Consider the reaction:
A(g)⇌2B(g)
Find the equilibrium partial pressures of A and B for each of the different values of Kp. Assume that the initial partial pressure of B in each case is 1.0 atm and that the initial partial pressure of A is 0.0 atm. Make any appropriate simplifying assumptions.
A) Kp= 3.0
B)Kp= 1.2×10^−4
C) Kp= 1.0×10^5
I know this is posted with different numbers on this site and that it is a quadratic but I can't get the right answer. Please help.
To solve this problem, we can start by writing the equilibrium expression for the given reaction:
Kp = (P_B)^2 / (P_A)
where Kp is the equilibrium constant, P_B is the partial pressure of B, and P_A is the partial pressure of A.
Now, let's solve for the equilibrium partial pressures of A and B for each case:
A) Kp = 3.0
Given: initial P_B = 1.0 atm, initial P_A = 0.0 atm
Substituting the given values into the equilibrium expression, we get:
3.0 = (1.0)^2 / P_A
Simplifying the equation, we find:
3.0 * P_A = 1.0
P_A = 1.0 / 3.0
P_A ≈ 0.333 atm
Since the initial partial pressure of A is 0.0 atm, and the reaction favors the formation of B, we can assume that the equilibrium partial pressure of B is nearly equal to the initial partial pressure of B:
P_B ≈ 1.0 atm
Therefore, the equilibrium partial pressures are approximately:
P_A ≈ 0.333 atm
P_B ≈ 1.0 atm
B) Kp = 1.2 × 10^(-4)
Given: initial P_B = 1.0 atm, initial P_A = 0.0 atm
Substituting the given values into the equilibrium expression, we get:
1.2 × 10^(-4) = (1.0)^2 / P_A
Simplifying the equation, we find:
1.2 × 10^(-4) * P_A = 1.0
P_A = 1.0 / (1.2 × 10^(-4))
P_A ≈ 8.33 × 10^3 atm
Since the initial partial pressure of A is 0.0 atm, and the reaction favors the formation of B, we can assume that the equilibrium partial pressure of B is nearly equal to the initial partial pressure of B:
P_B ≈ 1.0 atm
Therefore, the equilibrium partial pressures are approximately:
P_A ≈ 8.33 × 10^3 atm
P_B ≈ 1.0 atm
C) Kp = 1.0 × 10^(5)
Given: initial P_B = 1.0 atm, initial P_A = 0.0 atm
Substituting the given values into the equilibrium expression, we get:
1.0 × 10^(5) = (1.0)^2 / P_A
Simplifying the equation, we find:
1.0 × 10^(5) * P_A = 1.0
P_A = 1.0 / (1.0 × 10^(5))
P_A = 1.0 × 10^(-5) atm
Since the initial partial pressure of A is 0.0 atm, and the reaction favors the formation of B, we can assume that the equilibrium partial pressure of B is nearly equal to the initial partial pressure of B:
P_B ≈ 1.0 atm
Therefore, the equilibrium partial pressures are approximately:
P_A ≈ 1.0 × 10^(-5) atm
P_B ≈ 1.0 atm
In summary, the equilibrium partial pressures of A and B for each given value of Kp are:
A) Kp = 3.0: P_A ≈ 0.333 atm, P_B ≈ 1.0 atm
B) Kp = 1.2 × 10^(-4): P_A ≈ 8.33 × 10^3 atm, P_B ≈ 1.0 atm
C) Kp = 1.0 × 10^(5): P_A ≈ 1.0 × 10^(-5) atm, P_B ≈ 1.0 atm
To determine the equilibrium partial pressures of A and B for each value of Kp, we will assume that the initial partial pressure of B is 1.0 atm, and the initial partial pressure of A is 0.0 atm. We'll use the given reaction:
A(g) ⇌ 2B(g)
Let's assign variables to the equilibrium partial pressures:
P(A) = the partial pressure of A at equilibrium
P(B) = the partial pressure of B at equilibrium
Now, let's analyze each case separately:
A) Kp = 3.0
According to the given reaction, Kp = (P(B))^2 / P(A)
Since the initial partial pressure of A is 0.0 atm, we have:
3.0 = (1.0)^2 / P(A)
P(A) = (1.0)^2 / 3.0 = 0.333 atm
Therefore, at equilibrium, the partial pressures are:
P(A) = 0.333 atm
P(B) = 1.0 atm
B) Kp = 1.2 × 10^(-4)
Using the same approach as before:
1.2 × 10^(-4) = (1.0)^2 / P(A)
P(A) = (1.0)^2 / (1.2 × 10^(-4)) = 8.33 × 10^3 atm (approximately)
Therefore, at equilibrium, the partial pressures are:
P(A) = 8.33 × 10^3 atm (approximately)
P(B) = 1.0 atm
C) Kp = 1.0 × 10^5
Once again, using the same approach:
1.0 × 10^5 = (1.0)^2 / P(A)
P(A) = (1.0)^2 / (1.0 × 10^5) = 1.0 × 10^(-5) atm
Therefore, at equilibrium, the partial pressures are:
P(A) = 1.0 × 10^(-5) atm
P(B) = 1.0 atm
Remember to always double-check your calculations, as errors can occur during the process. If you're not achieving the correct answer, it's possible that there may be a calculation mistake.