A 50.0 L reaction vessel contains 1.00 moles of nitrogen gas, 3.00 moles of hydrogen gas and 0.500 moles of ammonia gas. Explain how this reaction will proceed if Kc=0.500 at 400 degrees C.
N2(g) + 3H2(g) ⇌ 2NH3(g)
To determine how the reaction will proceed, we need to compare the reaction quotient Qc to the equilibrium constant Kc. The reaction quotient is calculated the same way as the equilibrium constant, but it is calculated using the concentrations of the reactants and products at a specific point in time, rather than at equilibrium.
In this case, the reaction is N2(g) + 3H2(g) ⇌ 2NH3(g), and the equilibrium constant Kc is given as 0.500 at 400 degrees C.
The reaction quotient Qc can be calculated by dividing the concentration of NH3 raised to the power of its stoichiometric coefficient by the product of the concentrations of N2 and H2 raised to the power of their corresponding stoichiometric coefficients.
Qc = [NH3]^2 / ([N2] * [H2]^3)
Given that the reaction vessel initially contains 1.00 moles of N2, 3.00 moles of H2, and 0.500 moles of NH3, we can convert these values to concentrations by dividing by the volume of the reaction vessel, which is 50.0 L.
[N2] = 1.00 moles / 50.0 L
[H2] = 3.00 moles / 50.0 L
[NH3] = 0.500 moles / 50.0 L
Now we can substitute these values into the Qc expression:
Qc = (0.500/50.0)^2 / [(1.00/50.0) * (3.00/50.0)^3]
Simplifying further, we get:
Qc = (0.0100)^2 / [(0.0200) * (0.216)]
Calculating this, we find:
Qc ≈ 4.6296
Comparing Qc to Kc, we see that Qc (4.6296) is greater than Kc (0.500). According to Le Chatelier's principle, when Qc is greater than Kc, the reaction will shift toward the reactants to reach equilibrium. In this case, the reaction will proceed in the reverse direction, converting some of the ammonia gas back into nitrogen and hydrogen gas until the reaction reaches equilibrium.
To determine how the reaction will proceed, we need to compare the reaction quotient, Qc, to the equilibrium constant, Kc.
1. Calculate the concentration of nitrogen gas (N2), hydrogen gas (H2), and ammonia gas (NH3) in terms of moles per liter (mol/L).
Nitrogen gas:
Concentration of N2 = 1.00 moles / 50.0 L = 0.020 mol/L
Hydrogen gas:
Concentration of H2 = 3.00 moles / 50.0 L = 0.060 mol/L
Ammonia gas:
Concentration of NH3 = 0.500 moles / 50.0 L = 0.010 mol/L
2. Write down the expression for the reaction quotient, Qc, using the molar concentrations.
Qc = [NH3]^2 / ([N2] * [H2]^3)
3. Substitute the calculated concentrations into the reaction quotient equation to find Qc.
Qc = (0.010 mol/L)^2 / (0.020 mol/L * (0.060 mol/L)^3)
= 0.0001 mol^2/L^2 / (0.00672 mol^4/L^4)
= 14.88 L^2/mol^2
4. Compare Qc to Kc.
If Qc > Kc, the reaction will proceed in the reverse direction (from right to left) to reach equilibrium.
If Qc < Kc, the reaction will proceed in the forward direction (from left to right) to reach equilibrium.
If Qc = Kc, the reaction is already at equilibrium.
In this case, since Qc (14.88 L^2/mol^2) is greater than Kc (0.500 L^2/mol^2), the reaction will proceed in the reverse direction (from right to left) to reach equilibrium. This means more reactants (NH3) will be formed until the concentrations reach a new equilibrium.