Energetics and Thermodynamics: The Study of Chemical Energy
Welcome to the fascinating world of Energetics! This chapter is all about energy—why reactions happen, how much heat they give out (or take in), and what determines if a process is even possible. Understanding energy changes is crucial because it governs everything from how we cook food to how engineers design rocket fuels.
Don't worry if the terminology seems intimidating. We will break down these concepts step-by-step, using simple analogies to make sure you master these essential calculations!
3.1.4 Energetics (International AS)
3.1.4.1 Enthalpy Change ($\Delta H$)
When a chemical reaction occurs, energy is either released to the surroundings or absorbed from them. We call this energy change the enthalpy change ($\Delta H$).
Exothermic vs. Endothermic Reactions
- Exothermic Reactions: These reactions release heat energy into the surroundings. The surroundings get hotter.
Example: Burning fuels, setting cement, neutralisation reactions.
The enthalpy change ($\Delta H$) is negative (\(\Delta H < 0\)). Think of energy exiting the system.
- Endothermic Reactions: These reactions absorb heat energy from the surroundings. The surroundings get colder.
Example: Photosynthesis, dissolving certain salts (like ammonium nitrate in water), instant cold packs.
The enthalpy change ($\Delta H$) is positive (\(\Delta H > 0\)). Think of energy entering the system.
Standard Conditions and Notation
To compare reactions fairly, chemists measure enthalpy changes under standard conditions. These are:
- Pressure: 100 kPa (kilopascals)
- Temperature: A stated temperature, usually 298 K (25 °C)
- States: All substances must be in their standard physical states (e.g., water is liquid, oxygen is gas).
The symbol $\Delta H^{\ominus}$ (sometimes written as $\Delta H^{\circ}_{298}$) denotes a standard enthalpy change.
Key Definitions of Standard Enthalpy Changes
1. Standard Enthalpy of Combustion ($\Delta H^{\ominus}_{c}$):
This is the enthalpy change when one mole of a substance is completely burned in oxygen under standard conditions.
Example: Burning methane
$$
\text{CH}_4(\text{g}) + 2\text{O}_2(\text{g}) \longrightarrow \text{CO}_2(\text{g}) + 2\text{H}_2\text{O}(\text{l}) \quad \Delta H^{\ominus}_{c}
$$
Note: Combustion reactions are almost always exothermic ($\Delta H^{\ominus}_{c}$ is negative).
2. Standard Enthalpy of Formation ($\Delta H^{\ominus}_{f}$):
This is the enthalpy change when one mole of a compound is formed from its elements in their standard states under standard conditions.
Example: Forming liquid water
$$
\text{H}_2(\text{g}) + \frac{1}{2}\text{O}_2(\text{g}) \longrightarrow \text{H}_2\text{O}(\text{l}) \quad \Delta H^{\ominus}_{f}
$$
Tip: The $\Delta H^{\ominus}_{f}$ for any pure element in its standard state is zero.
Quick Review: Enthalpy Terminology
- $\Delta H$: Heat energy change at constant pressure.
- Exo: Negative $\Delta H$ (Releasing heat).
- Endo: Positive $\Delta H$ (Absorbing heat).
- $\Delta H^{\ominus}_{f}$: Forming 1 mole from elements.
- $\Delta H^{\ominus}_{c}$: Burning 1 mole completely.
3.1.4.2 Calorimetry (Measuring Energy)
Calorimetry is the experimental process of measuring the heat change, $q$, produced or absorbed during a reaction. If you know the heat change, you can calculate the molar enthalpy change ($\Delta H$) for the reaction.
The Heat Change Equation
The amount of heat energy ($q$) transferred can be calculated using this essential equation:
$$ q = mc\Delta T $$Where:
- $q$ = Heat energy change (usually measured in Joules, J)
- $m$ = Mass of the substance whose temperature changes (usually the water or solution, measured in g or kg).
- $c$ = Specific heat capacity of the substance (J g$^{-1}$ K$^{-1}$ or J kg$^{-1}$ K$^{-1}$). (You will not be expected to recall the value of $c$.)
- $\Delta T$ = Change in temperature (Final temperature – Initial temperature), measured in K or °C.
Analogy: Think of $c$ as how hard it is to heat something up. Water has a high $c$, so it takes a lot of energy ($q$) to raise the temperature ($\Delta T$) of a large mass ($m$).
Step-by-Step Calculation of Molar Enthalpy Change
The steps involve going from the measured heat ($q$) to the required molar enthalpy ($\Delta H$, measured in kJ mol$^{-1}$).
- Calculate $q$: Use $q = mc\Delta T$ to find the energy released or absorbed (in J).
- Convert $q$ to kJ: Divide the answer by 1000 (\(1 \text{ kJ} = 1000 \text{ J}\)).
- Calculate Moles ($n$): Determine the number of moles of the substance that actually reacted or was formed.
- Calculate Molar Enthalpy ($\Delta H$): Divide the energy released (in kJ) by the number of moles ($n$).
$$ \Delta H = \frac{q (\text{in kJ})}{n} $$ - Assign the Sign: Remember to look at the experiment. If the temperature increased (exothermic), $\Delta H$ must be negative. If the temperature decreased (endothermic), $\Delta H$ must be positive.
