LeChatelier Shot the Sheriff, But He Did Not Shoot the Deputy

LeChatelier's Principle sounds like a long shot horse at the Kentucky Derby. If it were, we definitely wouldn't want to bet on it. Why? Because betting on a horse that tries to maintain equilibrium and stay in the pack is a sure way to lose your money.

LeChatelier's Principle states that a reaction in equilibrium will resist a shock to the system. In other words, if something is introduced to the reaction, the system will change to reestablish equilibrium. Let's keep going with this horse example. Our horse is hanging in the middle of the pack, when the pack decides to slow down. Instead of bolting into the lead, that dolt horse of ours slows down with them. The horse maintains its equilibrium position by adjusting its speed to match the group. It adjusts itself to minimize the shock to the equilibrium.

To get more technical, Le Chatelier's Principle states that if an external stress is applied to a system at equilibrium, the system adjusts in such a way that the stress is offset to try to get the system back to equilibrium. These stresses can include temperature, concentration, pressure, or the addition of a catalyst.

Consider Joe Shmoe. Joe is lounging in his bedroom just chillin' out. Joe's mom comes home and turns the thermostat way up, just because. Joe starts to feel extra warm in his room. His equilibrium is disrupted because his mom has put stress on his system. How typical. In order to reestablish equilibrium, Joe replaces his Snuggy with shorts and flips, so he feels comfortable again.

A chemical reaction at equilibrium works in the same manner. Assume that we have a chemical reaction with the following formula: C₃H₆ + H₂ C₃H₈ and a K_eq= 1. If the pressure of each species is initially one atm, then the reaction is at equilibrium at that point because



Remember, the system is at equilibrium when Q = K, just like Joe in his Snuggy before his mom turned the heater onto full blast.

Consider the same reaction, but starting with 1.5 atm of C₃H_8. This reaction is not at equilibrium. You can go through the math and calculate Q. Basically, Q does not equal K, so the system is not at equilibrium. The reaction will work to reestablish equilibrium by shifting the reaction to the left. This means that more reactants will be formed and some of the products will disappear.

We can actually calculate what the final pressures of the reactants and products will be, with something called an ICE table.

• I = Initial conditions.
• C = Change due to LeChatelier's Principle
• E = Equilibrium

The table below summarizes the information given in the example above. We started with the initial pressures of the reactants and products. We want to figure out the equilibrium pressures.

As the reaction goes toward equilibrium, the concentrations of the reactants and products have to change. Like a teeter-totter, the concentrations on one side of the reaction go up, while the concentrations on the other side come down. Eventually, equilibrium is achieved and the concentrations no longer change. The teeter-totter is perfectly balanced.

	C3H6	H2	C3H8
Initial	1	1	1.5
Change	+x	+x	-x
Equilibrium	1 + x	1 + x	1.5 – x

Knowing that the K_p for this reaction is 1, we can eyeball these numbers and figure out quickly that the amount of C₃H₈ must decrease. Therefore, the reactant pressures must increase. Since the ratio of C₃H₆, H₂, and C₃H₈ was 1:1:1 (obtained from the reaction formula), the quantity of change for each type of molecule was found to be x.

That doesn't seem to be saying much, but stick with us for a sec. We'll be finding x soon enough.

At equilibrium, we take the initial concentration or pressure and modify it by the "change" value. For C₃H₈, we start with 1.5 atm and reduce it by that all-too-vague value of x.

We can now plug everything back into the equilibrium equation. . Algebra time. Ready, go!



At this point, we use the quadratic formula to solve for x. Reminder, the quadratic formula is .

Plug and chug the coefficients of the equation in for a, b, and c, and then you'll see that x = 0.16. Plug that into the ICE (ICE) table, and we get 1.16, 1.16, and 1.34 atm pressure for C₃H₆, H₂, and C₃H₈, respectively. Whew!

Brain Snack

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