Welcome to Energetics II!
In your earlier studies, you learned about Hess’s Law and how to calculate enthalpy changes. Now, we are going to dive deeper. We will explore why some reactions happen spontaneously while others don’t, even if they need heat to get started. We will also look at the "glue" that holds ionic lattices together and how we can use cycles to calculate energy changes that are impossible to measure directly. Don’t worry if this seems like a lot of math at first—think of it like a giant logic puzzle where all the pieces eventually fit together!
13A: Lattice Energy – The Strength of Ionic Bonds
Why is salt a solid and not a gas? It’s all down to Lattice Energy. This is a measure of the strength of the attractions between ions in a giant ionic 1attice.
Key Definitions
To build a "Born-Haber Cycle" (our big energy puzzle), you need to know these definitions by heart:
1. Lattice Energy (\(\Delta_{latt}H\)): The energy change when one mole of an ionic solid is formed from its gaseous ions.
Example: \(Na^+(g) + Cl^-(g) \rightarrow NaCl(s)\)
Note: This is always exothermic (negative value) because you are making bonds!
2. Enthalpy Change of Atomisation (\(\Delta_{at}H\)): The energy change when one mole of gaseous atoms is formed from the element in its standard state.
Example: \(\frac{1}{2}Cl_2(g) \rightarrow Cl(g)\)
3. First Electron Affinity: The energy change when one mole of electrons is added to one mole of gaseous atoms to form one mole of gaseous 1- ions.
Example: \(O(g) + e^- \rightarrow O^-(g)\)
The Born-Haber Cycle
Think of a Born-Haber Cycle as a specific type of Hess’s Law cycle. It allows us to calculate the Lattice Energy, which we can't measure directly in a lab.
Step-by-step to build a cycle:
1. Start with the elements in their standard states at the bottom left.
2. Atomise the metal (solid to gas).
3. Ionise the metal (remove electrons).
4. Atomise the non-metal (e.g., break \(\frac{1}{2}Cl_2\) into \(Cl\)).
5. Use Electron Affinity on the non-metal (add electrons).
6. Drop down to the ionic solid using Lattice Energy.
7. The direct route from elements to solid is the Enthalpy of Formation (\(\Delta_{f}H\)).
Quick Review Box:
The sum of the "up" arrows equals the sum of the "down" arrows.
\(\Delta_{f}H = \Delta_{at}H(metal) + IE(metal) + \Delta_{at}H(non-metal) + EA(non-metal) + \Delta_{latt}H\)
Theoretical vs. Experimental Lattice Energy
We can calculate what a lattice energy should be using math (the Theoretical value, assuming ions are perfect spheres). We then compare this to the Experimental value we get from our Born-Haber cycle.
1. If the values are close: The compound is almost purely ionic (like \(NaCl\)).
2. If the experimental value is much larger (more exothermic) than the theoretical: The compound has covalent character. This happens because the ions are polarised.
Did you know?
Polarisation is when a positive ion (cation) pulls the electron cloud of a negative ion (anion) towards itself. It’s like a tug-of-war where the cation is winning!
Factors affecting Polarisation:
- Cations: Most polarising if they have a high charge and small radius.
- Anions: Most easily polarised if they have a high charge and large radius (the outer electrons are far from the nucleus and easy to "distort").
Key Takeaway: Large differences between theoretical and experimental lattice energies prove that "pure" ionic bonding is actually quite rare!
13B: Enthalpy of Solution and Hydration
Why do some things dissolve and others don't? We use another cycle for this.
Definitions
1. Enthalpy Change of Solution (\(\Delta_{sol}H\)): Energy change when one mole of an ionic solid dissolves in water to form an infinitely dilute solution.
2. Enthalpy Change of Hydration (\(\Delta_{hyd}H\)): Energy change when one mole of gaseous ions dissolve in water to form one mole of aqueous ions.
The Energy Cycle:
To dissolve a salt, you must:
1. Break the lattice into gaseous ions (The opposite of Lattice Energy).
2. Wrap those gaseous ions in water molecules (Hydration Enthalpy).
\(\Delta_{sol}H = \Delta_{hyd}H(cation) + \Delta_{hyd}H(anion) - \Delta_{latt}H\)
Common Mistake: Remember that Lattice Energy is defined as forming the solid. When dissolving, you are breaking it, so you must flip the sign of the Lattice Energy value in your calculation!
13C: Entropy – The Logic of Disorder
Have you noticed that your bedroom naturally gets messy, but never naturally tidies itself? That is Entropy (\(S\))! Entropy is a measure of disorder.
What increases Entropy?
1. Changing State: Gases have much higher entropy than liquids, and liquids have higher entropy than solids.
2. Dissolving: Dissolving a solid usually increases entropy because the ions are free to move.
3. Number of Moles: If a reaction produces more moles of gas than it starts with, \(\Delta S_{system}\) will be positive (more disorder).
Entropy Calculations
1. \(\Delta S_{system}\):
\(\Delta S_{system} = \Sigma S_{products} - \Sigma S_{reactants}\)
2. \(\Delta S_{surroundings}\):
When a reaction releases heat (exothermic), it makes the particles outside move faster, increasing their entropy.
\(\Delta S_{surroundings} = -\frac{\Delta H}{T}\)
Crucial Tip: \(\Delta H\) is usually in kJ, but Entropy is in J. You must multiply \(\Delta H\) by 1000 before using this formula!
3. Total Entropy (\(\Delta S_{total}\)):
For a reaction to happen (to be feasible), the Total Entropy Change must be positive.
\(\Delta S_{total} = \Delta S_{system} + \Delta S_{surroundings}\)
Key Takeaway: A reaction can be endothermic (takes in heat) and still happen if the increase in system entropy is big enough to outweigh the decrease in surroundings entropy!
13D: Gibbs Free Energy (\(\Delta G\))
Gibbs Free Energy is another way to predict if a reaction is "feasible" (can happen on its own).
The Master Equation
\(\Delta G = \Delta H - T\Delta S_{system}\)
- If \(\Delta G\) is negative (\(<0\)), the reaction is feasible.
- If \(\Delta G\) is positive (\(>0\)), the reaction is not feasible.
Analogy: Imagine \(\Delta H\) is the "cost" of the reaction in energy, and \(T\Delta S\) is the "payoff" in disorder. If the payoff is bigger than the cost, the reaction is a "go"!
Finding the Temperature of Feasibility
Sometimes a reaction only becomes feasible at high temperatures (like baking a cake). To find the exact temperature where it starts being feasible, we set \(\Delta G = 0\).
\(0 = \Delta H - T\Delta S\)
Rearranged: \(T = \frac{\Delta H}{\Delta S}\)
Gibbs and Equilibrium
There is a link between how feasible a reaction is and its equilibrium constant (\(K\)):
\(\Delta G = -RT \ln K\)
- If a reaction has a very negative \(\Delta G\), it is very feasible, so it will have a large \(K\) value (mostly products at equilibrium).
- If \(\Delta G\) is very positive, \(K\) will be very small (mostly reactants).
Kinetic vs. Thermodynamic Feasibility
Wait! You might calculate that a reaction has a negative \(\Delta G\), but when you mix the chemicals in a lab, nothing happens. Why?
This is Kinetic Inhibition. The reaction is thermodynamically feasible (it wants to happen), but the activation energy is too high. It’s like a ball at the top of a hill that needs a tiny push to start rolling.
Quick Review Box:
- \(\Delta G < 0\): Feasible.
- \(\Delta S_{total} > 0\): Feasible.
- If it doesn't happen despite these, it's because the rate is too slow (high activation energy).