Video: Identifying the Possible Equilibrium Constant for a General Equilibrium from the Equation Without State Symbols, When the State of One Component Is Given

What could the equilibrium constant be for the following reaction if Y is a liquid? aW + bX ⇌ cY + dZ


Video Transcript

What could the equilibrium constant be for the following reaction if Y is a liquid?

And we’ve been given a generic reaction involving W and X transforming into Y and Z. An equilibrium constant is usually given the symbol K. For equilibrium like this, where we have components all in solution, we can calculate the value of the equilibrium constant using the equilibrium expression. We construct the equilibrium expression by first taking the concentrations of the products and raising them to the power of their stochiometric coefficients and multiplying them all together. We then divide that term by the equivalent for the reactants.

The value for K is dictated by the temperature and the nature of the equilibrium itself. No matter how we change the conditions, like pressure, volume, or various concentrations, we’ll always be able to calculate the same value for K. This of course assumes that we’re only ever measuring concentration when the system has reached equilibrium.

Our job is to look at the equation we’ve been given and see which of the expressions is consistent with the equation. Beyond the equation itself, the only piece of information we’ve been given is that Y is a liquid. The one thing we know about equilibrium expressions is that we ignore liquids and solids. The reasons for this are beyond the scope of this video. But they do boil down to the fact that changing the amounts of liquid and solid don’t change the rate of reactions as much as changing the concentration of gases and solutes.

So let’s return to the equation. We have three components for which we don’t know the phase. They could be gaseous. They could be aqueous. They could be solid. Or indeed they could be a liquid. We just don’t know. Rather than working through all the possible combinations, in this case, let’s have a look at the five options given and see which ones make sense.

The first thing we can do is eliminate any option that contains the concentration of Y. The first three options all contain a concentration of Y term. So they can’t be correct expressions for the equilibrium constant. Instead, let’s have a look at the fourth option. The term for Z here appears on the top, as it should, because it’s a product. And it’s raised to the power of d, which is its stochiometric coefficient. The term for W appears on the bottom, as it should as a reactant. And it’s raised to the power of a. And the term for X is also as it should be.

We’re looking for an equilibrium expression that’s consistent with the equation if Y is a liquid. And we’ve definitely found an answer. If W, X, and Z are all solutes or gases, this would definitely be a valid equilibrium expression. But let’s have a look at the last option just in case.

The expression for W appears on the top, which is the wrong way round. It’s a reactant, not a product. So it should appear on the bottom. And it’s paired with X, which should also be in the denominator. The term for Z is on the bottom when it should be on the top. So this entire expression is the wrong way up. Meaning that, of the five equilibrium expressions we’ve been given. The only one that could be the equilibrium constant for the reaction we’ve being given when Y is a liquid is the one where the term for Z is on the top. And the terms for W and X are on the bottom.

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