Enthalpy and entropy

Welcome to the World of Energy!

In this chapter, we are going explore why some chemical reactions happen in a flash while others don't happen at all. We will look at Enthalpy (the heat energy in a system), Entropy (the "chaos" or dispersal of energy), and finally, Gibbs Free Energy—the ultimate decider of whether a reaction is "feasible" (scientifically possible).

Don’t worry if this seems a bit heavy at first! We’ll break it down into bite-sized pieces with plenty of analogies to help it stick.

1. Enthalpy Changes: The Basics

Everything in the universe wants to be at the lowest energy possible. Think of a ball at the top of a hill; it naturally wants to roll down. In Chemistry, we measure these energy changes using Enthalpy (\(H\)). We can't measure the total enthalpy of a substance, but we can measure the Enthalpy Change (\(\Delta H\)) when a reaction occurs.

Exothermic vs. Endothermic

• Exothermic (\(\Delta H\) is negative): Energy is released to the surroundings. The chemicals lose energy, so the surroundings get hotter. Think of a hand warmer or a burning match.
• Endothermic (\(\Delta H\) is positive): Energy is absorbed from the surroundings. The chemicals gain energy, so the surroundings get colder. Think of an instant ice pack used for sports injuries.

Activation Energy (\(E_a\))

Even if a reaction releases energy, it often needs a "spark" to get going. This minimum energy required to start a reaction is the Activation Energy.
Analogy: Imagine you are trying to roll a boulder down a hill, but there is a small bump at the very top. You need to push the boulder over that small bump (the Activation Energy) before it can roll down the rest of the way.

Quick Review Box:
- Exothermic: Releases heat (\(-\Delta H\)).
- Endothermic: Absorbs heat (\(+\Delta H\)).
- Standard Conditions: Pressure of \(100 \text{ kPa}\) and temperature of \(298 \text{ K}\) (\(25^{\circ}\text{C}\)).

2. Key Enthalpy Definitions

The OCR syllabus requires you to know these specific definitions. Memory Aid: Always check the "Standard State" (the physical state of a substance under standard conditions, e.g., oxygen is a gas, water is a liquid).

• Enthalpy change of reaction (\(\Delta_r H\)): The enthalpy change that accompanies a reaction in the molar quantities shown in a chemical equation.
• Enthalpy change of formation (\(\Delta_f H\)): The enthalpy change when 1 mole of a compound is formed from its elements in their standard states. (Note: \(\Delta_f H\) of an element is always \(0\)).
• Enthalpy change of combustion (\(\Delta_c H\)): The enthalpy change when 1 mole of a substance reacts completely with oxygen.
• Enthalpy change of neutralisation (\(\Delta_{neut} H\)): The enthalpy change when an acid and a base react to form 1 mole of water.

Key Takeaway: Always ensure you are talking about 1 mole of the specific product (for formation/neutralisation) or reactant (for combustion) mentioned in the definition!

3. Measuring Enthalpy: \(q = mc\Delta T\)

We can calculate the energy change in a lab using calorimetry. We usually use the reaction to heat up (or cool down) a known mass of water.

The formula is: \(q = mc\Delta T\)

• \(q\): Heat energy exchanged (in Joules, J).
• \(m\): Mass of the substance being heated (usually the water or solution, in grams).
• \(c\): Specific heat capacity (for water, this is \(4.18 \text{ J g}^{-1} \text{ K}^{-1}\)).
• \(\Delta T\): Change in temperature (in \(K\) or \(^{\circ}\text{C}\)).

To find the molar enthalpy change (\(\Delta H\)), you then divide \(q\) (converted to kJ) by the number of moles (\(n\)) that reacted: \(\Delta H = \frac{-q}{n}\).
Common Mistake: Don't forget the negative sign for exothermic reactions! If the temperature goes up, \(\Delta H\) must be negative.

4. Bond Enthalpies

Breaking bonds requires energy (Endothermic), while making bonds releases energy (Exothermic).
Mnemonic: "BENDO MEXO" (Bond breaking = Endo; Making = Exo).

Average Bond Enthalpy: The energy needed to break 1 mole of a specified type of bond in a gaseous molecule.
Note: These are average values because the actual energy depends on the surrounding atoms in a specific molecule.

Calculation Tip:
\(\Delta H = \Sigma(\text{bond enthalpies of reactants}) - \Sigma(\text{bond enthalpies of products})\)

5. Hess’ Law and Enthalpy Cycles

Hess' Law states that the total enthalpy change for a reaction is the same, regardless of the route taken. This is like saying if you travel from London to Manchester, the total distance change is the same whether you drive direct or go via Birmingham.

