Difficulty: Intermediate | Prerequisites: Basic algebra, unit conversions, and a grasp of atomic structure (CHEM 101 Chapters 1–4 or equivalent).
Thermochemistry is the branch of chemistry that tracks where energy goes during chemical reactions and phase changes. It sits at the heart of general chemistry because nearly every reaction you study later (equilibrium, electrochemistry, kinetics) depends on energy bookkeeping you learn here. You should already be comfortable with moles, balanced equations, and the idea that matter is made of atoms and molecules. If the words "stoichiometry" or "molar mass" still feel shaky, revisit those chapters first.
Energy in chemical systems is conserved (First Law) and moves as heat (q) or work (w). Enthalpy (ΔH) is the heat exchanged at constant pressure, positive for endothermic reactions and negative for exothermic ones. You can calculate ΔH for any reaction using Hess's Law, standard enthalpies of formation, or calorimetry data.
Internal energy (E)
The total of all microscopic kinetic and potential energy in a system. Think of it as the sum of everything happening at the particle level inside your beaker.
Kinetic energy
Energy of particle motion (translation, rotation, vibration). In simple terms, the faster particles move, the more kinetic energy the system has.
Potential energy
Energy stored in the interactions between particles (bonds, intermolecular forces). Think of it as the energy locked in the arrangement of atoms.
First Law of Thermodynamics
Energy cannot be created or destroyed, only transferred or transformed. In simple terms, the universe's energy ledger always balances to zero.
Heat (q)
Energy transferred between a system and its surroundings because of a temperature difference. Positive when it flows in (endothermic), negative when it flows out (exothermic).
Work (w)
Energy transferred when a force acts through a distance, most commonly pressure-volume work in chemistry. Positive when done on the system (compression), negative when done by the system (expansion).
Enthalpy (H)
A thermodynamic quantity defined as H = E + PV. At constant pressure, the change in enthalpy equals the heat exchanged. Think of it as the "heat content" you measure in an open beaker.
Exothermic reaction
A reaction that releases heat to the surroundings (ΔH < 0). In simple terms, the products are lower in energy than the reactants, so energy leaves the system.
Endothermic reaction
A reaction that absorbs heat from the surroundings (ΔH > 0). The products sit higher in energy, so the system pulls energy in.
State function
A property whose value depends only on the current state of the system (temperature, pressure, composition), not on how it got there. Enthalpy and internal energy are state functions; heat and work are not.
Hess's Law
The total enthalpy change for a reaction is the same regardless of the pathway taken, provided the initial and final states are the same. Think of it as "enthalpy doesn't care about the route, only the start and finish."
Standard enthalpy of formation (ΔH°f)
The enthalpy change when one mole of a compound forms from its elements in their standard states (1 atm, usually 298 K). Elements in their standard forms have ΔH°f = 0 by definition.
Specific heat capacity (c)
The amount of heat needed to raise one gram of a substance by 1 °C (or 1 K). Water's value (4.184 J/g·K) is a number worth memorising.
Calorimetry
The experimental measurement of heat transfer during a physical or chemical process, typically using a coffee-cup calorimeter at constant pressure.
Thermochemical equation
A balanced equation that includes the enthalpy change (ΔH) for the reaction as written. Stoichiometric coefficients tell you the moles the ΔH value applies to.
Internal energy (E) = kinetic energy + potential energy at the microscopic level
Lower energy states are more stable, which is why systems tend to move toward them during reactions
Thermochemistry is fundamentally about tracking where energy goes when bonds break and form
Energy of the universe is constant: E_universe = E_system + E_surroundings = 0
Any energy the system loses, the surroundings gain, and vice versa
This is the backbone of every energy calculation in the course
ΔE = q + w
Heat (q) sign conventions:
Positive: heat flows into the system (endothermic)
Negative: heat flows out (exothermic)
Work (w) sign conventions:
Positive: work done on the system (compression)
Negative: work done by the system (expansion)
w = –PΔV (at constant external pressure)
Alternatively, w = Δn(gas) × R × T, where R = 8.314 J/(mol·K)
Gas expands (ΔV > 0): system does work on surroundings, w is negative
Gas compressed (ΔV < 0): surroundings do work on system, w is positive
H = E + PV
At constant pressure: ΔH = q_p (the heat you measure in an open container)
Enthalpy is an extensive property: double the amount of substance, double the ΔH
Most lab and real-world reactions happen at constant (atmospheric) pressure, which is why enthalpy is so commonly used
Endothermic: ΔH > 0, heat absorbed, often involves bond breaking
Example: ice melting, photosynthesis
Exothermic: ΔH < 0, heat released, often involves bond formation
Example: combustion, condensation
For reactions involving only solids and liquids (no gas volume change): ΔH ≈ ΔE
When moles of gaseous products equal moles of gaseous reactants: ΔH ≈ ΔE
The two diverge when there is a net change in moles of gas
Endothermic: heat written as a reactant (left side), e.g. A + B + heat → C
Exothermic: heat written as a product (right side), e.g. A + B → C + heat
The ΔH value applies to the equation exactly as balanced; if you halve the coefficients, you halve the ΔH
Internal energy (E) and enthalpy (H) are state functions: their change depends only on initial and final states
Heat (q) and work (w) are path-dependent: they depend on how the process occurs
This is why Hess's Law works
