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?
The remaining sample consists of liquid water at
So, you know that you're dealing 2.0 moles of water as ice at
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
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
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