#Chemical Equilibrium: Calculating Equilibrium Constants

#Introduction

Now that you're familiar with the concepts of $K_c$ and $K_p$, 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.

• $K_c$ (Equilibrium Constant in terms of concentration): Relates the concentrations of reactants and products at equilibrium.

• $K_p$ (Equilibrium Constant in terms of pressure): Relates the partial pressures of gaseous reactants and products at equilibrium.

#Formulas

Both $K_c$ and $K_p$ 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 $K_c$) or partial pressures (for $K_p$).

#$K_c$ 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.

#$K_p$ Formula

latex
<math-block>K\_p = \frac{P\_C^cP\_D^d}{P\_A^aP\_B^b}</math-block>

Where:

• $P_A$, $P_B$ are the partial pressures of reactants at equilibrium.

• $P_C$, $P_D$ are the partial pressures of products at equilibrium.

• a, b, c, d are the stoichiometric coefficients from the balanced chemical equation.

Image Courtesy of ScienceAid

Image Courtesy of Quora

#Calculating $K_c$

#Example

Let's calculate $K_c$ 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 $CO_2$
• 0.0908 moles of $H_2$
• 0.0092 moles of $CO$
• 0.0092 moles of $H_2O$
• Volume = 2.00 L

#Step-by-Step Solution

1. Write the $K_c$ expression:

latex $$K_c = \frac{[CO][H_2O]}{[CO_2][H_2]}$$ ```

2. Calculate equilibrium concentrations:

   • $[CO] = 0.0092 \text{ mol} / 2.00 \text{ L} = 0.0046 \text{ M}$
   • $[H_2O] = 0.0092 \text{ mol} / 2.00 \text{ L} = 0.0046 \text{ M}$
   • $[CO_2] = 0.1908 \text{ mol} / 2.00 \text{ L} = 0.0954 \text{ M}$
   • $[H_2] = 0.0908 \text{ mol} / 2.00 \text{ L} = 0.0454 \text{ M}$

3. Plug the concentrations into the $K_c$ expression:

latex $$K_c = \frac{(0.0046)(0.0046)}{(0.0954)(0.0454)} = 4.9 \times 10^{-3}$$ ```

Image Courtesy of Purdue University

#Calculating $K_p$

#Example

Let's calculate $K_p$ for the following reaction:

latex
<math-block>2N\_2O\_5(g) \rightleftharpoons O\_2(g) + 4NO\_2(g)</math-block>

Given:

• $P(N_2O_5) = 2.00 \text{ atm}$
• $P(O_2) = 0.296 \text{ atm}$
• $P(NO_2) = 1.70 \text{ atm}$

#Step-by-Step Solution

1. Write the $K_p$ expression:

latex $$K_p = \frac{P_{O_2}P_{NO_2}^4}{P_{N_2O_5}^2}$$ ```

2. Plug in the partial pressures:

latex $$K_p = \frac{(0.296)(1.70)^4}{(2.00)^2} = 0.618$$ ```

#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.

• 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.

• K = 1: The amount of reactants and products are roughly equal at equilibrium.

Image Courtesy of Labster Theory

#Tips for Calculating Equilibrium Constants

• 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.

• Correct Units: Always use molarity (mol/L) for $K_c$ and partial pressures (usually atm) for $K_p$.

• 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.

• Stoichiometry: Don't forget to raise the concentrations/pressures to the power of their stoichiometric coefficients in the balanced equation.

#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, $N_2(g)$ and $O_2(g)$ react to produce nitrogen monoxide, $NO(g)$, as represented by the equation above.

(a) Write the expression for the equilibrium constant, $K_p$, for the forward reaction.

#Solution

latex
<math-block>K\_p = \frac{P\_{NO}^2}{P\_{N\_2}P\_{O\_2}}</math-block>

#Final Exam Focus

#High-Priority Topics

• Writing $K_c$ and $K_p$ expressions: Make sure you know how to write the correct expressions, including the stoichiometric coefficients.
• Calculating equilibrium constants: Practice calculating $K_c$ and $K_p$ 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 $K_c$ or $K_p$ from given data, often involving unit conversions and multiple steps.

#Last-Minute Tips

• Double-check your units: Always make sure you're using the correct units for concentrations and pressures.

• Show your work: Even if you make a mistake, you can still earn partial credit for showing your steps.

• 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.

• Stay calm: Take a deep breath and trust your preparation. You've got this!

latex
<math-block>N\_2(g) + 3H\_2(g) \rightleftharpoons 2NH\_3(g)</math-block>