For the reaction: N₂(g)+ 2 O₂(g)⇌ 2 NO₂(g),K_c = 8.3 × 10^-10 at 25°C.What is the concentration of N₂ gas at equilibrium when the concentration of NO₂ is twice the concentration of O₂ gas?

Question

Quizplus · Accepted Answer

Let's assume that the initial concentration of OS1U1B12S1U1B0 is x M. Then, the initial concentration of NOS1U1B12S1U1B0 is 2x M. The initial concentration of NS1U1B12S1U1B0 is 0 M (since it is not given).

At equilibrium, let's assume that the concentration of NS1U1B12S1U1B0 is y M. Then, the concentration of OS1U1B12S1U1B0 becomes (x - 2y) M and the concentration of NOS1U1B12S1U1B0 becomes (2x + y) M.

We can now use the equilibrium constant expression to find the concentration of NS1U1B12S1U1B0:

KS1U1B1cS1U1B0 = [NOS1U1B12S1U1B0]2 / ([NS1U1B12S1U1B0][OS1U1B12S1U1B0]2)
8.3 × 10S1U1P1-10S1S1P0 = (2x + y)2 / (y(x - 2y)2)

Simplifying this expression and rearranging, we get:

y3 - 4xy2 + 4x2y - 8.3 × 10S1U1P1-10S1S1P0yx2 = 0

This is a cubic equation in y, and we can solve it using the cubic formula or numerical methods. However, in this case, the answer choices are all in some multiple of 10S1U1P19S1S1P0 M, which suggests that the problem can be solved using estimates.

Since the equilibrium constant is very small (10S1U1P1-10S1S1P0), we can assume that the concentration of NS1U1B12S1U1B0 is very small compared to the concentrations of OS1U1B12S1U1B0 and NOS1U1B12S1U1B0. This means that we can approximate:

y << x
y << 2x

With these approximations, we can simplify the cubic equation to:

- 8.3 × 10S1U1P1-10S1S1P0x2 ≈ 0

Solving for x, we get:

x ≈ √(8.3 × 10S1U1P1-10S1S1P0) ≈ 9.12 × 10S1U1P-6S1S1P0 M

Using this value of x, we can find y:

KS1U1B1cS1U1B0 = (2x + y)2 / (y(x - 2y)2)
8.3 × 10S1U1P1-10S1S1P0 ≈ (2x)2 / (y(x - 2y)2)
y(x - 2y)2 ≈ (2x)2 / 8.3 × 10S1U1P1-10S1S1P0
y(x2 - 4xy + 4y2) ≈ (2x)2 / 8.3 × 10S1U1P1-10S1S1P0
y(16x2) ≈ (2x)2 / 8.3 × 10S1U1P1-10S1S1P0
y ≈ (2x)2 / (16x2 × 8.3 × 10S1U1P1-10S1S1P0)
y ≈ 4.8 × 10S1U1P19S1S1P0 M

Therefore, the answer is D: 4.8 × 10S1U1P19S1S1P0 M.

For the Reaction: N2(g)+ 2 O2(g)⇌ 2 NO2(g),Kc = 8

For the Reaction: N₂(g)+ 2 O₂(g)⇌ 2 NO₂(g),K_c = 8