Introduction: Welcome to the "How Far?" Chapter!
In previous chapters, we looked at "how fast" a reaction happens (Rate of Reaction). Now, we are shifting our focus to a different question: "How far" does a reaction actually go? Does it turn all the reactants into products, or does it get stuck somewhere in the middle?
This chapter is all about chemical equilibrium. We will learn how to calculate exactly how much of each substance is present when a reaction settles down and how we can predict whether a reaction is "product-heavy" or "reactant-heavy." Don't worry if this seems a bit math-heavy at first—we'll break it down step-by-step!
1. Equilibrium in Gases: Mole Fraction and Partial Pressure
When we deal with gases, we often talk about pressure instead of concentration. To do this, we need to understand how much "share" of the total pressure each gas in a mixture is responsible for.
What is Mole Fraction?
Imagine you have a pizza cut into 10 slices. If 3 slices have pepperoni and 7 are plain, the "fraction" of pepperoni slices is \(3/10\) or \(0.3\). In Chemistry, the mole fraction \(x\) is the proportion of a specific gas in a total mixture.
The Formula:
\( \text{Mole Fraction of gas A} (x_A) = \frac{\text{number of moles of gas A}}{\text{total number of moles in the mixture}} \)
What is Partial Pressure?
The partial pressure \(p\) is the pressure that an individual gas in a mixture would exert if it were all alone in the container. The sum of all partial pressures equals the total pressure (\(P\)).
The Formula:
\( \text{Partial Pressure of gas A} (p_A) = \text{mole fraction of A} \times \text{total pressure} \)
\( p_A = x_A \times P \)
Example: If the total pressure is 100 kPa and the mole fraction of Oxygen is 0.2, its partial pressure is \(0.2 \times 100 = 20 \text{ kPa}\).
Quick Review:
• Mole fractions always add up to 1.
• Partial pressures always add up to the Total Pressure.
Key Takeaway: Mole fraction is the "share of moles," and partial pressure is the "share of pressure."
2. The Equilibrium Constants: \(K_c\) and \(K_p\)
To measure exactly "how far" a reaction has gone, we use an equilibrium constant. There are two main types you need to know:
1. \(K_c\): Calculated using concentrations (usually for solutions or gases).
2. \(K_p\): Calculated using partial pressures (only for gases).
Writing the Expressions
For a general reaction: \( aA + bB \rightleftharpoons cC + dD \)
The expression for \(K_c\) is:
\( K_c = \frac{[C]^c [D]^d}{[A]^a [B]^b} \)
The expression for \(K_p\) is:
\( K_p = \frac{p(C)^c p(D)^d}{p(A)^a p(B)^b} \)
Important Rule: Heterogeneous Equilibria
If a reaction involves different states (e.g., a solid and a gas), we ignore any solids (s) or pure liquids (l) in the \(K_c\) and \(K_p\) expressions. Their concentrations are considered constant and don't affect the "balance."
Memory Aid: Always remember "Products over Reactants" (P.O.R.). Just like a fan of POR-ridge, keep the products on top!
Did you know?
The small letters (\(a, b, c, d\)) in the chemical equation become the powers in the equilibrium expression. If there is a \(2\) in front of \(H_2O\), you must square the concentration: \([H_2O]^2\).
3. Calculating Equilibrium Quantities
Sometimes the exam will give you the starting amounts and ask you to find what's left at equilibrium. A great way to organize this is using the "RICE" method:
R - Ratio (from the balanced equation)
I - Initial moles (what you started with)
C - Change in moles (how much reacted/formed)
E - Equilibrium moles (Initial + Change)
Steps to calculate \(K_c\) or \(K_p\):
1. Find the moles of every substance at equilibrium using the RICE table.
2. For \(K_c\): Divide moles by volume (\(V\)) to get concentrations.
3. For \(K_p\): Calculate mole fractions and then partial pressures.
4. Plug these values into your \(K\) expression.
5. Units: Units aren't always the same! You must work them out by cancelling units in your expression. (e.g., \(\text{mol dm}^{-3}\) or \(\text{kPa}\)).
Common Mistake: Forgetting to divide moles by volume when calculating \(K_c\). Always check if the question gives you a volume (e.g., \(2.0 \text{ dm}^3\))!
Key Takeaway: Use the RICE table to stay organized. If you get the equilibrium moles right, the rest is just plugging in numbers!
4. What Actually Changes the Value of \(K\)?
This is a favorite exam trick question! Many things can shift the position of equilibrium (where the molecules are hanging out), but only ONE thing can change the actual value of the constant \(K\).
The Rule of Temperature
• Only Temperature changes the numerical value of \(K_c\) or \(K_p\).
• Concentration changes do NOT change \(K\).
• Pressure changes do NOT change \(K\).
• Catalysts do NOT change \(K\).
How does Temperature affect \(K\)?
It depends on whether the forward reaction is Exothermic or Endothermic:
1. Exothermic reactions (\(\Delta H\) is negative): Increasing temperature makes the equilibrium shift to the left. This means you get more reactants and fewer products. Because the "top" of our fraction gets smaller, \(K\) decreases.
2. Endothermic reactions (\(\Delta H\) is positive): Increasing temperature makes the equilibrium shift to the right. You get more products. Because the "top" of our fraction gets bigger, \(K\) increases.
What about Catalysts?
A catalyst speeds up both the forward and reverse reactions by the same amount. It helps you reach equilibrium faster, but it doesn't change the final balance. It’s like a faster escalator—it gets you to the top quicker, but the height of the building stays the same!
Quick Review Box:
• Increase Temp (Exo): \(K\) goes down.
• Increase Temp (Endo): \(K\) goes up.
• Change Pressure/Conc/Catalyst: \(K\) stays the same!
5. The Magnitude of \(K\): What does the number tell us?
The value of \(K\) gives us an immediate "snapshot" of the reaction:
• If \(K = 1\), the equilibrium is roughly in the middle.
• If \(K > 100\) (a large value), the equilibrium is shifted far to the right (lots of products).
• If \(K < 0.01\) (a small value), the equilibrium is shifted far to the left (mostly reactants).
Key Takeaway: A huge \(K\) means the reaction has gone nearly to completion. A tiny \(K\) means the reaction barely happened at all.
Summary: You have now mastered how to use mole fractions and partial pressures, how to write and calculate equilibrium constants (\(K_c\) and \(K_p\)), and most importantly, you know that only temperature can change the value of these constants. Great job!