A 10.0 L flask at 500 K is filled with 0.30 mol of hydrogen and 0.30 mol of iodine. They react as indicated below. The equilibrium constant K_c = 45.0. What are the equilibrium concentrations of the three gases?
H₂(g) + I₂(g) 2HI(g)

Question

A 10.0 L flask at 500 K is filled with 0.30 mol of hydrogen and 0.30 mol of iodine. They react as indicated below. The equilibrium constant K_c = 45.0. What are the equilibrium concentrations of the three gases?
H₂(g) + I₂(g)

A 10.0 L flask at 500 K is filled with 0.30 mol of hydrogen and 0.30 mol of iodine. They react as indicated below. The equilibrium constant K<sub>c</sub> = 45.0. What are the equilibrium concentrations of the three gases? H<sub>2</sub>(g) + I<sub>2</sub>(g) 2HI(g) A) [H<sub>2</sub>] = [I<sub>2</sub>] = 0.023 M, [HI] = 0.046 M B) [H<sub>2</sub>] = [I<sub>2</sub>] =0.0069 M, [HI] = 0.046 M C) [H<sub>2</sub>] = [I<sub>2</sub>] = [HI] = 0.023 M D) [H<sub>2</sub>] = [I<sub>2</sub>] = 0.0069 M, [HI] = 0.023 M E) [H<sub>2</sub>]= [I<sub>2</sub>] = 0.23 M, [HI] = 0.46 M

2HI(g)

Quizplus · Accepted Answer

The balanced chemical equation is:
H2(g) + I2(g) ⇌ 2HI(g)
At equilibrium, the equilibrium constant (Kc) is given as 45.0, which means that the reaction strongly favors the product (HI). Let's define the initial concentrations and the changes (x) in the concentrations as follows:

[H2] = 0.30 mol/10.0 L = 0.030 M
[I2] = 0.30 mol/10.0 L = 0.030 M
[HI] = 0.00 M (since no HI is initially present)
Change: -2x (since 2 moles of HI are produced for every mole of H2 and I2 that react)

Using the equilibrium constant expression, we can write:
Kc = [HI]^2/([H2][I2])
45.0 = (2x)^2/((0.030-x)(0.030-x))
Solving for x using the quadratic formula gives x = 0.0069 M.

Therefore, at equilibrium:
[HI] = 2x = 0.0138 M
[H2] = 0.030 - x = 0.0231 M
[I2] = 0.030 - x = 0.0231 M

Note: Choice A is incorrect because it assumes that the equilibrium concentrations of H2 and I2 are equal, which is not the case since they have a stoichiometric ratio of 1:1 in the balanced equation. Choice C is incorrect because it only lists the equilibrium concentration of HI and ignores the other two gases. Choice D is the correct answer, but choice B is more precise since it gives the concentrations to four significant figures. Choice E is incorrect because it gives concentrations that are too high, which violates the law of mass action.

A 100 L Flask at 500 K Is Filled with 0