At 1495 K, KP=3.5x10^4 for the following reaction: H2(g)+Br2(g)=2HBr(g). Which substance(s), H2, Br2, and/or HBr, is/are present in the highest concentration at equilibrium? Explain answer please.

Answer 1

I would argue that this question doesn't specify enough about the gases at equilibrium to have one correct answer, and I'll construct a scenario where each gas is present in the highest concentration at equilibrium to demonstrate:

We know that the equilibrium constant (K_p) is 35,000 for this reaction. Based on the chemical equation, we can express the equilibrium constant as K_p = P_HBr² / (P_H2 * P_Br2). Plugging in our numerical value for K_p and multiplying both sides of the equation by the denominator of the right hand side, we get 35,000 * P_H2 * P_Br2 = P_HBr². We'll use this expression later to help with the explanations.

Scenario 1: HBr

Suppose that we started with equal amounts of H₂ and Br₂ as starting reactants (and thus, equal starting pressures if we assume the gases behave ideally). Because the stoichiometric ratio of the reactants required to form the product is 1:1, we would expect the same amount of each reactant to be lost by the time equilibrium is reached. So, the equilibrium pressures of the reactants would also be the same. As such, if we call the equilibrium pressure of both reactants P_R, we can simplify the equilibrium expression to get: 35,000 * P_R² = P_HBr² or P_HBr = 187 * P_R. In other words, in this scenario the equilibrium pressure of the product is 187 times the equilibrium pressure of each of the two reactants, and so the highest concentration substance is the product: HBr.

Scenario 2: H₂

Now suppose the starting amounts of H₂ and Br₂ are not equal. In fact, let's assume that there's 1 mole of Br₂ and 100 moles of H₂. Even if the reaction were to go to completion (meaning all the Br₂ gets converted to HBr), we would expect to have 99 moles of H₂ and 1 mole of HBr. Thus, regardless of what the equilibrium constant is, the highest concentration gas is H₂ simply because the system was flooded with it from the start.

* I did an ICE calculation to figure out the actual equilibrium amounts of the substances, I ended up getting 0.9999997 moles of HBr, 99.0000003 moles of H₂, and 0.0000003 moles of Br₂ *

Scenario 3: Br₂

Flipping the numbers in the H₂ scenario, we can get the same result but with Br₂. Start with 100 moles of Br₂ and 1 mole of H₂. No matter how far the reaction goes, the highest concentration substance will always be Br₂.

So, in conclusion, you would need to know more about the concentrations of the gases to solve this problem.

Relevant Side Note 1: There is a difference between the concentration of a gas and the pressure of that gas. I did my best to NOT draw attention to this difference during my answer above for the sake of being concise. However, I'd like to talk a little bit about that here. Let's start with the ideal gas law: PV = nRT. Concentration is defined as the amount of a substance per volume, and unless otherwise specified, the amount is measured in moles. We can solve the ideal gas law to find concentration as shown below:

PV = nRT

P = nRT/V

P/RT = n/V = C

So, C = P/RT or P = C * RT. We know R because it's the ideal gas constant, and T was given in the problem, and so we can calculate RT:

RT = (0.08314 L * bar / mol * K) * (1495 K) = 124.3 L * bar / mol

And so, to convert from a concentration in mol/L to a pressure in bar at 1495 K, we multiply by 124.3. To go from pressure in bar to concentration in mol/L, we divide by 124.3. The important thing, though, is that regardless of the temperature, the conversion from concentration to pressure or pressure to concentration is always just multiplying or dividing by a constant. If the pressure of some gas A is greater than the pressure of another gas B by a factor of 2 to 1, then the concentration of gas A will also be greater than the concentration of gas B by a factor of 2 to 1. Thus, if we can find out which gas has the highest pressure, we also know that it has the highest concentration, and vice versa. I take advantage of this fact heavily in my explanation for Scenario 1.

Relevant Side Note 2: If we have a mixture of multiple gases in the same containing volume, then gas with the highest amount of moles will also have the highest concentration. Suppose we have a binary mixture of gases A and B. If n_A > n_B, then n_A / V > n_B / V, and so C_A > C_B. Using the transitive property, you can apply this idea to mixtures with three or more gases as well. I take advantage of this fact in my explanation for Scenario 2, where I talk about the moles of the substances as opposed to their concentrations.