Question

What amount of heat is required to completely melt a 29.95-gram sample of `H_2O`(s) at 0° C?

Answer 1

`"9.990 kJ"`

Explanation:

The question wants you to determine how much heat will be required in order to get a `"29.95-g"` sample of ice to undergo a solid `->` liquid phase change at its melting point of `0^@"C"`.

So, in essence, all you need to know in order to answer this question is the value of water's enthalpy of fusion, `DeltaH_"fus"`.

The enthalpy of fusion essentially tells you one thing from two different perspectives

• how much heat is needed in order to melt one gram of a substance at its melting point
• how much heat is released when one gram of a substance freezes at its freezing point

In your case, water is going from solid to liquid, so `DeltaH_"fus"` will be positive. For water, you have

`DeltaH_"fus" = "333.55 J g"^(-1)`

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

So, if you need `"333.55 J"` in order to get `"1 g"` of ice at `0^@"C"` to go to liquid water at `0^@"C"`, it follows that `"29.95 g"` of ice would require

`29.95 color(red)(cancel(color(black)("g"))) * overbrace("333.55 J"/(1color(red)(cancel(color(black)("g")))))^(color(blue)(DeltaH_"fus")) = "9989.8 J"`

Rounded to four sig figs, the answer will be

`"heat required " = color(green)(" 9990. J")`

Expressed in kilojoules, you will have

`"heat required " = color(green)(" 9.990 kJ")`