5.2 Calorimetry

Calorimetry

Calorimetry is the method used to measure heat transfer during chemical reactions or physical changes. It's built on a simple but powerful idea: energy is conserved, so any heat released by a reaction must be absorbed by the surroundings, and vice versa. By tracking temperature changes in a known substance (usually water), you can calculate exactly how much energy a reaction involves.

Heat Transfer Measurement in Calorimetry

A calorimeter is the device that makes these measurements possible. It holds a known mass of substance (the calorimeter's contents, typically water) and monitors how the temperature changes when a reaction occurs inside it.

The temperature change you observe is directly proportional to the heat transferred. The proportionality constant linking them is the heat capacity of the calorimeter's contents. A larger heat capacity means more heat is needed to produce the same temperature change.

For precise results, you also need to account for the heat absorbed or released by the calorimeter itself. This is captured by the calorimeter constant ($C$), which represents the heat capacity of the physical device. Ignoring it can throw off your calculations, especially in more sensitive experiments.

Calculations with Calorimetry Data

The core equation for calculating heat transfer is:

$q = mc\Delta T$

• $q$ = heat energy transferred (J)
• $m$ = mass of the substance (g)
• $c$ = specific heat capacity (J/g°C)
• $\Delta T$ = change in temperature (°C), calculated as $T_{\text{final}} - T_{\text{initial}}$

Specific heat capacity is the amount of heat needed to raise the temperature of 1 g of a substance by 1°C. Every substance has its own value (water's is 4.18 J/g°C), and you'll find these in reference tables.

When you need to include the calorimeter's own heat absorption, the equation expands to:

$q = (mc\Delta T)_{\text{contents}} + (C\Delta T)_{\text{calorimeter}}$

• The first term covers the heat change of the water (or other contents).
• The second term covers the heat change of the calorimeter device itself, where $C$ is the calorimeter constant in J/°C.

The central principle tying it all together is conservation of energy:

$q_{\text{system}} + q_{\text{surroundings}} = 0$

This means the heat lost by the system equals the heat gained by the surroundings (and vice versa), assuming no heat escapes to the environment. So if a reaction releases 500 J, the calorimeter and its contents absorb 500 J.

Steps for a typical calorimetry calculation:

1. Record the mass of the calorimeter's contents (e.g., water).
2. Measure the initial and final temperatures to find $\Delta T$.
3. Use $q = mc\Delta T$ to calculate the heat gained or lost by the contents.
4. If given a calorimeter constant, add the term $C\Delta T$ for the calorimeter itself.
5. Apply conservation of energy: $q_{\text{reaction}} = -q_{\text{surroundings}}$ (the sign flips because heat lost by one is gained by the other).

Types of Calorimeters and Applications

There are two main types you need to know: constant-pressure calorimeters and bomb calorimeters.

Constant-pressure calorimeters (often called coffee-cup calorimeters) operate at atmospheric pressure. They're simple, cheap, and good for measuring heat changes in solution-based reactions like dissolving a salt, acid-base neutralizations, or combustion of small food/fuel samples. The tradeoff is that they're less precise because some heat inevitably escapes through the cup walls.

Bomb calorimeters operate at constant volume. The reaction takes place inside a sealed, rigid steel container (the "bomb") filled with excess oxygen, and this bomb sits submerged in a known mass of water inside an insulated jacket. Because the system is sealed and well-insulated, bomb calorimeters are much more precise. They're the standard tool for measuring heats of combustion for solids, liquids, and gases. The downside is that they're more expensive and complex to operate.

Thermal Equilibrium and Energy Transfer

Calorimetry depends on the system and surroundings reaching thermal equilibrium, the point where both are at the same temperature and heat stops flowing. Heat always moves from hotter regions to cooler regions until this balance is reached.

The total energy of the system plus surroundings stays constant throughout the process. Accurate calorimetry measurements require that thermal equilibrium is actually achieved before you take your final temperature reading. If you read the thermometer too early, you'll underestimate the true heat transfer.