Let's analyze the given chemical equilibrium reaction and identify the correct equilibrium expression:
Reaction:
[tex]\[ \text{H}_2\text{(g)} + \text{I}_2\text{(g)} \longleftrightarrow 2 \text{HI(g)} \][/tex]
The general form of the equilibrium expression for a balanced chemical reaction:
[tex]\[ aA + bB \longleftrightarrow cC + dD \][/tex]
is given by:
[tex]\[ K = \frac{[C]^c [D]^d}{[A]^a [B]^b} \][/tex]
For the given reaction:
[tex]\[ \text{H}_2\text{(g)} + \text{I}_2\text{(g)} \longleftrightarrow 2 \text{HI(g)} \][/tex]
- [tex]\( \text{A} \)[/tex] is [tex]\( \text{H}_2 \)[/tex], [tex]\(a = 1\)[/tex]
- [tex]\( \text{B} \)[/tex] is [tex]\( \text{I}_2 \)[/tex], [tex]\(b = 1\)[/tex]
- [tex]\( \text{C} \)[/tex] is [tex]\( \text{HI} \)[/tex], [tex]\(c = 2\)[/tex] (since there are 2 moles of HI produced)
- There is no [tex]\( \text{D} \)[/tex]
Therefore, the equilibrium expression (K) would be:
[tex]\[ K = \frac{[\text{HI}]^2}{[\text{H}_2][\text{I}_2]} \][/tex]
Now let's look at the given options and determine which one matches this form:
1. [tex]\( K = \frac{[\text{HI}]}{[\text{H}_2][\text{I}_2]} \)[/tex]
2. [tex]\( K = \frac{|\text{HY}|}{[\text{I}_2] \text{floor}} \)[/tex]
3. [tex]\( K = \frac{[\text{HI}]^2}{[\text{I}_2][\text{H}_2]} \)[/tex]
4. [tex]\( K = \frac{\text{floor} \text{HI}}{\left[\text{I}_2 \mid \left[\text{H}_2\right]\right.} \)[/tex]
The correct equilibrium expression for the given reaction is therefore:
[tex]\[ K = \frac{[\text{HI}]^2}{[\text{H}_2][\text{I}_2]} \][/tex]
Thus, the answer is the third option:
[tex]\[ K = \frac{[\text{HI}]^2}{[\text{I}_2][\text{H}_2]} \][/tex]
The correct equilibrium expression for the reaction [tex]\( \text{H}_2\text{(g)} + \text{I}_2\text{(g)} \longleftrightarrow 2 \text{HI(g)} \)[/tex] is:
[tex]\[ K = \frac{[\text{HI}]^2}{[\text{H}_2][\text{I}_2]} \][/tex]
