- Define the reaction quotient formula: \(Q = \frac{[HI]^2}{[H_2] \times [I_2]}\).
- Substitute the given concentrations into the formula: \(Q = \frac{(3.50)^2}{0.100 \times 0.200}\).
- Calculate the result: \(Q = \frac{12.25}{0.020} = 612.5\).
- Round the result to the nearest integer to select the best option, which is \(\boxed{613}\).
Explanation
- Analysis of the Reaction Quotient Expression
The problem asks for the reaction quotient, \(Q\), of the chemical system \(H_2(g) + I_2(g) \Leftrightarrow 2HI(g)\) given the specific molar concentrations \([H_2] = 0.100 \, M\), \([I_2] = 0.200 \, M\), and \([HI] = 3.50 \, M\). The reaction quotient \(Q\) is calculated using the ratio of the products of the concentrations of the reaction products to the reactants, each raised to the power of its stoichiometric coefficient in the balanced chemical equation. For this reaction, the expression is:
\[Q = \frac{[HI]^2}{[H_2] \times [I_2]}\]
- Calculation of the Reaction Quotient
To determine the value of \(Q\), we substitute the given molar concentrations into our expression:
\[Q = \frac{(3.50)^2}{(0.100) \times (0.200)}\]
First, calculate the numerator: \((3.50)^2 = 12.25\).
Next, calculate the denominator: \(0.100 \times 0.200 = 0.020\).
Finally, perform the division:
\[Q = \frac{12.25}{0.020} = 612.5\]
- Comparison and Conclusion
Comparing our calculated value of \(612.5\) to the provided options:
A\(175\)
B\(87.5\)
C\(613\)
D\(350\)
The calculated value of \(612.5\) is closest to option (c). Given standard practices for such problems, we round the result to the nearest integer, which gives us \(613\). Therefore, the correct choice is (c).
Examples
The reaction quotient \(Q\) is a crucial tool in chemistry for predicting the direction of a chemical reaction. By comparing \(Q\) to the equilibrium constant \(K\), chemists can determine if a reaction is at equilibrium, moving toward the products, or shifting back toward the reactants. For example, if a chemical plant produces hydrogen iodide, calculating \(Q\) helps engineers adjust temperature or reactant flow to maintain the desired production efficiency.