Thermochemistry — Enthalpy, Hess's Law & Calorimetry

Thermochemistry is the part of chemistry that studies heat changes in reactions and physical changes. In most intro problems, the same three tools appear again and again: enthalpy change $\Delta H$, Hess's law, and calorimetry.

Here is the quick meaning of each one:

• $\Delta H < 0$: the system releases heat under constant-pressure conditions
• $\Delta H > 0$: the system absorbs heat under constant-pressure conditions
• Hess's law: if reactions add up, their enthalpy changes add up
• calorimetry: measure $\Delta T$, convert it to $q$, then relate that heat to the reaction

If you remember one sentence, remember this: thermochemistry is about keeping track of where heat goes, under clearly stated conditions.

What Thermochemistry Means In Practice

In thermochemistry, the quantity you usually calculate is a change in enthalpy, not an absolute enthalpy. For many chemistry classes, enthalpy is useful because it connects heat flow to reactions done at constant pressure.

For a process at constant pressure where pressure-volume work is the relevant work term,

$$\Delta H = q_p$$

That condition matters. You should not replace $\Delta H$ with heat in every situation. The shortcut works for constant-pressure setups such as many open-beaker reactions and coffee-cup calorimetry problems.

This gives the common sign language:

• exothermic process: $\Delta H < 0$
• endothermic process: $\Delta H > 0$

Combustion is a standard exothermic example. Melting ice is a standard endothermic one.

How Hess's Law Finds An Unknown Enthalpy

Hess's law says that the enthalpy change for an overall reaction depends on the initial and final states, not on the route used to get there. That works because enthalpy is a state function.

So if adjusted chemical equations add to the target equation, their enthalpy changes add too:

$$\Delta H_{overall} = \Delta H_1 + \Delta H_2 + \Delta H_3 + \cdots$$

The two adjustments that cause most mistakes are:

• if you reverse a reaction, reverse the sign of $\Delta H$
• if you multiply a reaction by a factor, multiply $\Delta H$ by the same factor

Hess's law is especially useful when a target reaction is hard to measure directly but related reactions are known.

How Calorimetry Turns Temperature Change Into Heat

Calorimetry estimates heat by observing how much a material's temperature changes. In a simple solution-based problem, the heat absorbed or released by the surroundings is often modeled with

$$q = mc\Delta T$$

where:

• $m$ is mass
• $c$ is specific heat capacity
• $\Delta T = T_{final} - T_{initial}$

In an idealized coffee-cup calorimeter, if heat exchange with the outside is negligible, then the reaction and the surroundings balance each other:

$$q_{rxn} = -q_{surr}$$

If the reaction is run at constant pressure, that often lets you connect the measured heat to enthalpy change for the amount of reaction that occurred.

Worked Example: Coffee-Cup Calorimetry

Suppose a reaction takes place in a coffee-cup calorimeter and warms $50.0\ \mathrm{g}$ of solution from $22.0^\circ \mathrm{C}$ to $28.0^\circ \mathrm{C}$. Assume the solution behaves like water, so $c = 4.18\ \mathrm{J/(g\cdot^\circ C)}$, and ignore the calorimeter's own heat capacity.

First find the heat gained by the solution:

$$\Delta T = 28.0 - 22.0 = 6.0^\circ \mathrm{C}$$ $$q_{solution} = mc\Delta T = (50.0)(4.18)(6.0) = 1254\ \mathrm{J}$$

So the solution absorbs $1.254\ \mathrm{kJ}$ of heat.

If the cup is effectively isolated from the outside, the reaction must have released the same amount:

$$q_{rxn} = -1.254\ \mathrm{kJ}$$

Because this is a constant-pressure setup, we commonly take

$$\Delta H_{rxn} \approx -1.25\ \mathrm{kJ}$$

for the amount of reaction that happened in that trial.

The key idea is simple: the surroundings got warmer, so the reaction gave heat to the surroundings. That makes the reaction exothermic.

If your problem also gives the amount of reactant used, you can go one step further and convert this result to $\mathrm{kJ/mol}$.

Common Thermochemistry Mistakes

Getting The Sign Backwards

If the solution gets warmer, the solution absorbed heat, but the reaction released it. That means $q_{solution}$ and $q_{rxn}$ have opposite signs.

Using $\Delta H = q$ Without Stating The Condition

The shortcut is $\Delta H = q_p$, not just $\Delta H = q$ in every setting. Constant pressure is the key condition.

Forgetting To Adjust $\Delta H$ In Hess's Law

When you reverse a chemical equation, the sign of $\Delta H$ must flip. When you scale the equation, $\Delta H$ scales too.

Ignoring Physical States

In thermochemistry, states matter. $H_2O(l)$ and $H_2O(g)$ do not carry the same enthalpy, so a state mismatch can break a Hess's law setup.

Not Defining The System First

Before calculating anything, decide what is the system and what is the surroundings. Many sign mistakes start there.

When Enthalpy, Hess's Law, And Calorimetry Are Used

Thermochemistry is used when chemists or engineers need to know how much heat a process releases or absorbs. Common cases include combustion, neutralization, dissolving, phase changes, reactor design, and energy balances in industrial processes.

It also helps you decide which tool fits the problem:

• use calorimetry when temperature data are measured directly
• use Hess's law when the desired reaction heat must be assembled from known steps
• use enthalpy language when you need to describe heat flow under constant-pressure conditions

A Simple Way To Choose The Right Tool

A practical way to think about the topic is:

1. Identify the process and the condition.
2. Decide whether the heat is being measured directly or inferred from known reactions.
3. Calculate the heat carefully, including the sign.
4. Translate that result into $\Delta H$ only when the condition supports it.

That small checklist prevents a large share of beginner mistakes.

Try A Similar Problem

Try your own version with a neutralization reaction in a coffee-cup calorimeter. Calculate $q_{solution}$ first, then switch the sign to get $q_{rxn}$. After that, explore a Hess's law problem where the reaction heat is not measured directly and compare how the two methods reach the same kind of answer from different information.