Question

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

Answer 1

`"50.1 g H"_2"O"`

Explanation:

Your tool of choice here will be the enthalpy of fusion, `DeltaH_"fus"`, for water.

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

Water has an enthalpy of fusion equal to

`DeltaH_"fus" = "333.55 J"`

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

This tells you that when `"1 g"` of water goes from liquid at its freezing point to solid at its freezing point, `"333.55 J"` of heat are being given off.

In your case, you know that `"16,700 J"` of heat are being given off when a mass of water undergoes a liquid `->` solid phase change at `0^@"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.