Calculating the Equilibrium Constant

Caleb Thomas
9 min read
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Study Guide Overview
This study guide covers calculating equilibrium constants (Kc and Kp). It explains the formulas, provides example calculations, and discusses the meaning of K values. The guide also includes tips for calculations, a sample AP question, and practice problems with an answer key. Key concepts include equilibrium, stoichiometric coefficients, partial pressures, and molar concentrations.
#Chemical Equilibrium: Calculating Equilibrium Constants
#Introduction
Now that you're familiar with the concepts of and , let's dive into how to calculate them! This guide will help you master these calculations, ensuring you're ready for anything the AP Chemistry exam throws your way. Remember, equilibrium is all about the balance between reactants and products. Let's get started!
Equilibrium calculations are a cornerstone of AP Chemistry. Expect to see them in both multiple-choice and free-response questions. Mastering this topic is crucial for a strong exam performance.
#Equilibrium Constant Formulas
#Key Concepts
-
Equilibrium: A state where the rate of forward and reverse reactions are equal, and the concentrations of reactants and products remain constant.
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(Equilibrium Constant in terms of concentration): Relates the concentrations of reactants and products at equilibrium.
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(Equilibrium Constant in terms of pressure): Relates the partial pressures of gaseous reactants and products at equilibrium.
Remember, solids and pure liquids are NOT included in the equilibrium expression. Only aqueous solutions and gases are considered.
#Formulas
Both and follow the same basic formula: products over reactants, each raised to the power of their stoichiometric coefficients. The difference lies in whether you're using concentrations (for ) or partial pressures (for ).
# Formula
latex
<math-block>K\_c = \frac{[C]^c[D]^d}{[A]^a[B]^b}</math-block>
Where:
- [A], [B] are the equilibrium concentrations of reactants.
- [C], [D] are the equilibrium concentrations of products.
- a, b, c, d are the stoichiometric coefficients from the balanced chemical equation.
# Formula
latex
<math-block>K\_p = \frac{P\_C^cP\_D^d}{P\_A^aP\_B^b}</math-block>
Where:
-
, are the partial pressures of reactants at equilibrium.
-
, are the partial pressures of products at equilibrium.
-
a, b, c, d are the stoichiometric coefficients from the balanced chemical equation.
Pay close attention to the units! uses molar concentrations (mol/L), while uses partial pressures (usually in atm).
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#Calculating
#Example
Let's calculate for the following reaction:
latex
<math-block>CO\_2(g) + H\_2(g) \rightleftharpoons CO(g) + H\_2O(g)</math-block>
Given:
- 0.1908 moles of
- 0.0908 moles of
- 0.0092 moles of
- 0.0092 moles of
- Volume = 2.00 L
#Step-by-Step Solution
-
Write the expression:
latex ```
-
Calculate equilibrium concentrations:
-
Plug the concentrations into the expression:
latex ```
is unitless, but always make sure you have the correct units for your concentrations (mol/L).
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#Calculating
#Example
Let's calculate for the following reaction:
latex
<math-block>2N\_2O\_5(g) \rightleftharpoons O\_2(g) + 4NO\_2(g)</math-block>
Given:
#Step-by-Step Solution
-
Write the expression:
latex ```
-
Plug in the partial pressures:
latex ```
#Understanding the Equilibrium Constant
#What Does K Tell Us?
The equilibrium constant (K) is a ratio that tells us the extent to which a reaction will proceed. It compares the amount of products to the amount of reactants at equilibrium.
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K > 1: Product-favored reaction. At equilibrium, there are more products than reactants.
-
K < 1: Reactant-favored reaction. At equilibrium, there are more reactants than products.
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K = 1: The amount of reactants and products are roughly equal at equilibrium.
Think of K as a seesaw: if K is greater than 1, the seesaw tips toward the products; if K is less than 1, it tips toward the reactants. ⚖️
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#Tips for Calculating Equilibrium Constants
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Equilibrium Values Only: Make sure you're using concentrations or partial pressures at equilibrium. Using values at any other point will calculate the reaction quotient (Q), not K.
