A researcher put 10.0 moles of N2O into a 2-L container at some temperature where it decomposes according to the following: N2O = 2N2+ O2. At equilibrium 2.20 moles of N2O remain. Calculate the Kc for the reaction.
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To calculate the equilibrium constant Kc for the given reaction, you need to use the expression for the equilibrium constant, which relates the concentrations of reactants and products at equilibrium.
The balanced equation for the reaction is: N2O = 2N2 + O2
Given:
Initial moles of N2O (before decomposition) = 10.0 moles
Moles of N2O at equilibrium = 2.20 moles
First, you need to find the change in moles for N2O. Since N2O is decreasing, the change is calculated as the initial moles minus the moles at equilibrium:
Change in moles of N2O = Initial moles - Moles at equilibrium
= 10.0 moles - 2.20 moles
= 7.80 moles
Next, you need to determine the moles of N2 and O2 produced, taking into account the stoichiometry of the reaction. According to the balanced equation, for every 1 mole of N2O decomposed, 2 moles of N2 and 1 mole of O2 are produced.
Moles of N2 produced = 2 × moles of N2O decomposed
= 2 × 7.80 moles
= 15.6 moles
Moles of O2 produced = 1 × moles of N2O decomposed
= 1 × 7.80 moles
= 7.80 moles
Now, you can calculate the concentrations of N2, O2, and N2O at equilibrium by dividing the number of moles by the volume of the container:
Concentration of N2O = Moles of N2O at equilibrium / Volume of container
= 2.20 moles / 2 L
= 1.10 M
Concentration of N2 = Moles of N2 / Volume of container
= 15.6 moles / 2 L
= 7.80 M
Concentration of O2 = Moles of O2 / Volume of container
= 7.80 moles / 2 L
= 3.90 M
Lastly, you can calculate the equilibrium constant Kc using the expression:
Kc = [Concentration of N2]^2 × [Concentration of O2] / [Concentration of N2O]
= (7.80 M)^2 × (3.90 M) / (1.10 M)
= 86.522 M^2
Therefore, the equilibrium constant Kc for the given reaction is 86.522 M^2.