# Assume 12,500 J of energy is added to 2.0 moles of #H_2O# as an ice sample at #0^@"C"#. The molar heat of fusion is 6.02 kJ/mol. The specific heat of liquid water is 4.184 J/g K. The remaining sample consists of?

##### 1 Answer

The remaining sample consists of *liquid water* at

So, you know that you're dealing **2.0 moles** of water as ice at **12,500 J**, to supply to the sample.

The first thing you need to determine is whether or not that much energy is enough to *melt* all the ice, i.e. to make the entire sample undergo a phase change.

Since water goes from *solid* to *liquid* at constant temperature, more specifically at

*molar enthalpy of fusion*.

Plug in your values to get

Expressed in Joules, you have

This means that **all the ice** has melted, and whatever energy you still have will now go into **heating** the liquid water.

Now, the specific heat of liquid water is actually equal to

You need to convert this to the **molar heat capacity** of water, which represents the amount of heat required to raise the temperature of **1 mole** of water by

To do that, use water's molar mass

Since you don't know how much the temperature of the water will *increase* by using your remaining energy, you can say that the final temperature is equal to

**molar heat capacity** of water;

After all the ice melted, you are left with

This many Joules will get your water to a temperature of

Rounded to two sig figs, the answer will be

Therefore, the remaining sample consists of *liquid water* at