Will thinking of Le Chatelier on your wedding day help take some of the stress away? Le Chatelier’s Principle says that if you “stress” a system that’s performing a reversible reaction like a wedding (I know “I do” is supposed to be “forever” but divorces do happen…) you take the system away from its “happy place” (equilibrium) so the system will adjust the rates of the forward & reverse reactions (e.g. marriages & divorces) to get back to that happy place (e.g. if you add a bunch more single people you’ll get more marriages)
Le Chatelier’s Principle is “simple” in theory but SOOOOOO useful! Because you can basically use it to understand any type of equilibrium situation (where you have a reaction that can be “done” and “undone” that will eventually reach a happy place called equilibrium where the rate of doing = the rate of undoing. First, some intuition, then some more hard-core sciencing for those who want it.
When I talk about a “reaction” I’m not just talking about individual weddings. In chemical reactions you don’t just have a couple of molecules – you have LOTS – so instead of thinking about 2 singles deciding whether or not to get married, we’re dealing at the huge population level. So there are tons of weddings – and divorces – going on.
The actual likelihood of any 2 people who meet getting married or any married couple getting divorced depends on the inherent properties of the people (so this is a constant for the reaction, which we’ll talk about later), but the rates at which we observe marriages or divorces depends on the “availability” of the different types (e.g. the divorce lawyer’s not gonna get any business if there aren’t any married couples!)
Equilibrium is the name for a system’s “happy place” – say we have a big population of people that can get married and divorced. We can start with any # of single people or couples – marriages (forward reaction) & divorces (reverse reaction) will happen and eventually the rate at which people are getting married will equal the rate at which people are getting divorced (the wedding planners & divorce lawyers have equal business). The *rates* are equal but not necessarily the amounts of singles & couples.
How does it get there? Think of the extremes of non-equilibrium – there can’t be any marriages if there aren’t any single people. And there can’t be any divorces if no one’s married, but in between, things are more complicated. As more people get married, it becomes harder and harder to find a partner. And with more married couples, even if each couple still has the same likelihood of getting divorced, since there are more to begin with you’ll start seeing more divorces.
Instead of directly measuring the rates (which would be kinetics) we can turn to thermodynamics – at any point in time we can take a “census” of how many people are single and how many people are married and compare. And then we can compare the current census to the “happy place” census. That “happy place” census (relative #s) would be the same regardless of how many of each demographic you started with.
It’s not just the actual # of people that matters – they have to be able to find each other (e.g. without the internet it’d be really hard for someone in the U.S. & someone in Australia to find each other & tie the knot). So what we really care about is # of people in a defined “space” – i.e. we want concentrations. A common unit of concentration is molarity, and we define 1 molar (1M) as being 1 mol/L (a mol is just like a “dozen” except it means 6.02 x 10^23 instead of 12)
We can put square brackets [ ] around something to indicate “concentration of” (e.g. [reactants] means “concentration of reactants”) and you can think of it a bit like walls of a house whose inhabitants are whatever’s inside the brackets. And concentration’s kinda like taking a census of how many of that type of house you have in a certain neighborhood.
So, in our analogy, C is a house with a married couple living in it & [C] is how many of those houses are in the neighborhood. Similarly, [M] would be the # of houses with single males in the neighborhood & [W] the # of single women in the neighborhood.
Note: for the sake of a simple analogy, I’m going to talk in terms of single men and single women but this is not meant in any way to delegitimize non-heterosexual marriages – love is love and I hope everyone finds it!)
The reason I need to bring this in is that reactants are NOT interchangeable (A+B makes C but A+A doesn’t). To account for the fact that in this analogy we need 1 single man (M) and 1 single woman (W) for every couple (C), we can’t just add together the # M & # W to get the # of single people to use for this comparison. (e.g. we can’t just divide C by (M+W)).
Instead we have to take into account how many of each type of reactant there is, which we do by raising the concentration to the power of the stoichiometric coefficient (that big number in front of the reactant in an equation (e.g. the 3 in front of the H in the equation for the Haber Process, which combines nitrogen gas & hydrogen gas to make ammonia: N₂(g) + 3H₂(g) ⇌ 2NH₃(g))
We can make a modified ratio of [products] to [reactants] to get a value we call the REACTION QUOTIENT (Q) : [NH₃]²/[N₂][H₂]³
We’ll look more at this reaction later but for now let’s go back to our “reaction:” M + W ⇌ C. We can write a Q as [C]/[M][W]
Say a bunch of single people more into an empty neighborhood. As the reaction proceeds in the forward direction (couples marry), Q will increase.
But eventually this ratio Q will stop changing 👉 the system has reached point called EQUILIBRIUM where there’s NO NET CHANGE in [products] & [reactants]. Q at this point gets a special name – the EQUILIBRIUM CONSTANT (K). So K is just Q at the reaction’s happy place (equilibrium)
If K is high, products are favored at equilibrium. But If K is low, reactants are favored at equilibrium
A system is only at equilibrium when K & Q are twinsies. At all other times, the system is at non-equilibrium, so it does what it can to reach equilibrium.
Say you have some investors who want to know whether they should invest in a marriage planning company or a divorce lawyer company. So they want to know which will have more business, which will depend on the relative amounts of couples (products) to singles (reactants).
So they take a census of the current population (get the reaction quotient Q) and compare it to the happy place census (equilibrium constant K).
