Chemistry | Energy cycles in reactions

Welcome to Thermochemistry: Energy Cycles in Reactions!

Hello future Chemist! This chapter, Energy Cycles in Reactions (Reactivity 1.2), is the cornerstone of predicting and understanding energy flow in chemical systems. You already know that reactions either release heat (exothermic) or absorb heat (endothermic). But how do we calculate exactly how much energy is involved, especially for reactions that are impossible or too dangerous to measure directly?

The answer lies in mastering Hess's Law and energy cycles. Don't worry if this seems tricky at first; we will break down the complex calculations into simple, repeatable steps, using analogies you encounter every day. Let's dive in!

Quick Review: Enthalpy Change (\(\Delta H\))

Before tackling cycles, we must remember the fundamental measure of energy change: Enthalpy (\(H\)).

• Enthalpy Change (\(\Delta H\)): The heat absorbed or released during a chemical reaction at constant pressure.
• Exothermic Reactions: Energy is released (feels hot). Products have lower energy than reactants.
  \(\Delta H\) is negative (\(\Delta H < 0\)).
  Analogy: Burning wood releases energy.
• Endothermic Reactions: Energy is absorbed (feels cold). Products have higher energy than reactants.
  \(\Delta H\) is positive (\(\Delta H > 0\)).
  Analogy: Melting ice absorbs energy from your hand.

Key Takeaway: The sign of \(\Delta H\) tells you the direction of heat flow (negative = released, positive = absorbed).

Section 1: Hess's Law – The Chemical Shortcut

1.1 What is Hess's Law?

Hess's Law (also known as the Law of Constant Heat Summation) states that the total enthalpy change for a reaction is independent of the pathway taken between the initial and final states.

Think of it this way: If you want to travel from your home (Reactants) to your school (Products), the total distance traveled (Enthalpy Change) is the same, whether you take the direct road or stop at three friends' houses along the way.

Why is Hess's Law so important?

It allows us to calculate the \(\Delta H\) for reactions that:

1. Are too slow to measure accurately.
2. Produce unwanted side products, contaminating the measurement.
3. Are too explosive or difficult to manage in a calorimeter.

1.2 Rules for Manipulating Equations in Hess's Cycles

When using known reactions (steps in the journey) to find the unknown reaction (the total journey), you must follow these algebraic rules:

• Reversing an Equation: If you reverse a chemical equation, you must reverse the sign of the corresponding \(\Delta H\).
  Example: If \(\text{A} \rightarrow \text{B}\) has \(\Delta H = +50 \text{ kJ}\), then \(\text{B} \rightarrow \text{A}\) must have \(\Delta H = -50 \text{ kJ}\).
• Multiplying an Equation: If you multiply the coefficients of an equation by a factor (\(n\)), you must multiply the \(\Delta H\) by the same factor (\(n\)).
  Example: If \(\text{C} \rightarrow \text{D}\) has \(\Delta H = -10 \text{ kJ}\), then \(2\text{C} \rightarrow 2\text{D}\) must have \(\Delta H = -20 \text{ kJ}\).
• Adding Equations: When you add two or more equations together, you add their \(\Delta H\) values to get the overall \(\Delta H\). (Species appearing on both sides of the arrow can be canceled out).

Key Takeaway: Hess’s Law allows us to treat chemical equations like algebraic formulas, manipulating them and their \(\Delta H\) values to find the net energy change.

Section 2: Calculating \(\Delta H\) using Standard Enthalpy Data

We often use tables of standard enthalpy values (measured under standard conditions: 100 kPa pressure, 298 K temperature, and 1 mol/L concentration) to apply Hess's Law.

2.1 Standard Enthalpy of Formation (\(\Delta H_f^\circ\))

The standard enthalpy of formation (\(\Delta H_f^\circ\)) is the enthalpy change when one mole of a compound is formed from its constituent elements in their standard states.

