Consider the reaction [tex]H _2(g)+ I _2(g) \Leftrightarrow 2 HI ( g )[/tex]. What is the reaction quotient, [tex]Q[/tex], for this system when [tex][ H _2]=0.100 M[/tex], [tex][ I _2]=0.200 M[/tex], and [tex][ HI ]=3.50 M[/tex]?
Answer (2)
Write the expression for the reaction quotient: Q = [ H 2 ] [ I 2 ] [ H I ] 2 .
Substitute the given concentrations: Q = ( 0.100 ) ( 0.200 ) ( 3.50 ) 2 .
Calculate the value of Q: Q = 612.5 .
The reaction quotient, Q, for this system is 612.5 .
Explanation
Understanding the Problem We are given the reaction H 2 ( g ) + I 2 ( g ) ⇔ 2 H I ( g ) and the concentrations [ H 2 ] = 0.100 M , [ I 2 ] = 0.200 M , and [ H I ] = 3.50 M . We need to calculate the reaction quotient, Q , for this system.
Setting up the Calculation The reaction quotient, Q , is a measure of the relative amounts of products and reactants present in a reaction at any given time. For the given reaction, the expression for Q is: Q = [ H 2 ] [ I 2 ] [ H I ] 2 This formula tells us that we need to square the concentration of the product ( H I ) and divide it by the product of the concentrations of the reactants ( H 2 and I 2 ).
Calculating the Reaction Quotient Now, we substitute the given concentrations into the expression for Q :
Q = ( 0.100 ) ( 0.200 ) ( 3.50 ) 2 Q = 0.02 12.25 Q = 612.5 Therefore, the reaction quotient, Q , for this system is 612.5.
Final Answer The reaction quotient Q is 612.5.
Examples
Understanding the reaction quotient is crucial in various real-world applications, such as optimizing industrial chemical processes. For instance, in the production of ammonia via the Haber-Bosch process, maintaining the correct ratio of nitrogen and hydrogen is essential for maximizing yield and minimizing waste. By continuously monitoring and adjusting the concentrations of reactants and products, engineers can ensure that the reaction operates at its optimal point, leading to significant cost savings and increased efficiency. The reaction quotient helps to predict the direction a reversible reaction will shift to reach equilibrium, which is vital for controlling and improving chemical reactions in many industries.
The reaction quotient Q for the reaction H 2 ( g ) + I 2 ( g ) ⇔ 2 H I ( g ) with given concentrations is calculated as 612.5 . Using the expression Q = [ H 2 ] [ I 2 ] [ H I ] 2 and substituting the concentrations leads to this result. Thus, the final answer is 612.5 .
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