Hess’s Law

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Core Concept

Hess’s Law states that the total enthalpy change for a chemical reaction is the same, regardless of the pathway taken from reactants to products. This principle allows us to calculate the enthalpy change (ΔH) for reactions that may be challenging to measure directly by using known enthalpy changes for related reactions.

Practice Tips

  • Check Each Step: Always confirm that adding reactions gives you the target reaction.

  • Use Correct Signs: Remember to flip the sign of ΔH when reversing a reaction.

  • Multiply Carefully: If you multiply or divide a reaction by a factor, adjust ΔH by the same factor.

  • Cancel Intermediates: Ensure intermediate substances are canceled out when adding reactions, so only the desired reactants and products remain.

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Steps for Applying Hess’s Law

  1. Write the Target Equation: Identify the reaction you want to calculate the enthalpy change for.

  2. Identify Known Equations: Find reactions with known ΔH values that involve the reactants and products of the target reaction.

  3. Manipulate Equations: Reverse, multiply, or divide the known equations to match the reactants and products in the target reaction.

  4. Add or Subtract Reactions: Combine the manipulated reactions, ensuring that all intermediate species cancel out and only the target reaction remains.

  5. Calculate $\Delta H_{\text{overall}}$​: Sum the enthalpy changes of the adjusted reactions to find the enthalpy change for the target reaction.

Problem:

Calculate the standard enthalpy change (ΔH°) for the formation of methane (CH₄) from its elements in their standard states:

C(s) + 2H₂(g) → CH₄(g)

You are given the following thermochemical equations:

  1. CH₄(g) + 2O₂(g) → CO₂(g) + 2H₂O(l) ΔH° = -890.3 kJ

  2. C(s) + O₂(g) → CO₂(g) ΔH° = -393.5 kJ

  3. H₂(g) + ½O₂(g) → H₂O(l) ΔH° = -285.8 kJ

Solution:

Here's how we can solve this problem using Hess's Law:

Step 1: Analyze the target equation and the given equations.

Our target equation is: C(s) + 2H₂(g) → CH₄(g)

We need to manipulate the given equations so that when we add them together, they result in the target equation.

Step 2: Manipulate the given equations.

  • Equation 1: We need CH₄ on the product side, but it's currently on the reactant side. Therefore, we reverse equation 1 and change the sign of its ΔH°:

    CO₂(g) + 2H₂O(l) → CH₄(g) + 2O₂(g) ΔH° = +890.3 kJ

  • Equation 2: This equation already has C(s) on the reactant side, as in the target equation. So, we leave it as is:

    C(s) + O₂(g) → CO₂(g) ΔH° = -393.5 kJ

  • Equation 3: We need 2H₂(g) on the reactant side, but the equation only has 1H₂(g). Therefore, we multiply the entire equation by 2, including its ΔH°:

    2H₂(g) + O₂(g) → 2H₂O(l) ΔH° = -571.6 kJ (2 * -285.8 kJ)

Step 3: Add the manipulated equations.

Now, let's add the manipulated equations together:

CO₂(g) + 2H₂O(l) → CH₄(g) + 2O₂(g) ΔH° = +890.3 kJ

C(s) + O₂(g) → CO₂(g) ΔH° = -393.5 kJ

2H₂(g) + O₂(g) → 2H₂O(l) ΔH° = -571.6 kJ

Notice that CO₂(g), 2H₂O(l), and 2O₂(g) appear on both sides of the equations and cancel out:

C(s) + 2H₂(g) → CH₄(g)

This is our target equation!

Step 4: Add the manipulated ΔH° values.

Now, we add the ΔH° values of the manipulated equations:

ΔH°(reaction) = (+890.3 kJ) + (-393.5 kJ) + (-571.6 kJ)

ΔH°(reaction) = -74.8 kJ

Answer:

The standard enthalpy change (ΔH°) for the formation of methane (CH₄) is -74.8 kJ. This means the reaction is exothermic.

Key Concepts

  1. Enthalpy as a State Function:

    • Because enthalpy (H) is a state function, the enthalpy change only depends on the initial and final states, not on the pathway.

    • Hess’s Law is based on this property, meaning that the sum of enthalpy changes in a series of steps is equal to the enthalpy change of the overall reaction.

  2. Equation Format for Hess’s Law:

    • If you have two or more reactions that sum to your target reaction, you can add their enthalpy changes to find the total enthalpy change for the target reaction: $\Delta H_{\text{overall}} = \Delta H_1 + \Delta H_2 + \ldots + \Delta H_n$

  3. Using Hess’s Law:

    • Rearrange given reactions to form the target reaction.

    • Adjust enthalpy values based on changes made to the reactions:

      • Reversing a Reaction: Flip the sign of ΔH.

      • Multiplying or Dividing by a Factor: Multiply or divide ΔH by the same factor.

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