Chemistry Study Notes: Stoichiometric Calculations Involving Energy Terms

Hello! Welcome to the fascinating world of Chemical Energetics. Ever wondered why a hand warmer gets hot, or why a cold pack feels icy without being in a freezer? It's all about energy changes in chemical reactions! In this chapter, we'll explore how to measure and calculate the energy involved in these changes. Don't worry if this sounds tricky at first; we'll break it all down with simple examples and analogies. Let's get started!


1. Energy In, Energy Out: Exothermic & Endothermic Reactions

Every chemical reaction involves an energy change. Think of it like a transaction. Sometimes energy is paid out, and sometimes it's taken in. These are the two main types:

Exothermic Reactions (Energy EXITS)

These reactions release energy into the surroundings, usually as heat. This makes the surroundings feel warmer.

  • Think about: A bonfire, a hand warmer, or the combustion of fuel in a car engine.
  • Key feature: The products have less energy stored in their chemical bonds than the reactants did. The extra energy is released.
  • Memory Aid: EXOthermic sounds like EXIT. Heat is exiting the system!
Endothermic Reactions (Energy ENTERS)

These reactions absorb energy from the surroundings. This makes the surroundings feel colder.

  • Think about: An instant cold pack, photosynthesis, or cooking an egg. The egg absorbs heat energy to become cooked.
  • Key feature: The products have more energy stored in their chemical bonds than the reactants. They had to absorb this energy from the outside.
  • Memory Aid: ENDOthermic sounds like ENTER. Heat is entering the system!

Key Takeaway

Exothermic = Releases heat (gets hot).
Endothermic = Absorbs heat (gets cold).


2. Putting a Number on It: Enthalpy Change (ΔH)

Chemists need a way to measure the exact amount of heat released or absorbed. We use a concept called enthalpy change.

Enthalpy (H) is a measure of the total heat content of a system. We can't measure it directly, but we can measure the change in enthalpy during a reaction.

Enthalpy Change (ΔH) is the heat energy change of a system at constant pressure. Its sign tells us whether a reaction is exothermic or endothermic.

The All-Important Sign Convention:
  • For an exothermic reaction, heat is lost from the system, so ΔH is negative (e.g., $$ \Delta H = -100 \text{ kJ mol}^{-1} $$).
  • For an endothermic reaction, heat is gained by the system, so ΔH is positive (e.g., $$ \Delta H = +50 \text{ kJ mol}^{-1} $$).
Visualising Energy: Enthalpy Profile Diagrams

These diagrams are simple graphs that show the energy level of reactants and products.

Exothermic Reaction Profile:

Reactants start with high energy, release energy, and end up as lower-energy products. It's like rolling a ball downhill.

Reactants
↓ (Energy released, ΔH is negative)
Products


Endothermic Reaction Profile:

Reactants start with low energy, absorb energy, and end up as higher-energy products. It's like pushing a ball uphill.

Products
↑ (Energy absorbed, ΔH is positive)
Reactants

Key Takeaway

Negative ΔH = Exothermic (heat released).
Positive ΔH = Endothermic (heat absorbed).


3. The Story of Bonds: Why Energy Changes Happen

The energy changes in a reaction all come down to one thing: chemical bonds.

Think of it like building with Lego bricks:

  • Bond Breaking: To start a reaction, you must first break the existing bonds in the reactants. This always requires energy input. (It takes effort to pull Lego bricks apart!)
  • Bond Forming: When new bonds are made to form the products, energy is always released. (There's a satisfying 'click' of energy release when Lego bricks snap together!)

The overall enthalpy change (ΔH) is the net result of these two processes.

$$ \Delta H = \text{(Total energy absorbed to break bonds)} - \text{(Total energy released when forming bonds)} $$

  • If more energy is released than absorbed → Exothermic reaction (ΔH is negative).
  • If more energy is absorbed than released → Endothermic reaction (ΔH is positive).

Key Takeaway

Bond Breaking is ENDOthermic.
Bond Forming is EXOthermic.


4. Keeping it Fair: Standard Enthalpy Changes

To compare the energy changes of different reactions, we need to test them under the same, fair conditions. These are called standard conditions.

Standard Conditions:

  • Temperature: 298 K (25 °C)
  • Pressure: 1 atmosphere (atm)
  • Concentration: 1.0 M for all solutions

When an enthalpy change is measured under these conditions, we call it a standard enthalpy change and give it the symbol $$ \Delta H^\ominus $$ (pronounced 'delta H standard').

Important Types of Standard Enthalpy Changes

Here are three key definitions you need to know. The "per mole" part is crucial!

1. Standard Enthalpy Change of Formation ($$\Delta H_f^\ominus$$)

  • Definition: The enthalpy change when one mole of a compound is formed from its elements in their standard states.
  • Example: $$ C(s) + 2H_2(g) \rightarrow CH_4(g) \quad \Delta H_f^\ominus = -74.8 \text{ kJ mol}^{-1} $$
  • Note: The $$ \Delta H_f^\ominus $$ of any element in its standard state (like O₂(g) or C(s)) is ZERO.

