Question

Question #27012

Answer 1

`1.50 * 10^4"kJ"`

Explanation:

You need to know the value of water's enthalpy of fusion, `DeltaH_"fus"`

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

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

The enthalpy of fusion tells you the amount of heat needed to convert `"1 g"` of a substance from solid at its melting point to liquid at its melting point.

For water, you need `"333.55 J"` to convert `"1 g"` of water from solid at `0^@"C"`, i.e. from ice, to liquid at `0^@"C"`.

This implies that `"45.0 g"` of ice will require

`45.0 color(red)(cancel(color(black)("g"))) * "333.55 J"/(1color(red)(cancel(color(black)("g")))) = "15009.75 J"`

Expressed in kilojoules and rounded to three sig figs, the answer will be

`color(darkgreen)(ul(color(black)("heat needed" = 1.50 * 10^4color(white)(.)"kJ")))`