Introductory General Chemistry  ·  Unit 11

Energy & Thermochemistry

Start here if heat problems all look the same right now. Building from bonding, this unit helps you separate the big ideas: temperature change vs phase change, heat released vs heat absorbed, and reaction energy vs activation energy — leading into gas laws.

What you'll learn

Calculate heat transfer using q = mcΔT for temperature changes and phase transitions. Interpret heating curves and identify what is happening at each segment. Apply Hess's Law to find ΔH for reactions not easily measured directly. Use thermochemical equations in stoichiometric calculations.

11.1Start Here: Heat vs. Temperature

Heat is energy transferred because of a temperature difference. Temperature is a measure of the average kinetic energy of particles. They are related but not the same thing.

Get this straight first: temperature tells you how energetic particles are on average; heat is energy moving from one place to another.

The two rows below show exactly how heat and temperature differ — and why a large mass of warm water can hold more total energy than a tiny cup of hotter water.

IdeaMeaningExample
HeatEnergy moving from hotter to colder matterA hot metal block warms cooler water
TemperatureHow energetic particles are on average100°C water and 100°C steam have the same temperature but different total heat content

Do not miss this

  • A large bucket of warm water can contain more total thermal energy than a tiny cup of hotter water.
  • Temperature alone does not tell you total heat because mass matters too.

11.2Energy Units: Know What the Number Means

Thermochemistry uses several related energy units. Make sure you can convert between them before solving problems.

If this feels shaky, fix it now. A correct setup can still fail if you mix up joules, calories, kilojoules, and food Calories.

1 cal = 4.184 J 1 kcal = 1000 cal 1 food Calorie = 1 kcal
UnitNameCommon use
JjouleSI energy unit
kJkilojouleReaction enthalpy
calcalorieOlder heat unit
kcal or CaloriekilocalorieFood energy labels

11.3Specific Heat and Calorimetry: Which Equation Fits the Situation?

Start with one question: is the substance changing temperature, or is heat moving between substances?

That decision matters more than the arithmetic. Memorizing q = mcΔT and applying it everywhere is the most common setup error. Do not do that.

Choose the situation first
  • If one substance changes temperature and stays in the same phase, use q = mcΔT.
  • If two substances exchange heat in a calorimetry problem, use energy conservation: qlost = −qgained.

When a substance changes temperature without changing phase, use the specific heat equation:

Temperature-change equation
q = mcΔT q = heat (J) m = mass (g) c = specific heat (J/g°C) ΔT = Tfinal − Tinitial

In a calorimetry experiment, energy is conserved.

That means the heat lost by one substance equals the heat gained by the other.

qlost = −qgained
  • Always calculate ΔT = final − initial.
  • A negative q means the substance released heat.
  • Water’s specific heat (4.184 J/g°C) is unusually high, which is why lakes resist temperature swings.

11.4Phase Changes: When Energy Changes the State, Not the Temperature

During a phase change, temperature stays constant.

Notice the trap here: if the sample is melting or boiling, the added energy is not raising temperature. It is pulling particles apart enough to change phase.

The energy goes into breaking or forming intermolecular forces instead of changing temperature, so you must use a different equation for each type of phase change.

Phase-change equations
q = mΔHfus for melting or freezing q = mΔHvap for boiling or condensation
ProcessEnergy directionType
MeltingAbsorbs heatEndothermic
FreezingReleases heatExothermic
Boiling or evaporationAbsorbs heatEndothermic
CondensationReleases heatExothermic

11.5Heating Curves: Read the Segment Before You Pick the Formula

A heating curve shows how temperature changes as heat is added. You must split every heating-curve problem into separate segments and apply the correct equation to each — never use a single equation for the whole problem.

How to read each segment
  • Sloped segment — temperature is rising → use q = mcΔT (identify which phase is present to get the right c)
  • Flat segment at 0°C — melting or freezing → use q = mΔHfus
  • Flat segment at 100°C — boiling or condensing → use q = mΔHvap
  • Total heat = sum of q from every step that applies to your problem

The curve below shows all five segments for water from ice to steam. Each segment has a label — match it to the correct equation before you calculate.

Heat Added (J) Temperature (°C) -40 0 100 140
Ice warming (q = mcΔT) Melting (q = mΔHfus) Liquid warming (q = mcΔT) Boiling (q = mΔHvap) Steam warming (q = mcΔT)

11.6Enthalpy: Endothermic vs. Exothermic

Enthalpy change (ΔH) tells you the overall heat change of a reaction at constant pressure.

Start here if the signs keep flipping on you. The sign of ΔH is always about the system. If the system releases heat, ΔH is negative. If the system absorbs heat, ΔH is positive.

ΔH = Hproducts − Hreactants ΔH < 0 → exothermic (heat moves from the system to the surroundings) ΔH > 0 → endothermic (heat moves from the surroundings into the system)
Do not confuse ΔH with activation energy
  • ΔH compares the energy of reactants and products.
  • EA is the energy barrier that must be overcome to start the reaction.

On an energy diagram, ΔH is the vertical difference between reactants and products. EA is the vertical rise from the reactant level to the peak.

Section 11.7 focuses on activation energy and catalysts in more detail.