🔹If K < Q 👉 rxn goes to form more products (happy wedding planners)
🔹If K = Q 👉 no drive (equal business)
🔹If K > Q 👉 reaction favorable in reverse direction (happy divorce lawyers)
Now here’s where Le Chatelier comes into play! Say the divorce lawyer finds out the investor’s looking so they want to “trick him” – they can’t change the chances that any one couple will get divorced (no love-meddling) but they can influence how many but there aren’t enough married couples. They need to make it seem like there’s an excess of couples. So they “hide” the singles or get them to move out of the neighborhood and/or brings in couples from out of town.
The investor takes a census, see that Q > K, predicts that divorces will dominate and invests in the lawyer.
But then the wedding planner finds out and plans a plan of their own. – they needs to make it seem like there’s an excess of single people. So they “hide” the couples or get them to move out of the neighborhood. And/or they bring in single people from out of town.
So a bunch of people start getting married and a preschool teacher gets excited and decides to open up a preschool in hopes that M + W ⇌ C ⇌ T (where T is a house with 3 people – happy birthday baby!). And that makes the wedding planner even happier because converting C to T “removes couples” so marriages are favored in the first of these coupled reactions (pun NOT intended for once)
Let’s get a little more serious now to see where all this K Q stuff comes from and how Le Chatelier in a more traditional way…
K is constant for a given reaction. No matter what concentrations you start with (any # of singles or couples) you should settle at the same place BUT getting there’s more or less favorable depending on how far away you are from equilibrium to begin with. This is like how whether you’re at the top of a slide or close to the bottom, you’ll “settle” at the same place BUT you release more energy (& have more fun) going from the top.
Instead of dealing with the kinetic potential energy provided by gravity, we’re dealing with something called Gibb’s free energy, and you can learn more about it here: http://bit.ly/2pSmc2B
Just like you don’t “fall up” a slide but you can climb up to the top, reactions only *spontaneously* go in the direction that decreases their free energy (though you can often get them to go the other way if you give them some energy).
So we want to look at the change in free energy (ΔG where “Δ” is pronounced “delta” and means “change in”) between what goes into a reaction (reactants)(singles) and what comes out (products)(couples). And for a spontaneous reaction, the products will be “comfier” (have a lower free energy) than the reactants so ΔG will be negative.
And we can directly relate ΔG to K (the equilibrium constant we’re talking about now). ΔG is more ➖ & thus the reaction’s more favorable when Q<<K
2 keep the reaction going, we need to keep Q < K, & Le Chatelier’s principle tells us we can trick the reaction into proceeding by keeping it unbalanced.
We can do this by doing things like increasing [reactants] (any of them) – say we have 2 reactants, A & B that combine 2 make product C. We can ⬇️Q by ⬆️[A] OR ⬆️[B]. Raising EITHER will ⬇️Q so you can use excess of cheaper reactant to maximize product yield
removing (or making unavailable) products – sometimes we do this physically, like by changing out the “bath water” to drive diffusion during dialysis (there we’re just dealing with molecules moving not reacting with one another but Le Chatelier’s Principle still applies – but here we’re reaching an equilibrium between concentrations inside & outside a membrane.
We can do this chemically by “coupling” it to another reaction so products of the 1st reaction are reactants for 2nd. So the 2nd rxn “steals” 1st’s products, keeping Q for 1st reaction low. This is a common technique our cells use when making & breaking things (metabolism)
So, by using SAME amount of B, we can get MORE PRODUCT if we ⬆️[A] or ⬇️[C]
⚠️ Changing concentrations DOESN’T change K! The reaction just “adjusts” to “de-stress” & reach concentrations that fulfill K.
Temperature (T) on the other hand DOES change K because K’s directly related to ΔG which is directly related to T. So you can ⬆️K (make products more favorable) by manipulating T
🔹For endothermic reactions (reactions that take in heat), heat can be treated like a “reactant” 👉 reaction’s more favorable at higher temperatures.
🔹For exothermic reactions (reactions that release heat), heat can be treated like a “product” 👉 reaction is more favorable at lower temperatures (but the reaction *rate* is slower at lower temps because the molecules have less energy to collide & interact)
⚠️ We’re still talking about *thermodynamics* NOT *kinetics* 👉 Le Chalelier’s Principle DOESN’T tell us about the *rate* of a reaction just *where* the reaction will try to end up (it’s happy place of equilibrium) (we don’t know how long it will take to find its happy place. Speaking of which – things called catalysts (like enzymes) speed up forward & backward reaction rates equally so they don’t change the equilibrium positions (they DO NOT CHANGE K!) But they’re still really useful especially if the reaction is thermodynamically favorable (K is high) – reactants want to be products & don’t want to turn back, they just need help being brought together, etc.
more on enzymes & catalysts: http://bit.ly/2CJdr3o
If you’re dealing with gases, there’s sometimes another way to change the equilibrium balance without changing K – changing the pressure. Gas molecules try to escape their container, putting pressure on its walls. The more molecules of gas, the higher the pressure (see yesterday’s post: http://bit.ly/2Px1Mvq)
So pressure can be considered a “product” or “reactant” and increasing the pressure even further (e.g. by compressing the container) will favor the reaction direction that decreases the number of gas molecules formed.
Going back to that Haber Process for ammonia-making:
N₂(g) + 3H₂(g) ⇌ 2NH₃(g) ΔH = -92 kJ mol⁻¹
ΔH = -92 kJ mol⁻¹ tells us the reaction is exothermic – so temperature is a “product” and we can shift equilibrium towards products by lowering temp. But when we lower temp we also lower reaction rate.
We have 4 gas molecules on the left side of the equation (1 N₂ + 3 H₂) and 2 on the right side (2 NH₃). So we have fewer gas molecules in the products so decreasing the pressure will favor the forward reaction.