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4.2.2 - Applications of Hess's Law

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Introduction to Hess's Law

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0:00
Teacher
Teacher

Today, we're going to explore Hess's Law. Can someone remind us what Hess's Law states?

Student 1
Student 1

It says that the total enthalpy change is the same no matter how a reaction occurs.

Teacher
Teacher

Exactly! Hess's Law tells us that if a reaction can happen in multiple steps, the total change in enthalpy will be the sum of the changes in each step. Why is this important?

Student 2
Student 2

It helps us calculate heat changes for reactions that are hard to measure directly!

Teacher
Teacher

Very good! Remember that enthalpy is a state function. This means it depends only on the initial and final states, not the path taken. Let's move to how we can use it practically.

Standard Enthalpies of Formation

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0:00
Teacher
Teacher

Now, let’s look at how we can use standard enthalpies of formation. What do we mean by standard enthalpy of formation?

Student 3
Student 3

It’s the enthalpy change when one mole of a compound forms from its elements at standard conditions!

Teacher
Teacher

Exactly! The equation to calculate the reaction's enthalpy change using these values is: $$Ξ”H_{rxn}^{ ext{Β°}} = Ξ£nΞ”H_f^{ ext{Β°}}( ext{products}) - Ξ£mΞ”H_f^{ ext{Β°}}( ext{reactants})$$. Let’s practice this. Can anyone calculate the Ξ”H for the combustion of methane?

Student 4
Student 4

If I have Ξ”H_fΒ°(CHβ‚„) = -74.8 kJ mol⁻¹, Ξ”H_fΒ°(COβ‚‚) = -393.5 kJ mol⁻¹, and Ξ”H_fΒ°(Hβ‚‚O) = -285.8 kJ mol⁻¹, I can set it up!

Teacher
Teacher

That's right! And remember, for Oβ‚‚, Ξ”H_fΒ° is 0. Let’s do the final calculation together.

Manipulating Known Reactions

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0:00
Teacher
Teacher

Now, let's talk about how we can manipulate known reactions. Can anyone explain why we would reverse a reaction?

Student 2
Student 2

When we reverse a reaction, we also change the sign of the enthalpy change!

Teacher
Teacher

Exactly! And if we multiply a reaction by a factor, what must we do with the enthalpy change?

Student 1
Student 1

We multiply the enthalpy change by the same factor!

Teacher
Teacher

Great! Let’s look at an example: we start with the reaction C + Oβ‚‚ β†’ COβ‚‚ and want C + Β½Oβ‚‚ β†’ CO. What do we do?

Student 3
Student 3

We keep the first one as is, reverse the second, and change the sign!

Teacher
Teacher

Perfect! After adding these, we can cancel out common terms. Let’s summarize: Hess's Law gives us a powerful method to calculate enthalpy for complex pathways!

Introduction & Overview

Read a summary of the section's main ideas. Choose from Basic, Medium, or Detailed.

Quick Overview

Hess's Law simplifies the calculation of enthalpy changes for chemical reactions that occur in multiple steps by stating that the total enthalpy change is independent of the pathway taken.

Standard

This section explores the applications of Hess's Law in calculating enthalpy changes using standard enthalpies of formation and through the manipulation of known reactions. Examples illustrate its significance and utility in thermochemistry.

Detailed

Applications of Hess's Law

Hess's Law, a fundamental concept in thermochemistry, asserts that the total enthalpy change for a reaction is constant, regardless of the number of steps the reaction undergoes. This property stems from enthalpy being a state functionβ€”it depends only on the initial and final states, not on the pathway. This section highlights two major applications of Hess's Law:

1. Using Standard Enthalpies of Formation (Ξ”H_fΒ°)

The section describes how to calculate the overall enthalpy change (Ξ”H_rxnΒ°) of a reaction using the standard enthalpies of formation of reactants and products. The formula used is:

$$Ξ”H_{rxn}^{ ext{Β°}} = Ξ£nΞ”H_f^{ ext{Β°}}( ext{products}) - Ξ£mΞ”H_f^{ ext{Β°}}( ext{reactants})$$

Where 'n' and 'm' are the stoichiometric coefficients. A practical example is providedβ€”calculating the combustion of methane (CHβ‚„), demonstrating how standard enthalpy values are applied.

2. Manipulating Known Reactions

This part emphasizes the importance of algebraically adjusting known reaction equations and their corresponding enthalpy changes to derive the enthalpy change for a desired reaction. An illustrative example calculates the enthalpy change for the conversion of carbon to carbon monoxide by reversing and adding known reactions.

