# How can I calculate thermochemistry equations for phase changes?

Dec 24, 2014

Phase changes represent the transformation of a thermodynamic system from one state of matter to another by way of heat transfer. A state of matter (or phase) is described as having uniform physical properties; during phase changes, certain properties change.

Now, heating stuff up takes energy; for a pure substance in a single phase, this energy can be calculated using the equation

$q = m \cdot c \cdot \Delta T$, where

$q$ - energy;
$m$ - mass of the substance;
$c$ -specific heat;
$\Delta T$ - change in temperature, ${T}_{f i n a l} - {T}_{i n i t i a l}$.

However, this equation cannot be used for phase changes, since temperature does not change during a phase change,as you can see in this diagram depicting water's phase changes:

We know that the difference between any two phases is simply the energy difference, therefore all we need to know is that amount of energy to be able to calculate the heat involved. The equation used is

$q = m \cdot \Delta H$, where

$\Delta H$ - the heat required for one gram of the substance to undergo the phase change.

If you're going from solid to liquid, you use $\Delta {H}_{f u s i o n}$ (called the heat of fusion), which represents the heat required for 1 gram of substance to change from solid to liquid at melting point.

If you're going from liquid to gas, you use $\Delta {H}_{v a p o r i z a t i o n}$ (called the heat of vaporization), which represents the heat required for 1 gram of the substance to change from liquid to gas at boiling point.

For water, the values are usually given to be

$\Delta {H}_{f u s}$ = $334 \text{J/g}$ and $\Delta {H}_{v a p}$ = $2257 \text{J/g}$.

Therefore, all you need to know in order to determine the heat needed to go through a specific phase change is the substance's mass and the values for its heat of fusion and/or heat of vaporization.