To determine the reaction quotient, [tex]\( Q \)[/tex], for the reaction [tex]\( H_2(g) + I_2(g) \Leftrightarrow 2 HI(g) \)[/tex], we need to use the formula for [tex]\( Q \)[/tex]:
[tex]\[ Q = \frac{[HI]^2}{[H_2][I_2]} \][/tex]
Given the concentrations:
- [tex]\([H_2] = 0.100 \, \text{M}\)[/tex]
- [tex]\([I_2] = 0.200 \, \text{M}\)[/tex]
- [tex]\([HI] = 3.50 \, \text{M}\)[/tex]
Now, plug these concentrations into the reaction quotient formula:
[tex]\[ Q = \frac{[HI]^2}{[H_2][I_2]} \][/tex]
Substitute the given values:
[tex]\[ Q = \frac{(3.50)^2}{(0.100)(0.200)} \][/tex]
Calculate the numerator (the concentration of [tex]\( HI \)[/tex] squared):
[tex]\[ (3.50)^2 = 12.25 \][/tex]
Then, calculate the denominator (the product of the concentrations of [tex]\( H_2 \)[/tex] and [tex]\( I_2 \)[/tex]):
[tex]\[ (0.100)(0.200) = 0.020 \][/tex]
Now, put these together to find [tex]\( Q \)[/tex]:
[tex]\[ Q = \frac{12.25}{0.020} \][/tex]
Finally, perform the division:
[tex]\[ Q = 612.5 \][/tex]
So, the reaction quotient [tex]\( Q \)[/tex] for this system is approximately [tex]\( 613 \)[/tex]. Hence, the correct answer is:
[tex]\[ \boxed{613} \][/tex]
