Consider the reaction: 2 SO2(g) + O2(g) ↔ 2 SO3(g). If, at equilibrium at a certain temperature, [SO2] = 1.50 M, [O2] = 0.120 M, and [SO3] = 1.25 M, what is the value of the equilibrium constant?
To find the value of the equilibrium constant (K), we need to use the concentrations of the reactants and products at equilibrium.
The balanced equation for the reaction is: 2 SO2(g) + O2(g) ↔ 2 SO3(g).
From the given information, we have:
[SO2] = 1.50 M
[O2] = 0.120 M
[SO3] = 1.25 M
However, to calculate K, we need to consider the stoichiometry of the balanced equation. In this case, the coefficients are 2 for SO2 and SO3, and 1 for O2.
The expression for the equilibrium constant (Kc) is given by:
Kc = ([SO3]^2) / ([SO2]^2 * [O2])
Substituting the given values:
Kc = (1.25^2) / (1.50^2 * 0.120)
Calculating the value:
Kc = 1.56 / 0.27
Kc ≈ 5.78
Therefore, the value of the equilibrium constant (K) is approximately 5.78.
To find the value of the equilibrium constant for the given reaction, you can use the concentrations of the reactants and products at equilibrium. In this case, you have the following concentrations:
[SO2] = 1.50 M
[O2] = 0.120 M
[SO3] = 1.25 M
The equilibrium constant (Kc) is defined as the ratio of the product concentrations to the reactant concentrations, each raised to the power of their respective stoichiometric coefficients. In this reaction, the stoichiometric coefficients are:
2 SO2(g) + O2(g) ↔ 2 SO3(g)
Hence, the equation for the equilibrium constant is:
Kc = ([SO3]²) / ([SO2]² × [O2])
Now we can substitute the values into the equation:
Kc = (1.25 M)² / ((1.50 M)² × (0.120 M))
Simplifying the equation gives:
Kc = 1.5625 M² / (2.25 M² × 0.120 M)
Further simplifying the expression gives:
Kc = 1.5625 / (2.25 × 0.120)
Finally, performing the calculation gives the value of the equilibrium constant:
Kc = 5.55 (rounded to two decimal places)
Therefore, the value of the equilibrium constant is 5.55 for the given reaction at the specified concentrations.