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

Jan 27, 2016

$\text{9.990 kJ}$

#### Explanation:

The question wants you to determine how much heat will be required in order to get a $\text{29.95-g}$ sample of ice to undergo a solid $\to$ liquid phase change at its melting point of ${0}^{\circ} \text{C}$.

So, in essence, all you need to know in order to answer this question is the value of water's enthalpy of fusion, $\Delta {H}_{\text{fus}}$.

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 $\Delta {H}_{\text{fus}}$ will be positive. For water, you have

$\Delta {H}_{\text{fus" = "333.55 J g}}^{- 1}$

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

So, if you need $\text{333.55 J}$ in order to get $\text{1 g}$ of ice at ${0}^{\circ} \text{C}$ to go to liquid water at ${0}^{\circ} \text{C}$, it follows that $\text{29.95 g}$ 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")