2. Standard Enthalpy Change of Combustion ($$\Delta H_c^\ominus$$)

  • Definition: The enthalpy change when one mole of a substance is completely burned in excess oxygen under standard conditions.
  • Example: $$ CH_4(g) + 2O_2(g) \rightarrow CO_2(g) + 2H_2O(l) \quad \Delta H_c^\ominus = -890 \text{ kJ mol}^{-1} $$
  • Note: Combustion is always exothermic, so $$ \Delta H_c^\ominus $$ is always negative!

3. Standard Enthalpy Change of Neutralisation ($$\Delta H_{neut}^\ominus$$)

  • Definition: The enthalpy change when one mole of water is formed from the reaction between an acid and an alkali under standard conditions.
  • Example: $$ H^+(aq) + OH^-(aq) \rightarrow H_2O(l) \quad \Delta H_{neut}^\ominus \approx -57.3 \text{ kJ mol}^{-1} $$ for any strong acid and strong alkali.

Key Takeaway

Standard conditions allow for fair comparison. The definitions of formation, combustion, and neutralisation are all for the change involving ONE MOLE of a specific substance.


5. The Experiment: Simple Calorimetry

How do we actually measure heat change in the lab? We use a technique called calorimetry. For our purposes, a simple setup with a polystyrene cup works well because it's a good heat insulator.

The key idea is to measure the temperature change of the surroundings (usually water or a solution) and use it to calculate the heat absorbed or released by the reaction.

The Magic Formula:

$$ q = mc\Delta T $$

Where:

  • q = heat change (in Joules, J)
  • m = mass of the solution being heated or cooled (in grams, g). For solutions, we often assume the density is 1 g cm⁻³, so volume = mass.
  • c = specific heat capacity of the solution (usually taken as that of water, 4.2 J g⁻¹ K⁻¹). This is the energy needed to raise 1g of a substance by 1K.
  • $$ \Delta T $$ = the change in temperature (in K or °C). $$ T_{final} - T_{initial} $$
Step-by-Step Calculation Guide:
  1. Find q: Use $$ q = mc\Delta T $$ to find the heat change in Joules.
  2. Find Moles: Calculate the number of moles of the reactant that was the limiting factor (or moles of product formed, e.g., water in neutralisation).
  3. Find ΔH: Calculate the enthalpy change per mole. $$ \Delta H = \frac{q}{\text{moles}} $$
  4. Add the Sign: If the temperature increased, the reaction was exothermic, so make ΔH negative. If the temperature decreased, it was endothermic, so make ΔH positive.
  5. Check Units: Your answer from step 3 will be in J mol⁻¹. Divide by 1000 to get the standard unit, kJ mol⁻¹.
Common Mistakes to Avoid!
  • Forgetting to add the negative sign for exothermic reactions.
  • Using the mass of a solid reactant instead of the total mass of the final solution for 'm'.
  • Mixing up Joules and kiloJoules. Always convert at the end!

6. The Clever Shortcut: Hess's Law

What if a reaction is too slow, too explosive, or produces unwanted side products? We can't measure its ΔH directly. This is where Hess's Law comes to the rescue!

Hess's Law: The total enthalpy change of a reaction is the same, no matter which route is taken from reactants to products.

The Mountain Analogy: Imagine climbing a mountain. The total change in your altitude is the same whether you take a short, steep path directly to the top (Route A) or a long, winding path (Route B). The start and end points are all that matter.

We use this principle to build Hess's Cycles. We find an indirect route between reactants and products using reactions whose ΔH values we already know (like formation or combustion).

Applying Hess's Law (The Calculation)

Let's say we want to find the enthalpy change for reaction A → B.

If we know the values for an indirect route (e.g., A → C and B → C), we can set up a cycle.

Hess's Law states: $$ \Delta H_{Route 1} = \Delta H_{Route 2} $$

To solve the cycle, you follow the arrows. If you go with an arrow, you add the ΔH value. If you have to go against an arrow, you subtract its ΔH value (or flip the sign).

Two Common Types of Hess's Cycles:
1. Using Enthalpies of Formation ($$\Delta H_f^\ominus$$):
  • The indirect route involves forming both reactants and products from their constituent elements.
  • The arrows for $$ \Delta H_f^\ominus $$ always point UP from the elements to the compounds.
  • Formula shortcut: $$ \Delta H_{reaction}^\ominus = \sum \Delta H_f^\ominus (\text{Products}) - \sum \Delta H_f^\ominus (\text{Reactants}) $$
2. Using Enthalpies of Combustion ($$\Delta H_c^\ominus$$):
  • The indirect route involves burning both reactants and products to form common combustion products (like CO₂ and H₂O).
  • The arrows for $$ \Delta H_c^\ominus $$ always point DOWN from the compounds to the combustion products.
  • Formula shortcut: $$ \Delta H_{reaction}^\ominus = \sum \Delta H_c^\ominus (\text{Reactants}) - \sum \Delta H_c^\ominus (\text{Products}) $$

Pro Tip: Always write out the balanced equations and draw the cycle. It helps you see the routes clearly and avoid mistakes!

Key Takeaway

Hess's Law allows us to calculate unknown enthalpy changes by finding an indirect route with known energy steps. The destination is all that matters, not the path!