To determine the equilibrium constant (Kc) for the reaction A + 2B ⇌ 2C and assess if the reaction is proceeding forward, we need to analyze the initial amounts of each substance and compare them to the equilibrium concentrations.
Setting Up the Problem
We start with the initial amounts of A, B, and C provided:
- Initial moles of A = 2 moles
- Initial moles of B = 3 moles
- Initial moles of C = 2 moles
Since the reaction occurs in a 2 L flask, we can calculate the initial concentrations:
- [A] = 2 moles / 2 L = 1 mol/L
- [B] = 3 moles / 2 L = 1.5 mol/L
- [C] = 2 moles / 2 L = 1 mol/L
Equilibrium Concentrations
It's given that at equilibrium, the concentration of C is 0.5 mol/L. From the balanced equation, we can see that for every 2 moles of C produced, 1 mole of A is consumed and 2 moles of B are consumed. If we denote the change in concentration of C from the initial to equilibrium as x, we can express this change as follows:
- [C] changes from 1 mol/L to 0.5 mol/L (decrease of 0.5 mol/L)
- Since 2 moles of C are produced for every mole of A consumed, the change in concentration of A will be half of that of C: 0.5 mol/L decrease in A.
- For B, since 2 moles are consumed for every 2 moles of C produced, the change will also be 0.5 mol/L decrease in B.
Calculating Changes
Now, let's calculate the equilibrium concentrations:
- Equilibrium [A] = 1 mol/L - 0.25 mol/L = 0.75 mol/L
- Equilibrium [B] = 1.5 mol/L - 0.5 mol/L = 1 mol/L
- Equilibrium [C] = 0.5 mol/L (given)
Finding Kc
The equilibrium constant Kc is determined using the equilibrium concentrations:
Kc = [C]^2 / ([A][B]^2)
Now substituting the equilibrium concentrations:
- Kc = (0.5)^2 / (0.75)(1)^2
- Kc = 0.25 / 0.75
- Kc = 1/3 or approximately 0.333.
Determining Reaction Direction
To evaluate whether the reaction is moving forward or backward, we can calculate the reaction quotient (Q) using the initial concentrations:
Q = [C]^2 / ([A][B]^2)
Using the initial concentrations:
- Q = (1)^2 / (1)(1.5)^2 = 1 / 2.25 = 0.444.
Since Q (0.444) is less than Kc (0.333), this indicates that the reaction will proceed in the forward direction to reach equilibrium.
Summary
In summary, we calculated the equilibrium constant Kc to be approximately 0.333 and found out that the reaction is moving forward because the reaction quotient Q is lower than Kc. This means that more products will form until the system reaches equilibrium.