Hess Cycles from Formation Data

If you are given \(\Delta_f H\) values, the elements go at the bottom of the cycle.
Formula: \(\Delta H_{reaction} = \Sigma \Delta_f H (\text{products}) - \Sigma \Delta_f H (\text{reactants})\)

Hess Cycles from Combustion Data

If you are given \(\Delta_c H\) values, the combustion products (\(\text{CO}_2\) and \(\text{H}_2\text{O}\)) go at the bottom.
Formula: \(\Delta H_{reaction} = \Sigma \Delta_c H (\text{reactants}) - \Sigma \Delta_c H (\text{products})\)

6. Lattice Enthalpy: Energy in Ionic Solids

Lattice Enthalpy (\(\Delta_{LE} H\)): The enthalpy change that accompanies the formation of 1 mole of an ionic lattice from its gaseous ions.
Example: \(\text{Na}^+(g) + \text{Cl}^-(g) \rightarrow \text{NaCl}(s)\)

Lattice enthalpy is always exothermic (negative) because you are making very strong ionic bonds. It is a measure of ionic bond strength.

Factors affecting Lattice Enthalpy

• Ionic Radius: Smaller ions can get closer together, leading to a stronger attraction and a more exothermic lattice enthalpy.
• Ionic Charge: Higher charged ions (e.g., \(\text{Mg}^{2+}\) vs \(\text{Na}^+\)) have a much stronger electrostatic attraction, leading to a more exothermic lattice enthalpy.

Enthalpy Change of Hydration and Solution

When an ionic solid dissolves, two things happen: the lattice breaks (requires energy) and the ions bond to water molecules (releases energy).

• Enthalpy change of solution (\(\Delta_{sol}H\)): Dissolving 1 mole of solute in water.
• Enthalpy change of hydration (\(\Delta_{hyd}H\)): Dissolving 1 mole of gaseous ions in water to form aqueous ions.

7. Entropy (\(S\)): The Measure of Disorder

Entropy is a measure of the dispersal of energy within a system. The more disordered a system is, the higher its entropy.
Analogy: Think of your bedroom. If all your clothes are folded in drawers, the entropy is low. If your clothes are scattered all over the floor, the entropy is high. Energy naturally tends to spread out (increase entropy).

Magnitude of Entropy

Gases > Liquids > Solids
Gases have the highest entropy because the particles are flying around randomly. Solids have the lowest because the particles are fixed in a neat lattice.

Predicting Entropy Changes (\(\Delta S\))

• If a reaction produces more moles of gas than it starts with, \(\Delta S\) is positive (disorder increases).
• If a reaction produces fewer moles of gas, \(\Delta S\) is negative (disorder decreases).

Calculation:
\(\Delta S = \Sigma S(\text{products}) - \Sigma S(\text{reactants})\)
Warning: Entropy values are usually given in \(\text{J K}^{-1} \text{ mol}^{-1}\). You must convert them to \(\text{kJ K}^{-1} \text{ mol}^{-1}\) (divide by 1000) before using them in the Gibbs equation!

8. Gibbs Free Energy (\(\Delta G\)): Is it Feasible?

A reaction is feasible (spontaneous) if it can happen on its own at a certain temperature. To decide this, we combine Enthalpy, Entropy, and Temperature into the Gibbs Equation:

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

• \(\Delta G\): Free energy change (in \(\text{kJ mol}^{-1}\)).
• \(\Delta H\): Enthalpy change (in \(\text{kJ mol}^{-1}\)).
• \(T\): Temperature in Kelvin (\(K = ^{\circ}\text{C} + 273\)).
• \(\Delta S\): Entropy change (must be in \(\text{kJ K}^{-1} \text{ mol}^{-1}\)).

The Golden Rule:
For a reaction to be feasible, \(\Delta G\) must be negative (\(\Delta G < 0\)).

Temperature and Feasibility

• If \(\Delta H\) is negative and \(\Delta S\) is positive, \(\Delta G\) is always negative. The reaction is feasible at all temperatures.
• If \(\Delta H\) is positive and \(\Delta S\) is negative, \(\Delta G\) is always positive. The reaction is never feasible.
• If both are positive (or both negative), the feasibility depends on the temperature.

Limitations of \(\Delta G\)

Even if \(\Delta G\) is negative, a reaction might not actually happen. Why? Because the Activation Energy might be too high, making the reaction too slow to observe. This is the difference between Thermodynamics (will it happen?) and Kinetics (how fast will it happen?).

Key Takeaway Summary:
- Enthalpy (\(\Delta H\)): Heat energy change.
- Entropy (\(\Delta S\)): Dispersal of energy/disorder.
- Feasibility: Occurs when \(\Delta G < 0\).
- Equation: \(\Delta G = \Delta H - T\Delta S\).