrm{P}}$ .

Thus, the reaction is not at equilibrium.

Step 2: Direction of reaction

If the value of ${\mathrm{Q}}_{\mathrm{P}}$ is less than ${\mathrm{K}}_{\mathrm{P}}$, the reaction proceeds toward the product’s side to

attain equilibrium. Here ${\mathrm{Q}}_{\mathrm{P}}$ is less than ${\mathrm{K}}_{\mathrm{P}}$.

Thus, the reaction shifts towards products.