Chemical equilibria, Le Chatelier’s principle and Kc

Welcome to the World of Equilibrium!

Ever felt like you’re running on a treadmill? You’re moving fast, putting in lots of effort, but you aren't actually going anywhere. In Chemistry, many reactions do something very similar. They reach a point called dynamic equilibrium where the forward and backward reactions happen at the exact same speed.

In these notes, we are going to explore why this happens, how we can "nudge" a reaction to give us more of what we want using Le Chatelier’s Principle, and how to prove it all with math using the equilibrium constant, \(K_c\). Don’t worry if this seems a bit abstract at first—we’ll use plenty of everyday analogies to make it click!

1. What is Dynamic Equilibrium?

Most reactions you’ve seen so far go from left to right until the reactants are all used up. These are "one-way" reactions. However, many reactions are reversible. This is shown by the double arrow symbol: \( \rightleftharpoons \).

The "Busy Shop" Analogy

Imagine a small shop. People are walking in (the forward reaction) and people are walking out (the backward reaction). If 5 people enter every minute and 5 people leave every minute, the number of people inside the shop stays constant, even though people are still moving. This is dynamic equilibrium.

For a reaction to reach equilibrium, two things must be true:

1. The reaction must be in a closed system (nothing can get in or out).
2. The rate of the forward reaction must equal the rate of the reverse reaction.

Quick Review: At equilibrium, the concentrations of reactants and products stay the same, but they are not necessarily equal to each other. There might be way more product than reactant, or vice-versa!

Key Takeaway: Dynamic equilibrium is a state of balance where the forward and backward reactions occur at the same rate, so concentrations remain constant.

2. Le Chatelier’s Principle

This is a fancy name for a simple rule: If you change the conditions of a system at equilibrium, the system will shift to oppose that change.

Think of it as the "Stubborn Teenager" principle—whatever you try to do, the reaction will try to do the opposite!

Changing Concentration

If you increase the concentration of a reactant, the system wants to decrease it. It does this by moving to the right (making more product).
Memory Aid: Add to the left \(\rightarrow\) shift to the right. Add to the right \(\rightarrow\) shift to the left.

Changing Pressure (Gases only)

Pressure is caused by gas molecules hitting the walls of a container. To use this rule, you must count the number of gas moles on each side of the equation.

Example: \( N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g) \)
Left side = 4 moles of gas. Right side = 2 moles of gas.

If you increase the pressure, the system tries to decrease it by moving to the side with fewer gas moles (to the right in this case).

Changing Temperature

This is the trickiest one! You need to know if the forward reaction is exothermic (gives out heat, \(-\Delta H\)) or endothermic (takes in heat, \(+\Delta H\)).

• If you increase the temperature, the system tries to cool down. It shifts in the endothermic direction to absorb the extra heat.
• If you decrease the temperature, the system tries to heat up. It shifts in the exothermic direction.

What about Catalysts?

Did you know? A catalyst does not change the position of equilibrium. It speeds up the forward and backward reactions by the same amount. It just helps you reach equilibrium faster!

Key Takeaway: The reaction always tries to "undo" what you just did. More pressure? Move to fewer moles. More heat? Move in the endothermic direction.

3. Industrial Compromises

In a factory, chemists want to make as much product as possible, as fast as possible, as cheaply as possible. Sometimes, Le Chatelier’s Principle tells us to use conditions that are actually bad for business!

Example: The Haber Process \( (N_2 + 3H_2 \rightleftharpoons 2NH_3) \) is exothermic. To get a high yield (lots of product), we should use a low temperature. However, low temperatures make the reaction too slow. Therefore, industry uses a compromise temperature (around 450°C) to get a decent amount of product in a reasonable time.

Key Takeaway: Industrial conditions are a balance between high yield (equilibrium), high speed (kinetics), and safety/cost.

4. The Equilibrium Constant (\(K_c\))

While Le Chatelier tells us which way the reaction shifts, \(K_c\) gives us a number that tells us exactly where the equilibrium lies.

Writing the \(K_c\) Expression

For a general reaction: \( aA + bB \rightleftharpoons cC + dD \)

The expression is: \( K_c = \frac{[C]^c[D]^d}{[A]^a[B]^b} \)

Always remember: [Products] over [Reactants]. The square brackets [ ] mean concentration in \(mol\ dm^{-3}\). The little numbers from the balanced equation become powers in the expression.

Calculating Units

Units for \(K_c\) aren't always the same! You have to work them out every time by cancelling them down.

Example: If you have \( \frac{(mol\ dm^{-3})^2}{(mol\ dm^{-3})^1} \), one set cancels out, leaving you with \( mol\ dm^{-3} \).

The Golden Rule of \(K_c\)

Only temperature changes the value of \(K_c\) for a specific reaction. If you change the concentration or pressure, the equilibrium shifts to keep \(K_c\) exactly the same. But if you change the temperature, the value of \(K_c\) will change.

Step-by-Step for \(K_c\) Calculations:
1. Write the balanced equation.
2. Write the \(K_c\) expression.
3. Use "ICE" (Initial, Change, Equilibrium) to find the moles at equilibrium.
4. Divide moles by volume to get concentration.
5. Plug numbers into the expression and solve.

Key Takeaway: \(K_c\) is a constant at a specific temperature. A large \(K_c\) (bigger than 1) means the equilibrium sits towards the products.

Common Mistakes to Avoid

• Forgetting the powers: Always use the big numbers from the equation as powers in your \(K_c\) expression.
• Using moles instead of concentration: Always divide moles by volume (\(V\)) before putting them into the \(K_c\) formula!
• Confusing Rate and Yield: A catalyst increases the rate but has no effect on the yield or \(K_c\).
• Wrong shift for pressure: Remember, pressure only affects gases. Ignore solids or liquids when counting moles for pressure shifts.

Quick Review Box

Equilibrium: Rates are equal, concentrations constant.
Le Chatelier: System opposes change.
Exothermic (\(-\Delta H\)): Favoured by low temp.
Endothermic (\(+\Delta H\)): Favoured by high temp.
Increasing Pressure: Shifts to side with fewer gas moles.
\(K_c\): [Products] / [Reactants]. Only changed by temperature.