# What mass of water would release 16700J of energy when freezing?

Jul 25, 2016

$\text{50.1 g H"_2"O}$

#### Explanation:

Your tool of choice here will be the enthalpy of fusion, $\Delta {H}_{\text{fus}}$, for water.

For a given substance, the enthalpy of fusion tells you how much heat is either needed to melt $\text{1 g}$ of the substance at its melting point or given off to freeze $\text{1 g}$ of the substance at its freezing point.

Water has an enthalpy of fusion equal to

$\Delta {H}_{\text{fus" = "333.55 J}}$

https://en.wikipedia.org/wiki/Enthalpy_of_fusion

This tells you that when $\text{1 g}$ of water goes from liquid at its freezing point to solid at its freezing point, $\text{333.55 J}$ of heat are being given off.

In your case, you know that $\text{16,700 J}$ of heat are being given off when a mass of water undergoes a liquid $\to$ solid phase change at ${0}^{\circ} \text{C}$.

Use the enthalpy change of fusion as a conversion factor to determine how many grams of liquid water would give off this much heat when freezing

"16,700" color(red)(cancel(color(black)("J"))) * overbrace(("1 g H"_ 2"O")/(333.55 color(red)(cancel(color(black)("J")))))^(color(blue)(= DeltaH_"fus")) = color(green)(|bar(ul(color(white)(a/a)color(black)("50.1 g H"_2"O")color(white)(a/a)|)))

The answer is rounded to three sig figs, the number of sig figs you have for the heat given off.