Significance

Hess's Law is a vital tool in thermochemistry, allowing chemists to ascertain enthalpy changes for complex reactions effectively and reinforcing the understanding of enthalpy as a state function.

Audio Book

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Using Standard Enthalpies of Formation

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Hess's Law is commonly used in two main ways:
1. Using Standard Enthalpies of Formation (Ξ”H_fΒ°): The standard enthalpy change of a reaction (Ξ”H_rxnΒ°) can be calculated from the standard enthalpies of formation of the products and reactants using the formula:

Ξ”H_rxnΒ° = Ξ£nΞ”H_fΒ°(products) - Ξ£mΞ”H_fΒ°(reactants)

Where 'n' and 'm' are the stoichiometric coefficients in the balanced chemical equation. Remember that the Ξ”H_fΒ° for elements in their standard states is zero.

Detailed Explanation

This chunk explains one of the practical applications of Hess's Law where we use standard enthalpies of formation to calculate the overall change in enthalpy for a reaction. The formula presented allows us to sum the enthalpy contributions of products and subtract those of the reactants. The coefficients (n and m) indicate how many moles of each substance are involved in the balanced equation. Standard enthalpy of formation values for elements in their standard state is always zero, which simplifies calculations.

Examples & Analogies

Imagine you are making a cake. You have a recipe that tells you how much of each ingredient you need (the enthalpy of formation). The total amount of cake you can make (the enthalpy change of the reaction) will depend on all the ingredients you use. If you know the energy contribution of each ingredient, you can easily tally up the total energy needed for the entire cake.

Example of Calculating Enthalpy Change

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Example: Calculate Ξ”H_rxnΒ° for the combustion of methane: CHβ‚„(g) + 2Oβ‚‚(g) β†’ COβ‚‚(g) + 2Hβ‚‚O(l)
Given:
Ξ”H_fΒ°(CHβ‚„(g)) = -74.8 kJ mol⁻¹
Ξ”H_fΒ°(COβ‚‚(g)) = -393.5 kJ mol⁻¹
Ξ”H_fΒ°(Hβ‚‚O(l)) = -285.8 kJ mol⁻¹
Ξ”H_fΒ°(Oβ‚‚(g)) = 0 kJ mol⁻¹

Ξ”H_rxnΒ° = [1 Γ— Ξ”H_fΒ°(COβ‚‚(g)) + 2 Γ— Ξ”H_fΒ°(Hβ‚‚O(l))] - [1 Γ— Ξ”H_fΒ°(CHβ‚„(g)) + 2 Γ— Ξ”H_fΒ°(Oβ‚‚(g))]
Ξ”H_rxnΒ° = [1 Γ— (-393.5) + 2 Γ— (-285.8)] - [1 Γ— (-74.8) + 2 Γ— (0)]
Ξ”H_rxnΒ° = [-393.5 - 571.6] - [-74.8]
Ξ”H_rxnΒ° = -965.1 + 74.8 = -890.3 kJ mol⁻¹

Detailed Explanation

This chunk presents a specific calculation example using Hess's Law. It details the enthalpy of formation for each involved species in the combustion of methane, showing how to utilize the earlier formula. The calculation combines the two parts: the total energy for products minus the total energy for reactants. Each element’s enthalpy change is multiplied by its coefficient from the balanced equation before summing and subtracting.

Examples & Analogies

Think of this as calculating how much money you spend when shopping. You have a list of items (reactants) and their costs (enthalpy values). The total cost for your shopping (enthalpy change) is what you would do by summing the costs of all the items you buy and subtracting any discounts you have (like energy released during the reaction). Just as with shopping, the total money spent gives an idea of how much your efforts cost.