Endothermic Profile

Potential Energy reaction progress EA ΔHrxn > 0 J

Exothermic Profile

Potential Energy reaction progress EA ΔHrxn < 0 J

11.7Catalysts and Activation Energy

A catalyst lowers activation energy by providing an alternate reaction pathway. It does not change ΔH — the reactant and product energy levels stay exactly the same.

Do not miss this distinction: catalysts change how hard it is to start the reaction, not where the reaction starts or ends energetically.

Potential Energy reaction progress EA EA with catalyst ΔHrxn < 0 J
Uncatalyzed path Catalyzed path ΔH unchanged

11.8Hess’s Law and Heats of Formation

Hess’s law: because enthalpy is a state function, the overall ΔH for a reaction equals the sum of ΔH values for any set of steps that add up to that reaction.

If this part feels abstract, focus on the procedure. Reverse, scale, and add equations carefully. The chemistry idea is that total enthalpy change depends only on start and finish, not the path in between.

Two common ways to find reaction enthalpy
  • Method 1: Hess’s law with given equations — use this when you are given full thermochemical equations.
  • Method 2: Standard heats of formation — use this when you are given a table of ΔH°f values.

Both methods are Hess’s law. Method 1 adds known thermochemical equations. Method 2 uses a table of formation reactions so the addition is built into one shortcut formula.

Method 1 example: Find ΔH for C(graphite) + 12O2(g) → CO(g)

Given equations:

1. C(graphite) + O2(g) → CO2(g)   ΔH = −393.5 kJ
2. CO(g) + 12O2(g) → CO2(g)   ΔH = −283.0 kJ
Step 1: Reverse the equation that has CO on the wrong side

The target reaction needs CO as a product, but equation 2 has CO as a reactant. Reverse equation 2 and reverse the sign of ΔH.

CO2(g) → CO(g) + 12O2(g)   ΔH = +283.0 kJ
Step 2: Add the equations

Now add equation 1 and the reversed equation 2. CO2 cancels because it appears once on each side.

C(graphite) + O2(g) → CO2(g)   ΔH = −393.5 kJ
CO2(g) → CO(g) + 12O2(g)   ΔH = +283.0 kJ
Visual cancellation:
C(graphite) + O2(g) → CO2(g)
CO2(g) → CO(g) + 12O2(g)
Overall: C(graphite) + 12O2(g) → CO(g)
ΔH = −393.5 kJ + 283.0 kJ = −110.5 kJ
Method 1 checklist

For equation problems, always ask three questions in order: reverse? scale? cancel? Then add the ΔH values only after the equations are in the correct form.

Reverse equation → change the sign of ΔH   |   multiply coefficients → multiply ΔH by the same factor
Method 2: Standard Enthalpy of Reaction
ΔH°rxn = Σ nΔH°f, products − Σ nΔH°f, reactants
Method 2 example: Find ΔH°rxn for CH4(g) + 2O2(g) → CO2(g) + 2H2O(l)

Use standard heats of formation at 25°C from a data table.

SubstanceΔH°f (kJ/mol)
CH4(g)−74.8
O2(g)0
CO2(g)−393.5
H2O(l)−285.8
Step 1: Add the products side

Multiply each formation enthalpy by its coefficient in the balanced equation.

Σ nΔH°f, products = [1(−393.5)] + [2(−285.8)]
Σ nΔH°f, products = −965.1 kJ
Step 2: Add the reactants side

Remember that O2(g) is an element in its standard state, so its ΔH°f is zero.

Σ nΔH°f, reactants = [1(−74.8)] + [2(0)]
Σ nΔH°f, reactants = −74.8 kJ
Step 3: Products minus reactants
ΔH°rxn = (−965.1) − (−74.8)
ΔH°rxn = −890.3 kJ

The negative sign means the combustion of methane is exothermic.

  • Elements in their standard states have ΔH°f = 0 by definition.
  • Examples include O2(g), Fe(s), and C(graphite).
  • That means they contribute nothing to the Hess’s law sum in a formation-enthalpy calculation.
  • If a problem gives full equations, use reverse-scale-add. If it gives a ΔH°f table, use products minus reactants.

11.9Thermochemical Stoichiometry: Using ΔH Like a Conversion Factor

When a ΔH value is attached to a balanced equation, it applies to that reaction as written — for the exact molar amounts shown by the coefficients.

This connects straight back to Unit 09. The only new idea is that the balanced equation now carries an energy amount along with the mole ratio.

If the reaction releases heat, the enthalpy change is negative. If the reaction absorbs heat, the enthalpy change is positive. Treat the enthalpy ratio like any other stoichiometric conversion factor after you convert to moles.

Reading ΔH from a Balanced Equation
2H2(g) + O2(g) → 2H2O(l), ΔH = −572 kJ
As written, 2 mol H2 releases 572 kJ.
So 1 mol H2 releases 286 kJ.
  • Always convert grams to moles first, then apply the mole ratio from the balanced equation to scale the enthalpy.
  • Do not skip the mol conversion.
✦ Practice Problems
Practice thermochemistry now, while the difference between temperature change, phase change, and reaction enthalpy is still clear.
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Next step after Unit 11

Thermochemistry teaches how energy changes. The next move is to study how gases behave under changing pressure, volume, and temperature in gas laws.

Introductory General Chemistry · Unit 11 · Energy & Thermochemistry