To determine the reaction quotient, [tex]\( Q \)[/tex], for the given reaction:
[tex]\[ \text{H}_2(g) + \text{I}_2(g) \leftrightarrow 2 \text{HI}(g) \][/tex]
you need to use the formula for the reaction quotient. For the reaction [tex]\( \text{H}_2 + \text{I}_2 \leftrightarrow 2 \text{HI} \)[/tex], the expression for [tex]\( Q \)[/tex] is:
[tex]\[ Q = \frac{[\text{HI}]^2}{[\text{H}_2] \cdot [\text{I}_2]} \][/tex]
Given the concentrations:
[tex]\[ [\text{H}_2] = 0.100 \, M \][/tex]
[tex]\[ [\text{I}_2] = 0.200 \, M \][/tex]
[tex]\[ [\text{HI}] = 3.50 \, M \][/tex]
Let's substitute these values into the formula.
1. Calculate the numerator of the reaction quotient:
[tex]\[ [\text{HI}]^2 = (3.50 \, M)^2 \][/tex]
[tex]\[ [\text{HI}]^2 = 12.25 \, M^2 \][/tex]
2. Calculate the denominator of the reaction quotient:
[tex]\[ [\text{H}_2] \cdot [\text{I}_2] = 0.100 \, M \cdot 0.200 \, M \][/tex]
[tex]\[ [\text{H}_2] \cdot [\text{I}_2] = 0.0200 \, M^2 \][/tex]
3. Now, divide the numerator by the denominator to find [tex]\( Q \)[/tex]:
[tex]\[ Q = \frac{[\text{HI}]^2}{[\text{H}_2] \cdot [\text{I}_2]} = \frac{12.25 \, M^2}{0.0200 \, M^2} \][/tex]
[tex]\[ Q = 612.5 \][/tex]
Therefore, the reaction quotient [tex]\( Q \)[/tex] for this system is closest to:
[tex]\[ \boxed{613} \][/tex]
So the correct answer is 613.