Always ensure the mass ($m$) in $q=mc\Delta T$ is the mass of the liquid being heated/cooled (usually water/solution), NOT the mass of the fuel or reacting solid. The specific heat capacity ($c$) used is usually that of water (4.18 J g$^{-1}$ K$^{-1}$).
3.1.4.3 Applications of Hess's Law
Sometimes, we cannot measure the enthalpy change for a reaction directly (e.g., if it's too slow, or multiple side reactions occur). This is where Hess's Law comes to the rescue.
Hess's Law Definition: The total enthalpy change for a reaction is independent of the route taken, provided the initial and final conditions are the same.
Analogy: Climbing a mountain. Whether you take a steep path directly or a winding, gentle path, the overall change in altitude (enthalpy) from base camp (reactants) to the summit (products) is the same.
Using Hess's Law Cycles
Hess's Law allows us to calculate an unknown $\Delta H$ by using known enthalpy changes. We arrange the reactions into a cycle and use the rule that the total energy change in one direction around the cycle equals the total energy change in the opposite direction.
1. Using Enthalpies of Formation ($\Delta H^{\ominus}_{f}$):
If you have formation data, the elements are the "common reference point" in the cycle.
$$ \Delta H_{\text{reaction}} = \sum \Delta H^{\ominus}_{f}(\text{products}) - \sum \Delta H^{\ominus}_{f}(\text{reactants}) $$2. Using Enthalpies of Combustion ($\Delta H^{\ominus}_{c}$):
If you have combustion data, the products of combustion ($\text{CO}_2$ and $\text{H}_2\text{O}$) are the "common reference point" in the cycle.
$$ \Delta H_{\text{reaction}} = \sum \Delta H^{\ominus}_{c}(\text{reactants}) - \sum \Delta H^{\ominus}_{c}(\text{products}) $$Tip: Notice the sign change! For formation, it’s Products minus Reactants. For combustion, it’s Reactants minus Products.
3.1.4.4 Bond Enthalpies
Chemical reactions involve breaking old bonds and forming new bonds. This process is accompanied by energy changes:
- Breaking bonds requires energy (endothermic, $+\Delta H$).
- Forming bonds releases energy (exothermic, $-\Delta H$).
Mean Bond Enthalpy Definition: The energy required to break one mole of a specified type of bond in a molecule in the gaseous state, averaged over many different compounds.
Calculating $\Delta H$ using Bond Enthalpies
The overall enthalpy change for a reaction can be estimated by summing the energy required to break bonds and the energy released when new bonds are formed:
$$ \Delta H_{\text{reaction}} \approx \sum (\text{Energy required to break bonds}) - \sum (\text{Energy released to form bonds}) $$ $$ \text{or simply: } \Delta H \approx \sum \Delta H_{\text{bonds broken}} - \sum \Delta H_{\text{bonds formed}} $$Why Bond Enthalpy Calculations are Approximate
Values calculated using mean bond enthalpies often differ from those calculated using Hess's Law (which are more accurate). This difference occurs because:
- Bond enthalpy values are mean (average) values, averaged across many different molecules. The exact energy to break a C–H bond in methane might be slightly different from breaking a C–H bond in propane.
- The calculation only works accurately for reactions in the gaseous phase, as bond enthalpy data refers to molecules in the gas state. If reactants or products are liquids or solids, extra energy changes (like vaporisation) are ignored, leading to an error.
3.1.8 Thermodynamics (International A2)
While AS Energetics covered enthalpy ($\Delta H$), A2 Thermodynamics introduces two more crucial concepts: Entropy ($\Delta S$) and Gibbs Free Energy ($\Delta G$). Together, these determine the true feasibility (spontaneity) of a reaction.
3.1.8.1 Born-Haber Cycles
Born-Haber cycles are special Hess's Law cycles used specifically for calculating the energy changes involved in forming ionic compounds (like salts) from their elements. They allow us to determine lattice enthalpy.
Key Definitions for Born-Haber Cycles
Born-Haber cycles rely on six definitions (all standard changes, $\Delta H^{\ominus}$):
- Standard Enthalpy of Formation ($\Delta H^{\ominus}_{f}$): Forming 1 mole of the compound from its elements (usually the final step).
- Enthalpy of Atomisation ($\Delta H^{\ominus}_{at}$): Forming 1 mole of gaseous atoms from the element in its standard state.
- First/Successive Ionisation Energy (IE): Energy required to remove 1 mole of electrons from 1 mole of gaseous atoms (forming cations).
- First/Successive Electron Affinity (EA): Energy change when 1 mole of electrons is added to 1 mole of gaseous atoms (forming anions).
- Lattice Enthalpy ($\Delta H^{\ominus}_{L}$): The energy change when 1 mole of an ionic compound is formed from its gaseous ions (Lattice Formation), or dissociated into gaseous ions (Lattice Dissociation).