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Correct Units: Always use molarity (mol/L) for and partial pressures (usually atm) for .
-
Unit Conversions: Be prepared to convert grams to moles, moles to molarity, or total pressure to partial pressures using the ideal gas law and mole fractions.
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Stoichiometry: Don't forget to raise the concentrations/pressures to the power of their stoichiometric coefficients in the balanced equation.
A very common mistake is to use initial concentrations instead of equilibrium concentrations. Always double-check that the values you're using are at equilibrium!
#AP Question - 2017 #3
Let's look at a real AP question to see how these concepts are applied.
latex
<math-block>N\_2(g) + O\_2(g) \rightleftharpoons 2NO(g)</math-block>
At high temperatures, and react to produce nitrogen monoxide, , as represented by the equation above.
(a) Write the expression for the equilibrium constant, , for the forward reaction.
#Solution
latex
<math-block>K\_p = \frac{P\_{NO}^2}{P\_{N\_2}P\_{O\_2}}</math-block>
In free-response questions, always show your work, including the equilibrium expression before plugging in values. This can earn you partial credit even if your final answer is incorrect.
#Final Exam Focus
#High-Priority Topics
- Writing and expressions: Make sure you know how to write the correct expressions, including the stoichiometric coefficients.
- Calculating equilibrium constants: Practice calculating and from given equilibrium concentrations or partial pressures.
- Understanding the meaning of K: Know what a K value greater than, less than, or equal to 1 means for the reaction.
- Unit conversions: Be comfortable converting between grams, moles, molarity, and partial pressures.
#Common Question Types
- Multiple Choice: Expect questions that test your understanding of the concepts and your ability to write the correct equilibrium expressions.
- Free Response: Look for questions that require you to calculate or from given data, often involving unit conversions and multiple steps.
#Last-Minute Tips
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Double-check your units: Always make sure you're using the correct units for concentrations and pressures.
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Show your work: Even if you make a mistake, you can still earn partial credit for showing your steps.
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Manage your time: Don't spend too much time on any one question. If you're stuck, move on and come back to it later.
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Stay calm: Take a deep breath and trust your preparation. You've got this!
Practice Question
#Practice Questions
Multiple Choice Questions
-
For the reaction , the equilibrium constant is 4.0 atm⁻¹. If the partial pressures of and at equilibrium are 0.20 atm and 0.10 atm respectively, what is the partial pressure of at equilibrium?
(A) 0.04 atm (B) 0.08 atm (C) 0.16 atm (D) 0.40 atm
-
The equilibrium constant, , for the reaction is 50 at 400°C. If 2.0 moles of and 2.0 moles of are placed in a 1.0 L container, what is the equilibrium concentration of HI?
(A) 0.22 M (B) 1.56 M (C) 3.11 M (D) 3.50 M
Free Response Question
Consider the following reaction:
latex
<math-block>N\_2(g) + 3H\_2(g) \rightleftharpoons 2NH\_3(g)</math-block>
Initially, a 10.0 L vessel contains 1.00 mol of and 3.00 mol of at 500 K. At equilibrium, the concentration of is 0.060 M.
(a) Calculate the initial concentrations of and .
(b) Calculate the equilibrium concentrations of and .
(c) Calculate the value of the equilibrium constant, , for the reaction.
(d) Calculate the value of for the reaction.
Answer Key
Multiple Choice Questions
- (D) 0.40 atm
- (C) 3.11 M
Free Response Question
(a) Initial concentrations:
- (1 point)
- (1 point)
(b) Equilibrium concentrations:
- Change in (given). From the balanced equation, the change in is -0.030 M and the change in is -0.090 M.
- (1 point)
- (1 point)
(c) calculation:
latex ``` (2 points for correct setup and answer)
(d) calculation:
latex ```
- (1 point)
-
latex ``` (1 point)
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