Using a Series of Known Reactions

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  1. Using a series of known reactions: This involves algebraically manipulating given equations to match the target equation.
    Example: Calculate Ξ”H for the reaction: C(s) + Β½Oβ‚‚(g) β†’ CO(g)
    Given:
  2. C(s) + Oβ‚‚(g) β†’ COβ‚‚(g) Ξ”H₁ = -393.5 kJ mol⁻¹
  3. CO(g) + Β½Oβ‚‚(g) β†’ COβ‚‚(g) Ξ”Hβ‚‚ = -283.0 kJ mol⁻¹
    To obtain the target equation:
    ● Keep equation (1) as is: C(s) + Oβ‚‚(g) β†’ COβ‚‚(g) Ξ”H₁ = -393.5 kJ mol⁻¹
    ● Reverse equation (2) and change the sign of Ξ”Hβ‚‚: COβ‚‚(g) β†’ CO(g) + Β½Oβ‚‚(g) -Ξ”Hβ‚‚ = +283.0 kJ mol⁻¹
    Add the manipulated equations: C(s) + Oβ‚‚(g) + COβ‚‚(g) β†’ COβ‚‚(g) + CO(g) + Β½Oβ‚‚(g)
    Cancel out common species (COβ‚‚ and Β½Oβ‚‚): C(s) + Β½Oβ‚‚(g) β†’ CO(g)
    Sum the manipulated enthalpy changes: Ξ”H_rxnΒ° = Ξ”H₁ + (-Ξ”Hβ‚‚) = -393.5 + 283.0 = -110.5 kJ mol⁻¹

Detailed Explanation

This segment describes an alternative method of using Hess's Law by manipulating known reactions to calculate the enthalpy change for a target reaction. The example illustrates how to rearrange two given reactions so that after summing them, the desired overall reaction emerges. It emphasizes the importance of reversing the equation, which necessitates changing the sign of the associated enthalpy change. After arranging the terms, you cancel out any repeated species, leading you to the required reaction and its associated enthalpy change.

Examples & Analogies

Imagine you are trying to get to a friend's house, but you need to take a detour because the main road is closed. You have a map (known equations) that shows you alternate paths (manipulated reactions) to reach your destination. You follow those paths, and when you reach your friend's house, you tally up the distances (enthalpy changes) for each segment. Just like calculating how far you traveled in total, you can gauge the overall β€˜cost’ of the journey in terms of energy.

Importance of Hess's Law

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Hess's Law is a powerful tool for calculating enthalpy changes for complex reactions and reinforcing the concept of enthalpy as a state function.

Detailed Explanation

The final chunk highlights the significance of Hess's Law in thermochemistry. It emphasizes how this law allows chemists to find enthalpy changes for reactions that are difficult to measure directly by simplifying the process with known reactions. It reiterates that enthalpy is a state function, meaning it only depends on the initial and final states, not how the reaction occurs. Thus, Hess's Law offers a way to understand and calculate energy changes systematically.

Examples & Analogies

Consider planning a vacation. Instead of visiting every place (complex reactions), you can look up travel guides (known reactions) that describe popular routes. You need only to piece together a journey with the best experiences while saving money on travel costs (enthalpy changes). This makes planning and costs clearer, similar to how Hess’s Law clarifies enthalpy in chemical reactions.

Definitions & Key Concepts

Learn essential terms and foundational ideas that form the basis of the topic.

Key Concepts

  • Hess's Law: Total enthalpy change is independent of the pathway taken.

  • Standard Enthalpy of Formation: It describes the enthalpy of compounds formed from their elements.

  • Manipulation of Reactions: Enthalpy changes can be summed through reaction manipulations.

Examples & Real-Life Applications

See how the concepts apply in real-world scenarios to understand their practical implications.

Examples

  • Calculating Ξ”H for the combustion of methane using standard enthalpies of formation.

  • Manipulating reactions for the formation of CO from C and Oβ‚‚ to illustrate Hess's Law.

Memory Aids

Use mnemonics, acronyms, or visual cues to help remember key information more easily.

🎡 Rhymes Time

  • Hess's Law we now know, pathways don't matter, that’s how it goes!

πŸ“– Fascinating Stories

  • Once upon a time, in a land of reactions, a clever chemist named Hess realized it didn’t matter how you got from starting materials to products; the total energy would always be the same, leading to his groundbreaking law!

🧠 Other Memory Gems

  • Acronym H.E.S.S. to remember Hess's Law: Heat Entropy States Same.

🎯 Super Acronyms

H.E.S.S. = Heat (constant) Enthalpy (same) State (function) Summation (pathways do not matter).

Flash Cards

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Glossary of Terms

Review the Definitions for terms.

  • Term: Hess's Law

    Definition:

    A principle stating that the total enthalpy change for a reaction is the sum of the enthalpy changes for each individual step.

  • Term: Standard Enthalpy of Formation (Ξ”H_fΒ°)

    Definition:

    The enthalpy change when one mole of a compound is formed from its elements in their standard states under standard conditions.

  • Term: Enthalpy Change (Ξ”H)

    Definition:

    The heat absorbed or released during a chemical reaction at constant pressure.

  • Term: Enthalpy (H)

    Definition:

    A thermodynamic property representing the total heat content of a system at constant pressure.