Consider the reaction: 2CO2(g)=2CO(g) + O2(g). A reaction mixture in a 5.0 L flask at a certain temperature. At equilibrium there are 85 g of CO2(g), 1.20 g of CO, and 0.688 g of O2(g). Calculate Kc.
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To calculate the equilibrium constant (Kc) for this reaction, we need to determine the concentration of each species involved in the reaction.
1. Calculate the number of moles for each substance.
Given:
Mass of CO2(g) = 85 g
Molar mass of CO2 = 44.01 g/mol
Number of moles of CO2 = Mass of CO2 / Molar mass of CO2
= 85 g / 44.01 g/mol
≈ 1.931 mol
Given:
Mass of CO(g) = 1.20 g
Molar mass of CO = 28.01 g/mol
Number of moles of CO = Mass of CO / Molar mass of CO
= 1.20 g / 28.01 g/mol
≈ 0.043 mol
Given:
Mass of O2(g) = 0.688 g
Molar mass of O2 = 32.00 g/mol
Number of moles of O2 = Mass of O2 / Molar mass of O2
= 0.688 g / 32.00 g/mol
≈ 0.022 mol
2. Determine the concentration of each species.
Since we know the reaction takes place in a 5.0 L flask, the concentration of each substance can be calculated by dividing the number of moles of that substance by the volume of the flask.
Concentration of CO2(g) = Number of moles of CO2 / Volume of flask
= 1.931 mol / 5.0 L
≈ 0.386 M
Concentration of CO(g) = Number of moles of CO / Volume of flask
= 0.043 mol / 5.0 L
≈ 0.0086 M
Concentration of O2(g) = Number of moles of O2 / Volume of flask
= 0.022 mol / 5.0 L
≈ 0.0044 M
3. Calculate the equilibrium constant (Kc).
The balanced equation for the reaction is:
2CO2(g) = 2CO(g) + O2(g)
According to the stoichiometry of the reaction, the equilibrium constant (Kc) expression can be written as:
Kc = ([CO(g)]^2 * [O2(g)]) / [CO2(g)]^2
Substituting the concentration values we calculated earlier:
Kc = ([0.0086 M]^2 * [0.0044 M]) / [0.386 M]^2
Simplifying the expression:
Kc ≈ 0.000671
Therefore, the equilibrium constant (Kc) for the given reaction is approximately 0.000671.