- Enthalpy of Hydration ($\Delta H^{\ominus}_{hyd}$): The enthalpy change when 1 mole of gaseous ions dissolves in water to form 1 mol of aqueous ions.
Did you know? Ionisation energy is always positive (energy input), but the first electron affinity is often negative (energy released), while the second and subsequent electron affinities are always positive (harder to force an electron onto an already negative ion).
Constructing and Using the Cycle
By applying Hess's Law, the direct route (Formation) must equal the indirect route (Atomisation + Ionisation + Electron Affinity + Lattice Formation).
$$ \Delta H^{\ominus}_{f} = \Delta H^{\ominus}_{at}(\text{M}) + \Delta H^{\ominus}_{at}(\text{X}) + \text{IE}(\text{M}) + \text{EA}(\text{X}) + \Delta H^{\ominus}_{\text{Lattice Formation}} $$Comparison: Born-Haber vs. Theoretical Lattice Enthalpies
Chemists can calculate a theoretical lattice enthalpy assuming the compound is 100% perfectly ionic (using electrostatic theory).
- If the Born-Haber (experimental) value is close to the theoretical value, the compound is predominantly ionic.
- If the Born-Haber value is significantly more negative than the theoretical value, it indicates that the compound has a degree of covalent character. This extra stability comes from the attraction between the ions and the electron cloud being distorted (polarization).
Enthalpies of Solution and Hydration
Born-Haber type cycles can also be used to relate Lattice Enthalpy ($\Delta H^{\ominus}_{L}$), Enthalpy of Hydration ($\Delta H^{\ominus}_{hyd}$), and Enthalpy of Solution ($\Delta H^{\ominus}_{sol}$): the enthalpy change when one mole of a solute dissolves in a solvent to form a solution.
$$ \Delta H^{\ominus}_{sol} = \Delta H^{\ominus}_{\text{Lattice Dissociation}} + \sum \Delta H^{\ominus}_{hyd}(\text{ions}) $$3.1.8.2 Gibbs Free-Energy Change ($\Delta G$) and Entropy Change ($\Delta S$)
Entropy ($\Delta S$): The Measure of Disorder
Entropy ($\Delta S$) is a measure of the disorder or randomness of a system.
- An increase in disorder (more randomness) means $\Delta S$ is positive. (Favourable)
- A decrease in disorder (more order) means $\Delta S$ is negative. (Unfavourable)
The general trend is: Gas > Liquid > Solid. A reaction that produces more moles of gas will generally have a positive $\Delta S$.
We calculate the standard entropy change for a reaction using the absolute entropy values:
$$ \Delta S^{\ominus}_{\text{reaction}} = \sum S^{\ominus}(\text{products}) - \sum S^{\ominus}(\text{reactants}) $$Gibbs Free Energy ($\Delta G$): The Key to Feasibility
While $\Delta H$ is important, it alone does not determine if a reaction will happen. Many endothermic reactions (positive $\Delta H$) still occur because the increase in entropy is favourable.
Gibbs Free Energy ($\Delta G$) combines $\Delta H$ and $\Delta S$ to determine the feasibility (spontaneity) of a chemical change:
$$ \Delta G = \Delta H - T\Delta S $$(Note: The derivation of this equation is not required.)
Where $T$ is the temperature in Kelvin (K).
Feasibility Condition
For a reaction or process to be feasible (to occur spontaneously) at a given temperature, the Gibbs Free Energy change must be zero or negative:
$$ \Delta G \leq 0 $$The Power of Temperature (T)
The term $T\Delta S$ in the Gibbs equation shows the influence of temperature on entropy. The higher the temperature, the more significant the entropy term becomes, often overriding an unfavourable positive $\Delta H$.
We can determine the temperature ($T$) at which a reaction becomes feasible by setting $\Delta G = 0$:
$$ 0 = \Delta H - T\Delta S $$
$$ T = \frac{\Delta H}{\Delta S} $$
Summary of Feasibility based on $\Delta H$ and $\Delta S$
| $\Delta H$ | $\Delta S$ | $\Delta G = \Delta H - T\Delta S$ | Feasibility |
|---|---|---|---|
| Negative (Exo) | Positive (Increase) | Always Negative | Feasible at all temperatures |
| Positive (Endo) | Negative (Decrease) | Always Positive | Never feasible |
| Negative (Exo) | Negative (Decrease) | Negative at low T | Feasible at low temperatures |
| Positive (Endo) | Positive (Increase) | Negative at high T | Feasible at high temperatures |
This table helps you predict the conditions needed for any reaction!
Key Takeaway: The Three Pillars of Energetics
Energetics is all about calculations and cycles. Ensure you can:
- Calculate $\Delta H$ from experimental data ($q=mc\Delta T$ and moles).
- Calculate $\Delta H$ using Hess's Law cycles (Combustion or Formation data).
- Calculate $\Delta H$ using Bond Enthalpies (recognizing its limitations).
- Calculate $\Delta S$ and use $\Delta G = \Delta H - T\Delta S$ to determine if a reaction is feasible.
- Construct and use Born-Haber cycles to find lattice enthalpy or related unknown values.