Consider the reaction below.
[tex]H_2(g)+CO_2(g) \rightarrow H_2 O(g)+CO(g)[/tex]
At equilibrium at 600 K, the following are true.
[tex]\begin{array}{l}
{\left[CO_2\right]=9.5 \times 10^{-4} M} \
{\left[H_2\right]=4.5 \times 10^{-2} M} \
{\left[H_2 O\right]=4.6 \times 10^{-3} M} \
{[CO]=4.6 \times 10^{-3} M}
\end{array}[/tex]
What is the value of the equilibrium constant for this reaction in correct scientific notation?
A. [tex]4.9 \times 10^{-3}[/tex]
B. [tex]4.9 \times 10^{-2}[/tex]
C. [tex]4.9 \times 10^{-1}[/tex]
Answer (2)
Define the equilibrium constant expression: K = [ H 2 ] [ C O 2 ] [ H 2 O ] [ CO ] .
Substitute the given concentrations: K = ( 4.5 × 1 0 − 2 ) ( 9.5 × 1 0 − 4 ) ( 4.6 × 1 0 − 3 ) ( 4.6 × 1 0 − 3 ) .
Calculate the value of K: K ≈ 0.49497 .
Express K in scientific notation: 4.9 × 1 0 − 1 .
Explanation
Problem Setup and Given Data The problem provides the equilibrium concentrations for the reaction:
H 2 ( g ) + C O 2 ( g ) ⇌ H 2 O ( g ) + CO ( g )
We are given:
[ C O 2 ] = 9.5 × 1 0 − 4 M
[ H 2 ] = 4.5 × 1 0 − 2 M
[ H 2 O ] = 4.6 × 1 0 − 3 M
[ CO ] = 4.6 × 1 0 − 3 M
Our goal is to calculate the equilibrium constant, K , for this reaction and express it in scientific notation.
Defining the Equilibrium Constant The equilibrium constant, K , is defined as the ratio of the product of the concentrations of the products to the product of the concentrations of the reactants, each raised to the power of their stoichiometric coefficients. For the given reaction, the expression for K is:
K = [ H 2 ] [ C O 2 ] [ H 2 O ] [ CO ]
Now, we will substitute the given equilibrium concentrations into this expression.
Calculating K Substituting the given concentrations into the expression for K , we get:
K = ( 4.5 × 1 0 − 2 M ) ( 9.5 × 1 0 − 4 M ) ( 4.6 × 1 0 − 3 M ) ( 4.6 × 1 0 − 3 M )
Now, we perform the calculation:
K = ( 4.5 × 1 0 − 2 ) ( 9.5 × 1 0 − 4 ) ( 4.6 × 1 0 − 3 ) 2 = 4.275 × 1 0 − 5 2.116 × 1 0 − 5 ≈ 0.49497
Expressing K in Scientific Notation To express the value of K in correct scientific notation, we write it as:
K ≈ 0.49497 = 4.9497 × 1 0 − 1
Rounding to two significant figures, we get:
K ≈ 4.9 × 1 0 − 1
Final Answer The equilibrium constant for the reaction is approximately 4.9 × 1 0 − 1 .
Examples
Understanding equilibrium constants is crucial in many real-world applications. For instance, in the Haber-Bosch process, which synthesizes ammonia for fertilizers, controlling the equilibrium is essential to maximize ammonia production. Similarly, in environmental science, equilibrium constants help predict the distribution of pollutants in different environmental compartments, such as air, water, and soil. By manipulating reaction conditions, such as temperature and pressure, we can shift the equilibrium to favor desired outcomes, whether it's producing more of a valuable chemical or reducing harmful emissions. This concept is also vital in drug development, where understanding equilibrium helps optimize drug efficacy and minimize side effects.
The equilibrium constant, K , for the reaction H 2 ( g ) + C O 2 ( g ) ⇌ H 2 O ( g ) + CO ( g ) is calculated using the concentration of the reactants and products at equilibrium. After substituting the values into the equilibrium expression and calculating, we find that K ≈ 4.9 × 1 0 − 1 . Thus, the correct answer is option C.
;