The total ΔH for a reaction is the same no matter how many intermediate steps you use
Practical method: combine known thermochemical equations (reverse them and/or multiply) so they add up to the target reaction, then sum their ΔH values
Reversing a reaction flips the sign of ΔH; multiplying coefficients multiplies ΔH by the same factor
Standard state conditions: 1 atm for gases, 1 mol/L for solutions, most stable form of element at the specified temperature (usually 298 K)
ΔH°f = enthalpy change when 1 mol of a compound forms from its elements in standard states
Elements in their standard states: ΔH°f = 0 (by definition)
Reaction enthalpy from formation data: ΔH°_rxn = Σ[ΔH°f(products)] – Σ[ΔH°f(reactants)], each multiplied by its stoichiometric coefficient
q = c × m × ΔT (specific heat capacity version)
Coffee-cup calorimeter: constant pressure, measures ΔH
The heat lost by one substance equals the heat gained by the other (assuming no heat escapes)
Common exam setup: mixing hot and cold water, or dissolving a salt and measuring temperature change
Formula | What it means |
|---|---|
ΔE = q + w | Change in internal energy = heat + work |
w = –PΔV | PV work at constant external pressure |
w = Δn(gas) × R × T | PV work using change in gas moles (R = 8.314 J/mol·K) |
H = E + PV | Definition of enthalpy |
ΔH = q_p | Enthalpy change = heat at constant pressure |
q = c × m × ΔT | Heat from specific heat capacity, mass, and temperature change |
ΔH°_rxn = ΣΔH°f(products) – ΣΔH°f(reactants) | Reaction enthalpy from formation data |
E_universe = E_system + E_surroundings = 0 | First Law of Thermodynamics |
c = λ × ν | Speed of light = wavelength × frequency (useful when thermochemistry meets photon energy) |
Enthalpy calculations underpin the design of heat exchangers, engine cooling systems, and chemical reactors. Your car radiator relies on the high specific heat capacity of water to absorb engine heat without boiling. Industrial chemists use Hess's Law every day to predict energy requirements for reactions that are too dangerous or impractical to run directly in a calorimeter.
Students often think ΔH and ΔE are always interchangeable. They are close only when no net change in gas moles occurs. When gases are produced or consumed unevenly, PV work makes them differ.
Students often confuse the sign of work. In chemistry's convention, work done on the system is positive. Physics courses sometimes use the opposite convention, which causes mix-ups.
Students often think exothermic reactions are always spontaneous. Spontaneity also depends on entropy (ΔS) and temperature, which you will meet in the thermodynamics chapter.
Students often believe that a higher temperature means more heat was transferred. Temperature change depends on both the heat transferred and the heat capacity of the substance. A small amount of heat can produce a large temperature change in a low-mass, low-heat-capacity material.
⚠️ Sign conventions for q and w are tested heavily. Know which direction is positive for each.
⚠️ Hess's Law problems appear on nearly every general chemistry exam. Practice flipping and scaling equations.
⚠️ Standard enthalpy of formation: remember that ΔH°f = 0 for any element in its standard state. This trips students up on calculation problems.
⚠️ Calorimetry problems typically assume no heat loss to the environment. Read the problem to confirm whether a coffee-cup (constant pressure) or bomb (constant volume) calorimeter is described, because they measure ΔH and ΔE respectively.
⚠️ Expect questions that ask you to distinguish state functions (E, H) from path-dependent quantities (q, w).
True or false: Enthalpy is a state function.
True.
Fill in the blank: When a gas expands against a constant external pressure, the sign of work (w) is ______.
Negative (the system does work on the surroundings).
True or false: ΔH°f for O₂(g) at 298 K is zero.
True. O₂ is oxygen's most stable form at standard conditions.
Fill in the blank: In the equation ΔE = q + w, "q" represents ______.
Heat transferred.
True or false: Reversing a thermochemical equation changes the sign of ΔH.
True.
Q: A reaction has ΔH = –285.8 kJ/mol. Is it endothermic or exothermic, and does the system gain or lose heat?
A: Exothermic. The system loses heat to the surroundings (negative ΔH means heat flows out).
Q: Using Hess's Law, if Reaction 1 has ΔH = +100 kJ and Reaction 2 has ΔH = –250 kJ, what is the overall ΔH when the two reactions are added?
A: ΔH_total = +100 + (–250) = –150 kJ.
Q: 50.0 g of water (c = 4.184 J/g·K) is heated from 25.0 °C to 75.0 °C. How much heat is absorbed?
A: q = 4.184 × 50.0 × 50.0 = 10,460 J (about 10.5 kJ).
Q: Why is ΔH°f for Fe(s) equal to zero?
A: Iron in its solid metallic form is its most stable allotrope at standard conditions. By definition, elements in their standard state have ΔH°f = 0.
Q: A gas-phase reaction produces 3 moles of gas from 1 mole of gas. Would you expect ΔH to be close to ΔE? Why or why not?
A: They would differ noticeably. There is a net gain of 2 moles of gas, so PV work is significant, and ΔH = ΔE + Δn(gas) × RT.
Q: In a coffee-cup calorimetry experiment, the temperature of the solution rises. Is the reaction endothermic or exothermic?
A: Exothermic. The reaction releases heat into the solution, raising its temperature.
Thermochemistry connects directly to chemical kinetics: the activation energy barrier for a reaction is an energy concept built on the same framework. It also feeds into thermodynamics (Gibbs free energy combines enthalpy with entropy to predict spontaneity) and electrochemistry (cell potentials relate to ΔG, which relates to ΔH). If you are studying quantum theory alongside this, the photon energy equation E = hν bridges the two topics, because light energy absorbed or emitted during electronic transitions is measured and reported using the same energy units (joules, kJ/mol) you use here.
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