• Elements in their standard state (e.g., \(\text{O}_2(g)\), \(\text{C}(s)\), \(\text{Fe}(s)\)) have a \(\Delta H_f^\circ\) value of zero.
• This is the most common data set used for Hess's Law calculations.

Calculation Method 1: Using \(\Delta H_f^\circ\)

When using formation data, the reaction can be visualized as all reactants decomposing into their elements, and then these elements reforming into the products.

The standard formula derived from Hess's Law for calculating the enthalpy change of a reaction (\(\Delta H_{rxn}^\circ\)) is:

\(\Delta H_{rxn}^\circ = \sum n \Delta H_f^\circ (\text{Products}) - \sum m \Delta H_f^\circ (\text{Reactants})\)

Where \(n\) and \(m\) are the stoichiometric coefficients from the balanced equation.

2.2 Standard Enthalpy of Combustion (\(\Delta H_c^\circ\))

The standard enthalpy of combustion (\(\Delta H_c^\circ\)) is the enthalpy change when one mole of a substance is completely burned in oxygen under standard conditions.

• Combustion reactions always release energy, so \(\Delta H_c^\circ\) values are always negative.

Calculation Method 2: Using \(\Delta H_c^\circ\)

Combustion data is used when all reactants and products can be combusted. The cycle is formed around the common products of combustion (like \(\text{CO}_2\) and \(\text{H}_2\text{O}\)).

\(\Delta H_{rxn}^\circ = \sum m \Delta H_c^\circ (\text{Reactants}) - \sum n \Delta H_c^\circ (\text{Products})\)

Notice the flip! Combustion is Reactants minus Products. This is because the combustion reactions must be reversed (products of the target reaction are turned back into elements/combustion products) to complete the cycle pathway.

Did you know? The concept of using formation energies to calculate reaction energy is widely used in computational chemistry to predict the viability of new synthetic pathways before ever stepping into a lab.

Key Takeaway: Hess's Law calculations rely on defining a common intermediate state (usually elements for formation, or combustion products for combustion) to complete the cycle path.

Section 3: Bond Enthalpies and Energy Profiles

3.1 Using Average Bond Enthalpies

Instead of using standard heats of formation, we can estimate \(\Delta H\) by looking at the energy required to break and form chemical bonds.

• Bond Enthalpy: The energy required to break one mole of a specific bond in the gaseous state.

The calculation is based on the idea that energy is required to break bonds (endothermic, \(\Delta H\) positive) and energy is released when new bonds form (exothermic, \(\Delta H\) negative).

The Calculation

\(\Delta H_{rxn} = (\text{Energy required to break bonds}) - (\text{Energy released to form bonds})\)

\(\Delta H_{rxn} = \sum (\text{Bond Enthalpies of Reactants}) - \sum (\text{Bond Enthalpies of Products})\)

Mnemonics: Broken minus Formed (BB-BF). Bonds are Broken (reactants) before they are Formed (products).

Limitations of Bond Enthalpy Calculations

Calculations using bond enthalpies are usually estimates, not exact values, because:

1. Average Values: The tabulated values are average bond enthalpies taken from a range of molecules, not the specific energy for that bond in the molecule being studied.
2. Gaseous State: Bond enthalpies are defined only for substances in the gaseous state. If the reaction involves liquids or solids, the calculated value ignores the energy needed for phase changes (like vaporization).

3.2 Energy Profile Diagrams (Reaction Profiles)

Energy profile diagrams visually represent the energy changes during a reaction. They are essential for linking thermodynamics (\(\Delta H\)) with kinetics (activation energy).

• Activation Energy (\(E_a\)): The minimum energy required to start a reaction (to break the initial bonds). It is the energy difference between the reactants and the highest point on the curve (the transition state).
• \(\Delta H\): The energy difference between the final products and the initial reactants.

(Note: In exam situations, you would draw or interpret these diagrams. For an exothermic reaction, the products line is lower than the reactants line, and for an endothermic reaction, the products line is higher.)

Visualizing Exothermic vs. Endothermic Reactions

• Exothermic: The initial reactants are higher than the products. Heat is given off.
• Endothermic: The initial reactants are lower than the products. Heat is taken in.

