# Calorimetry

Enthalpy change cannot be measured directly. Instead, the heat added to or lost from the surroundings is measured. Calorimetry, one method of doing this, is the experimental technique of measuring energy changes in a chemical reaction or other process using an apparatus called a calorimeter (see page 309 for an example). It makes the following three assumptions:

- No heat is transferred between the calorimeter and the environment.
- Any heat absorbed or released by the calorimeter itself is negligible.
- Dilute aqueous solutions have the density and specific heat capacity of pure water (1 g/mL and 4.18 J/gºC respectively).

The magnitude of the system’s enthalpy change is equal to the heat transferred to or from the surroundings:

$\displaystyle \left \lvert \Delta{} H_{\text{system}} \right \rvert = q_{\text{surroundings}}$.

Keeping in mind that the left side refers to the system and the right side refers to the surroundings, we can rewrite this as

$\displaystyle n \left \lvert \Delta{} H_{x} \right \rvert = m c \Delta{} T$.

## Example

10.0 g of urea, NH_{2}CONH_{2(s)}, is dissolved in 150 mL of water in a simple calorimeter. A temperature change from 20.4 ºC to 16.7 ºC is observed. Calculate the molar enthalpy of solution for urea.

First, we can find the amount of urea in terms of moles by divided by the molar mass of NH_{2}CONH_{2(s)}:

$\displaystyle n = \frac{m}{M} = \frac{10.0 \, \text{g}}{60.07 \, \text{g/mol}} = 0.16647 \, \text{mol}$.

Now we can rearrange $\displaystyle n \left \lvert \Delta{} H_{\text{sol}} \right \rvert = m c \Delta{} T$ to

$\displaystyle \left \lvert \Delta{} H_{\text{sol}} \right \rvert = \frac{m c \Delta{} T}{n}$,

and substitute the known variables, giving us

$\displaystyle \left \lvert \Delta{} H_{\text{sol}} \right \rvert = \frac{\left ( 150 \, \text{g} \right ) \left ( 4.18 \, \text{J/gºC} \right ) \left ( 20.4 \, \text{ºC} - 16.7 \, \text{ºC} \right )}{0.16647 \, \text{mol}} = 13.9 \, \text{kJ/mol}$.

Since the temperature decreased in the surroundings, this was an *endothermic* reaction, and the molar enthalpy of solution for urea has the positive value of 13.9 kJ/mol.