6. Determine Keq for the reaction: 2 SO2 (g) + O2(g) 2 SO3(g), given that 1.00 x 10-2 moles of SO2 and 2.00 x 10-2 moles of O2 were placed in a 2.00L reaction chamber. The chamber contained 7.5 x 10-3 moles of SO3 when equilibrium was established at 727oC.
(PV = nRT, R = 0.0821L• atm/mol • K)
To determine the equilibrium constant (Keq) for the given reaction, we need to first calculate the concentrations of SO2, O2, and SO3 at equilibrium.
Given:
Initial moles of SO2 = 1.00 x 10^-2 moles
Initial moles of O2 = 2.00 x 10^-2 moles
Initial moles of SO3 = 7.5 x 10^-3 moles
Volume of the reaction chamber = 2.00 L
We can use the ideal gas law, PV = nRT, to calculate the concentrations.
1. Calculate the concentrations:
Concentration of SO2 = moles/volume = (1.00 x 10^-2 moles) / (2.00 L) = 5.00 x 10^-3 M
Concentration of O2 = moles/volume = (2.00 x 10^-2 moles) / (2.00 L) = 1.00 x 10^-2 M
Concentration of SO3 = moles/volume = (7.5 x 10^-3 moles) / (2.00 L) = 3.75 x 10^-3 M
2. Write the balanced equation:
2 SO2 (g) + O2(g) -> 2 SO3(g)
3. Calculate the equilibrium constant (Keq):
Keq = [SO3]^2 / ([SO2]^2 * [O2])
Substituting the given values:
Keq = (3.75 x 10^-3 M)^2 / ((5.00 x 10^-3 M)^2 * (1.00 x 10^-2 M))
Keq = 1.125 x 10^-8 / (2.50 x 10^-8 * 1.00 x 10^-4)
Keq = 1.125 x 10^-8 / 2.50 x 10^-12
Keq = 4.5 x 10^3
To determine the equilibrium constant (Keq) for the given reaction, we first need to understand the reaction equation:
2 SO2(g) + O2(g) ⇌ 2 SO3(g)
Keq is defined as the ratio of the products' raised to the power of their stoichiometric coefficients divided by the ratio of the reactants raised to the power of their stoichiometric coefficients. In this case, the stoichiometric coefficient for SO2 is 2, the stoichiometric coefficient for O2 is 1, and the stoichiometric coefficient for SO3 is also 2.
The formula for Keq is:
Keq = [SO3]^2 / ([SO2]^2 * [O2])
Here, [SO3] represents the concentration of SO3, [SO2] represents the concentration of SO2, and [O2] represents the concentration of O2 at equilibrium. We need to calculate the concentrations of each substance.
First, let's calculate the concentrations at equilibrium:
- For SO3, the given value is 7.5 x 10^(-3) moles, and the volume of the reaction chamber is 2.00 L. Therefore, the concentration of SO3 at equilibrium is: [SO3] = (7.5 x 10^(-3) moles) / (2.00 L) = 3.75 x 10^(-3) M.
- For SO2 and O2, we are given the moles of each substance but not their volumes. Since the reaction chamber has a volume of 2.00 L, we need to calculate the concentrations based on the moles and volume.
- For SO2, the given value is 1.00 x 10^(-2) moles. The concentration of SO2 is: [SO2] = (1.00 x 10^(-2) moles) / (2.00 L) = 5.00 x 10^(-3) M.
- For O2, the given value is 2.00 x 10^(-2) moles. The concentration of O2 is: [O2] = (2.00 x 10^(-2) moles) / (2.00 L) = 1.00 x 10^(-2) M.
Now, we have all the necessary values to calculate Keq:
Keq = (3.75 x 10^(-3) M)^2 / ((5.00 x 10^(-3) M)^2 * (1.00 x 10^(-2) M))
= 14.1
Therefore, the equilibrium constant (Keq) for the given reaction is 14.1.