To calculate the equilibrium constant, Kc, for the given reaction, we need to use the stoichiometric coefficients of the balanced equation.
The given reaction is: N2O = 2N2 + O2
At the start, we have 10.0 moles of N2O in a 2-L container. After reaching equilibrium, 2.20 moles of N2O remain.
To find the concentrations of N2O, N2, and O2 at equilibrium, we need to convert the moles of each component into molar concentrations.
1) Concentration of N2O (initial):
Molar concentration = moles/volume = 10.0 moles/2 L = 5.0 M
2) Concentration of N2O (at equilibrium):
Molar concentration = moles/volume = 2.20 moles/2 L = 1.10 M
3) Concentration of N2 (at equilibrium):
We have 2N2 formed for every 1 mole of N2O that decomposes.
Since 2.20 moles of N2O remained, we can use the stoichiometric ratio to find the moles of N2 formed.
Moles of N2 = 2 * 2.20 moles = 4.40 moles
Molar concentration = moles/volume = 4.40 moles/2 L = 2.20 M
4) Concentration of O2 (at equilibrium):
We have 1 mole of O2 formed for every 1 mole of N2O that decomposes.
Since 2.20 moles of N2O remained, we can use the stoichiometric ratio to find the moles of O2 formed.
Moles of O2 = 1 * 2.20 moles = 2.20 moles
Molar concentration = moles/volume = 2.20 moles/2 L = 1.10 M
Now, we can write the expression for the equilibrium constant (Kc) using the molar concentrations:
Kc = [N2]^2 * [O2] / [N2O]^2
= (2.20)^2 * (1.10) / (1.10)^2
= 2.42
Therefore, the value of Kc for the given reaction is approximately 2.42.