# 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?

Apr 3, 2015

Since you don't give the temperature of the ice, I'll assume it to be ${0}^{\circ} \text{C}$. In this case, you'd release $\text{51,400 J}$ to get that much water at ${0}^{\circ} \text{C}$ to ice at ${0}^{\circ} \text{C}$.

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

The only information you need to solve this problem is the value of water's enthalpy of fusion, $\Delta {H}_{\text{fus}}$, 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

$q = \textcolor{g r e e n}{\text{-51,400 J}}$