For the following reaction, Kc = 2.7×108 at 300 K.
3 H2(g) + N2(g) ⇌ 2 NH3(g)
In an experiment carried out at 300 K, the initial concentrations of H2(g) and N2(g) are each equal to 2.0 mol L−1 .
Which of the following statements about the equilibrium concentrations is correct? Note: In the statements below, << means "much less than".
a. [NH3] << [N2] ≈ [H2]
b. [H2] ≈ [N2] ≈ [NH3]
c. [H2] ≈ [N2] << [NH3]
d. [H2] << [N2] ≈ [NH3]
e. [N2] << [H2] < [NH3]
is it a?
To determine the equilibrium concentrations, we can use the given initial concentrations and the equilibrium constant. The equilibrium constant expression for the given reaction is:
Kc = [NH3]^2 / ([H2]^3 * [N2])
We are told that Kc = 2.7×10^8, and the initial concentrations of H2 and N2 are both 2.0 M. We can substitute these values into the equilibrium constant expression and solve for [NH3].
2.7×10^8 = [NH3]^2 / (2.0^3 * 2.0)
2.7×10^8 = [NH3]^2 / 16
[NH3]^2 = 2.7×10^8 * 16
[NH3]^2 = 4.32×10^9
[NH3] ≈ 6.573×10^4 M (taking the square root of both sides)
Looking at the equilibrium concentrations, we see that the concentration of NH3 is much smaller than the initial concentration of H2 and N2. Therefore, the correct statement is:
a. [NH3] << [N2] ≈ [H2]
To determine the equilibrium concentrations, we can use the equilibrium expression and the given value of Kc.
The equilibrium expression for the reaction is:
Kc = [NH3]^2 / ([H2]^3 * [N2])
Given that Kc = 2.7×10^8 and the initial concentrations of H2 and N2 are both 2.0 mol L^-1, we can substitute these values into the equilibrium expression:
2.7×10^8 = [NH3]^2 / (2.0^3 * 2.0)
Let's solve for [NH3]:
2.7×10^8 * (2.0^4) = [NH3]^2
2.7×10^8 * 16 = [NH3]^2
4.32×10^9 = [NH3]^2
Taking the square root of both sides:
[NH3] ≈ 6.57×10^4
Now, let's compare the equilibrium concentrations with the statements given:
a. [NH3] << [N2] ≈ [H2]
The equilibrium concentration of NH3 is not much less than N2 nor H2. This statement is incorrect.
b. [H2] ≈ [N2] ≈ [NH3]
The equilibrium concentrations of H2, N2, and NH3 are not equal. This statement is incorrect.
c. [H2] ≈ [N2] << [NH3]
The equilibrium concentrations of H2 and N2 are much less than NH3. This statement is incorrect.
d. [H2] << [N2] ≈ [NH3]
The equilibrium concentration of H2 is much less than N2 and approximately equal to NH3. This statement is closer to being correct.
e. [N2] << [H2] < [NH3]
The equilibrium concentration of N2 is much less than H2 and less than NH3. This statement is incorrect.
From the given statements, option d. [H2] << [N2] ≈ [NH3] is the most accurate statement. The concentration of H2 is much less than N2, and approximately equal to NH3 at equilibrium.