#AP Chemistry Study Guide: Hess's Law & State Functions

Hey there, future AP Chem master! 👋 Let's break down Hess's Law and state functions. This guide is designed to be your go-to resource, especially the night before the exam. We'll make sure everything clicks, so you can walk in feeling confident and ready to ace it!

#Thermodynamics: State Functions & Hess's Law

#State Functions

In thermodynamics, we're all about changes in a system's state. Think of it like this: we care about where we start and where we end, not how we get there. Let's define some key terms:

#Pathway Dependent

• A process or function that does depend on the specific route or sequence of steps taken. 🛤️
• The result changes if you take a different path.

#Pathway Independent

• A process or function that does not depend on the specific route or sequence of steps taken. 🚀
• The result is the same no matter which path you choose.

• Examples of state functions:
  • Energy (E)
  • Enthalpy (H)
  • Pressure (P)
  • Volume (V)
  • Temperature (T)

#Hess's Law

Hess's Law is a super useful tool that states: Enthalpy change (ΔH) is a state function. 💡 This means the total enthalpy change for a reaction is independent of the path taken. It's like a magic trick for calculating enthalpy changes! ✨

#Rules of Hess's Law

1. Reversing a reaction: When you reverse a reaction, the sign of ΔH changes (e.g., +ΔH becomes -ΔH). 🔄
2. Multiplying a reaction: If you multiply a reaction by a factor 'n', you also multiply the ΔH by 'n'. ✖️
3. Adding reactions: When you add two or more reactions, you add their corresponding ΔH values to get the overall ΔH. ➕

#Hess's Law Example Problem #1

Let's dive into an example to make this crystal clear. Here's the reaction we want to find the enthalpy change for:

C₂H₂ (g) → 2C (s) + H₂ (g)

And we have the following thermochemical equations:

#Thought Process

• Identify: Find the reactants and products in the given equations and the overall reaction.

• Manipulate: Adjust the equations to match the overall reaction. Remember, what you do to the equation, you do to the enthalpy! 🔁✖️

  • C (s): Needs a coefficient of 2, so we'll multiply equation #2 by 2. ❌
  • H₂ (g): Already correct in equation #3. ✔️
  • C₂H₂ (g): Is on the wrong side, so we'll flip equation #1. ❌

#Steps to Take

• Step 1: Flip reaction 1 to get C₂H₂ on the product side. Change the sign of ΔH. 🔄

  • 2CO₂ (g) + H₂O (l) → C₂H₂ (g) + 5/2O₂ (g) with ΔH° = +1299.5 kJ

• Step 2: Multiply reaction 2 by 2 to get 2 solid carbon atoms. Multiply the enthalpy by 2. ✖️

#Results of Steps

After these manipulations, we have:

• Cancel out: Spectator compounds (O₂, H₂O, CO₂) cancel out when you add the equations.
• Add Enthalpies: Add the manipulated ΔH values together. ➕

ΔH = +1299.5 kJ + (−787 kJ) + (−285.8 kJ) = +226.7 kJ

#Hess's Law Example Problem #2

Let's try another one! Calculate ΔH for:

6PCl₅ (g) + 10Cl₃PO (g) → 10PCl₃ (g) + P₄O₁₀ (s)

Using these thermochemical equations:

#Thought Process

• P₄O₁₀: Wrong side, manipulate equation 2. ❌
• PCl₅: Wrong side and needs a coefficient of 6, manipulate equation 3. ❌
• Cl₃PO: Needs a coefficient of 10, manipulate equation 4. ❌

#Steps to Take

• Step 1: Flip equation 2. Change the sign of ΔH. 🔁
• Step 2: Flip equation 3 and multiply by 6. Multiply ΔH by -6. 🔁✖️
• Step 3: Multiply equation 4 by 10. Multiply ΔH by 10. ✖️

#Results of Steps

After these manipulations, we have:

• Balance: Notice that P₄, Cl₂, and PCl₃ are not balanced. They are all in equation 1. We need to manipulate equation 1. * Multiply: Multiply equation 1 by 4. Multiply ΔH by 4. ✖️

• Cancel: Everything cancels out, and we are left with the overall equation! 🥳
• Add Enthalpies: Add all the manipulated ΔH values together. ➕

ΔH = -1225.6 kJ + 2967.3 kJ + 505.2 kJ + (−2857 kJ) = -610.1 kJ

#Final Exam Focus

• High-Priority Topics: Hess's Law, state functions, enthalpy changes, and manipulating thermochemical equations.
• Common Question Types:
  • Multiple-choice questions that test your understanding of state functions and pathway dependency.
  • Free-response questions that require you to apply Hess's Law to calculate enthalpy changes for complex reactions.
• Time Management: Practice doing these problems quickly. Focus on identifying the key species and manipulating equations efficiently.
• Common Pitfalls:
  • Forgetting to change the sign of ΔH when reversing a reaction.
  • Forgetting to multiply ΔH when multiplying a reaction by a coefficient.
  • Not canceling out spectator species correctly.

#

Practice Question

Practice Questions

#Multiple Choice Questions

1. Which of the following is NOT a state function? (A) Enthalpy (B) Internal Energy (C) Work (D) Volume

2. Given the following reactions:

   • A → B, ΔH = +20 kJ
   • B → C, ΔH = -15 kJ What is the ΔH for the reaction A → C? (A) +35 kJ (B) +5 kJ (C) -5 kJ (D) -35 kJ

3. Consider the following reaction: 2H₂(g) + O₂(g) → 2H₂O(l), ΔH = -572 kJ What is the enthalpy change for the decomposition of 1 mol of liquid water? (A) -572 kJ (B) -286 kJ (C) +286 kJ (D) +572 kJ

#Free Response Question

Consider the following reactions:

1. N₂(g) + O₂(g) → 2NO(g) ΔH₁ = +180 kJ
2. 2NO(g) + O₂(g) → 2NO₂(g) ΔH₂ = -112 kJ

(a) Calculate the enthalpy change for the reaction:

 N₂(g) + 2O₂(g) → 2NO₂(g)

(b) Draw an enthalpy diagram illustrating the relationship between the three reactions.

(c) If the reaction 2NO₂(g) → N₂(g) + 2O₂(g) is carried out, what is the enthalpy change?

#Scoring Breakdown

(a) (2 points)

• 1 point for correctly adding the two reactions
• 1 point for correctly calculating the enthalpy change: +180 kJ + (-112 kJ) = +68 kJ

(b) (2 points)

• 1 point for correctly labeling the reactants, products and intermediates
• 1 point for showing the correct enthalpy changes for each step

(c) (1 point)

• 1 point for correctly reversing the overall reaction and changing the sign of the enthalpy: -68 kJ