# Question 1c1c5

May 1, 2015

The energy change when that much ethanol freezes at its melting point will be q = -3,000 cal.

You're dealing with a phase change, more specifically with the freezing of ethanol. During a phase change, the energy supplied to or given off by the substance will not take into account a change in temperature because phase changes occur at constant temperature.

In your case, you need to determine how much heat will be given off by the ethanol when it goes from liquid at $\text{-112"^@"C}$ to solid at $\text{-112"^@"C}$.

The enthalpy of fusion, $\Delta {H}_{\text{fus}}$, represents the amount of heat given off by a substance when 1 gram of that substance undergoes a liquid to solid phase change.

In your case, your sample will give off 25 calories for every gram of ethanol that goes from liquid to solid.

Since you have more than 1 gram of ethanol, you'd expect the amount of heat given off to be larger than 25 calories.

$q = m \cdot \Delta {H}_{\text{fus}}$

q = 100cancel("g") * (-25"calories"/cancel("g")) = "-2,500 calories"#

Rounded to one sig fig, the number of sig figs given for the mass of ethanol, the answer will be

$q = \textcolor{g r e e n}{\text{-3,000 cal}}$