# Question #23db5

Jan 9, 2018

See below.

#### Explanation:

Latent heat is the heat required to make a phase change. By phase change, I mean going from solid to liquid, or liquid to solid, or liquid to gas, etc. Remember that the latent heat of a substance is a constant (meaning that it doesn't change). In mathematical terms, the latent heat of fusion is represented by $\Delta \text{H}$.

One example of latent heat is the latent heat of fusion. The latent heat of fusion tells you how much energy it takes to go from 1 mole of solid substance to liquid, or vice versa. For water ($\text{H"_2"O}$), the latent heat of fusion is $6.01 \text{kJ"/"mol}$. This means that it takes $6.01 \text{ kJ}$ of energy to convert 1 mole of solid $\text{H"_2"O}$ to liquid $\text{H"_2"O}$.

Another latent heat which you will need to be familiar with is the latent heat of vaporization. As you may or may not have already guessed, this is the energy it takes to go from 1 mole of liquid substance to gas, or vice versa. For water ($\text{H"_2"O}$), the latent heat of fusion is $40.79 \text{kJ"/"mol}$. This means that it takes (you guessed it) $40.79 \text{ kJ}$ of energy to convert 1 mole of $\text{H"_2"O}$ from liquid to gaseous state.

I know this answer is long. But bear with me please (I'm sorry). Remember that you won't always see the units $\text{kJ"/"mol}$ , and you may be faced with $\text{J"/"mol}$, or $\text{J"/"g}$. Don't panic: just use your dimensional analysis skills to convert (remember that $1 \text{ kJ"=1000" J}$, and to convert from moles to grams, use the molar mass).

Now, let's get into the equations. The first one you will see is this:

$\text{q"="m"Delta"H"_"vap}$

The second one is this:

$\text{q"="m"Delta"H"_"fus}$

Just note that fus is the same as fusion, and vap is the same as vaporization.

In the above equations, $\text{m}$ is the mass of substance, in grams ($\text{g}$). $\text{q}$ is the amount of energy required for a phase change (this could be Joules ($\text{J}$) or kilojoules ($\text{kJ}$), depending on what unit the latent heat is (see above for different units). And $\Delta \text{H"_"fus/vap}$ is your latent heat!

If there is ever a latent heat problem, then you will know because there won't be a temperature change involved. You know this because there is no $\Delta \text{T}$ (change in temperature) in either of the latent heat equations.