At 2000°C, 5.0×10-3 mol CO2 is introduced into a 1.0 L container and the following reaction comes to equilibrium:
2CO2(g) <-> 2CO(g) + O2(g)
Kc = 6.4×10-7
a. Calculate the equilibrium concentrations of CO and O2.
b. What fraction of the CO2 is decomposed at equilibrium? (37% or 6.3%)
Set up an ICE chart, substitute into the Kc expression, and solve for the concns. Post your work if you get stuck.
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A.
1.6×±0^-4 M
B.
6.3%
C.
3.2×±0^-4 M
To calculate the equilibrium concentrations of CO and O2, we need to set up an ICE (Initial, Change, Equilibrium) table and use the given information.
a. Calculating the equilibrium concentrations of CO and O2:
1. Start by writing down the balanced equation and the initial concentration of CO2:
2CO2(g) <-> 2CO(g) + O2(g)
Initial: CO2: 5.0×10^-3 mol
2. Define the change and equilibrium concentrations based on the stoichiometry of the reaction and the given equilibrium constant (Kc):
Change: -2x (for CO2)
+2x (for CO and O2)
Equilibrium: CO2: 5.0×10^-3 - 2x
CO: 2x
O2: 2x
3. Use the given equilibrium constant (Kc) to set up an expression relating the products and reactant concentrations in terms of x:
Kc = [CO]^2 * [O2] / [CO2]^2
6.4×10^-7 = (2x)^2 * (2x) / (5.0×10^-3 - 2x)^2
4. Solve the equation to find the value of x. This can be done by using quadratic equation or solving it iteratively with a calculator or software.
Using a calculator or software to solve the equation, x is approximately 3.648×10^-4.
5. Substitute the value of x into the equilibrium expressions to find the equilibrium concentrations:
CO: 2x = 2 * (3.648×10^-4) = 7.296×10^-4 mol/L
O2: 2x = 2 * (3.648×10^-4) = 7.296×10^-4 mol/L
Therefore, the equilibrium concentrations of CO and O2 are approximately 7.296×10^-4 mol/L.
b. To determine the fraction of CO2 decomposed at equilibrium, we need to compare the change in concentration of CO2 to the initial concentration.
1. Calculate the change in concentration of CO2:
Change in CO2 = Initial CO2 - Equilibrium CO2
= 5.0×10^-3 mol - (5.0×10^-3 - 2x)
= 5.0×10^-3 - (5.0×10^-3 - 2(3.648×10^-4))
= 5.0×10^-3 - (5.0×10^-3 - 7.296×10^-4)
= 7.296×10^-4 mol
2. Calculate the fraction of CO2 decomposed:
Fraction decomposed = Change in CO2 / Initial CO2
= (7.296×10^-4 mol) / (5.0×10^-3 mol)
≈ 0.146
Convert the fraction to a percentage:
Percentage decomposed = Fraction decomposed * 100
≈ 14.6%
Therefore, the fraction of CO2 decomposed at equilibrium is approximately 14.6%.