An equilibrium mixture of SO2, O2, and SO3 at 1000 K contains the gases at the following concentrations: [SO2] = 3.77 10-3 mol/L, [O2] = 4.30 10-3 mol/L, and [SO3] = 4.13 10-3 mol/L. Calculate the equilibrium constant, K, for the following reaction.
2 SO2(g) + O2(g) ---> 2 SO3(g)
Thanks. I put them in the Keq equation and solved and got .279. What am I doing wrong?
Nevermind I got it:)
To calculate the equilibrium constant, K, for the given reaction, you need to consider the molar concentrations of the reactants and products at equilibrium.
The balanced equation is:
2 SO2(g) + O2(g) ---> 2 SO3(g)
Let's denote the initial concentrations of SO2, O2, and SO3 as [SO2]0, [O2]0, and [SO3]0, respectively. Similarly, the equilibrium concentrations will be denoted as [SO2]eq, [O2]eq, and [SO3]eq.
Given:
[SO2]0 = 3.77 × 10^(-3) mol/L
[O2]0 = 4.30 × 10^(-3) mol/L
[SO3]0 = 4.13 × 10^(-3) mol/L
To find the equilibrium concentrations, we need to determine the changes in the concentrations of the reactants and products. Here, since the stoichiometry of the reaction is 2:1:2, the changes are:
Δ[SO2] = -2x (two moles of SO2 are consumed per mole of O2)
Δ[O2] = -x (one mole of O2 is consumed per mole of O2)
Δ[SO3] = +2x (two moles of SO3 are produced per mole of O2)
After equilibrium is established:
[SO2]eq = [SO2]0 + Δ[SO2]
[O2]eq = [O2]0 + Δ[O2]
[SO3]eq = [SO3]0 + Δ[SO3]
Substituting the values:
[SO2]eq = 3.77 × 10^(-3) - 2x
[O2]eq = 4.30 × 10^(-3) - x
[SO3]eq = 4.13 × 10^(-3) + 2x
The equilibrium constant expression, K, is given by the ratio of the equilibrium concentrations of the products to the reactants, each raised to the power of their stoichiometric coefficients.
K = ([SO3]eq^2) / ([SO2]eq^2 × [O2]eq)
Substituting the equilibrium concentrations:
K = ((4.13 × 10^(-3) + 2x)^2) / ((3.77 × 10^(-3) - 2x)^2 × (4.30 × 10^(-3) - x))
To find the value of x, we can use an ice table or solve it numerically using an iterative method like trial-and-error or Newton-Raphson. After finding the value of x, substitute it into the expression for K to get the equilibrium constant.
It seems that you obtained a value of 0.279, but it might be incorrect due to a miscalculation or a mistake in the algebraic manipulation. Please double-check your calculations and make sure to substitute the correct equilibrium concentrations.