Question

A 154 g sample of water at 0oC freezes into ice at °C How many joules (J) of energy are needed for the phase change?

Answer 1

Since you don't give the temperature of the ice, I'll assume it to be `0^@"C"`. In this case, you'd release `"51,400 J"` to get that much water at `0^@"C"` to ice at `0^@"C"`.

Note: technically the energy is NOT needed. This is the energy released by the liquid water at `0^@"C"` to become solid ice at `0^@"C"` - it is an exothermic change so some might say the answer is `"-51,400 J"`.

The only information you need to solve this problem is the value of water's enthalpy of fusion, `DeltaH_("fus")`, which is known to be

`DeltaH_("fus") = "-333.5 J/g"`

This value tells you that, for every gram of water, 333.5 J will be given off to transform it from liquid to solid, i.e. make it undergo a phase change.

Since you've got 154 g, the total energy needed will be

`q = m * DeltaH_("fus") = 154cancel("g") * (-333.5)"J"/cancel("g") = "-51,359 J"`

Rounded to three sig figs, the number of sig figs given for 154 g, and keeping in mind that the energy is given off, you can say that

`q = color(green)("-51,400 J")`