Given the reaction:
[tex]\[ 2 \text{NO} (g) + \text{Br}_2 (g) \rightleftharpoons 2 \text{NOBr} (g) \][/tex]
and the equilibrium concentrations:
[tex]\[ [\text{NO}] = 0.089 \, M \][/tex]
[tex]\[ [\text{Br}_2] = 0.070 \, M \][/tex]
[tex]\[ [\text{NOBr}] = 0.183 \, M \][/tex]
We need to determine:
(a) The value of the equilibrium constant, [tex]\( K_{eq} \)[/tex].
(b) The position of the equilibrium.
### Step by Step Solution:
#### (a) Calculating the Equilibrium Constant, [tex]\( K_{eq} \)[/tex]:
1. Write the expression for the equilibrium constant, [tex]\( K_{eq} \)[/tex], for the given reaction:
[tex]\[ 2 \text{NO} (g) + \text{Br}_2 (g) \rightleftharpoons 2 \text{NOBr} (g) \][/tex]
The equilibrium constant expression is:
[tex]\[ K_{eq} = \frac{[\text{NOBr}]^2}{[\text{NO}]^2 [\text{Br}_2]} \][/tex]
2. Substitute the equilibrium concentrations into the expression:
[tex]\[ [\text{NOBr}] = 0.183 \, M \][/tex]
[tex]\[ [\text{NO}] = 0.089 \, M \][/tex]
[tex]\[ [\text{Br}_2] = 0.070 \, M \][/tex]
3. Calculate the equilibrium constant:
[tex]\[ K_{eq} = \frac{(0.183)^2}{(0.089)^2 \times 0.070} \][/tex]
After performing the calculations, we find:
[tex]\[ K_{eq} \approx 60.398 \][/tex]
Thus,
[tex]\[ K_{eq} = 60.398 \][/tex]
#### (b) Determining the Position of the Equilibrium:
To determine the position of the equilibrium, we compare the value of [tex]\( K_{eq} \)[/tex] to 1:
- If [tex]\( K_{eq} > 1 \)[/tex], the reaction favors the formation of products.
- If [tex]\( K_{eq} < 1 \)[/tex], the reaction favors the formation of reactants.
- If [tex]\( K_{eq} \approx 1 \)[/tex], the reaction has no strong preference for either reactants or products.
Given that [tex]\( K_{eq} = 60.398 \)[/tex]:
Since [tex]\( K_{eq} \)[/tex] is significantly greater than 1, the reaction favors the formation of products.
Therefore, the position of the equilibrium is such that the reaction favors the products.
### To Summarize:
(a) The value of the equilibrium constant is:
[tex]\[ \boxed{60.398} \][/tex]
(b) The reaction is (select):
[tex]\[ \boxed{\text{products}} \][/tex]