Key Takeaway: Bond enthalpy calculations estimate the energy required to rearrange atoms, and profile diagrams visualize the energy path of the reaction.

Section 4: Energy from Fuels (Reactivity 1.3)

The combustion reactions we calculate using Hess's Law have critical real-world applications, especially concerning energy generation.

4.1 Calorific Value and Energy Density

When comparing fuels, we look at how much energy they release per unit of mass or volume.

• Calorific Value (Specific Energy): The energy released per unit mass (often \(\text{kJ/g}\) or \(\text{MJ/kg}\)). This is useful for comparing transport fuels where weight matters.
• Energy Density: The energy released per unit volume (often \(\text{J/cm}^3\)). This is useful for comparing fuels used in stationary power plants where storage space matters.

Real-World Example: Hydrogen gas has an extremely high calorific value (it releases a huge amount of energy per gram), making it very efficient by mass. However, because it is a gas and difficult to compress/store, it has a very low energy density compared to liquid gasoline or diesel.

4.2 Efficiency of Fuels

The combustion of fuels like coal, oil, and natural gas provides large amounts of energy, but the process is never 100% efficient due to energy losses (usually as waste heat).

The calculated enthalpy of combustion (\(\Delta H_c\)) represents the maximum theoretical energy yield. Practical energy yield is always lower.

Section 5: HL Extension – Entropy and Spontaneity (Reactivity 1.4)

Welcome HL students! While enthalpy (\(\Delta H\)) tells us about heat energy, it doesn't tell us if a reaction will happen naturally. To determine spontaneity (whether a reaction proceeds on its own), we must introduce entropy.

5.1 Defining Entropy (\(S\))

Entropy (\(S\)) is a measure of the disorder or randomness of a system.

• The more ways energy can be distributed among the particles, the higher the entropy.
• Second Law of Thermodynamics: For a process to be spontaneous, the total entropy of the universe must increase (\(\Delta S_{\text{universe}} > 0\)).

Predicting Entropy Change (\(\Delta S\))

A positive change in entropy (\(\Delta S > 0\)) means the system becomes more disordered. This usually happens when:

1. A solid or liquid turns into a gas (gas has much higher disorder).
2. A solid or liquid dissolves to form a solution.
3. The number of moles of gas increases during the reaction.
4. A complex molecule breaks down into simpler ones.

5.2 Gibbs Free Energy (\(\Delta G\))

To combine the effects of enthalpy (energy change) and entropy (disorder change) at a constant temperature (\(T\)), we use the Gibbs Free Energy (\(\Delta G\)) equation:

\(\Delta G = \Delta H - T \Delta S\)

Note: \(T\) must always be in Kelvin (\(\text{K}\)). \(\Delta S\) is often measured in \(\text{J K}^{-1} \text{mol}^{-1}\), while \(\Delta H\) is in \(\text{kJ mol}^{-1}\). Remember to convert one unit before calculating \(\Delta G\)!

5.3 Criteria for Spontaneity

The sign of \(\Delta G\) directly determines if a reaction is spontaneous:

• If \(\Delta G < 0\) (Negative): The reaction is spontaneous (or feasible) at the given temperature.
• If \(\Delta G > 0\) (Positive): The reaction is non-spontaneous.
• If \(\Delta G = 0\): The system is at equilibrium.

The Four Scenarios

Spontaneity depends on the combination of \(\Delta H\) and \(\Delta S\):

The Crossover Temperature: You can find the temperature (\(T\)) at which a reaction shifts from non-spontaneous to spontaneous by setting \(\Delta G = 0\):

\(0 = \Delta H - T \Delta S \Rightarrow T = \frac{\Delta H}{\Delta S}\)

Key Takeaway (HL): Enthalpy (energy minimum) favors spontaneity, but entropy (disorder maximum) also favors it. Gibbs Free Energy combines these factors to give the definitive answer on whether a reaction will proceed naturally.