Start with the delta H = mC delta T (delta h = mcat formula)
How much energy is needed to raise the temperature of 350 grams of water by 77°C?
delta H = 350 x 4.2 x 77 = 113190 Joules. So it takes 113190 Joules (113.190 kJ) of heat energy to raise the temp of 350 g of water by 77°C.
Second: how many moles of ethanol needs to be burnt to provide that much energy? If you burn one mole of ethanol you get 1360 kJ. So 113.19/1360 = 0.08322794 moles of ethanol needs to be burnt to release 113.19 kJ of heat energy.
The mass of one mole of ethanol (C2H6O) is 2 x 12.01 + 6 x 1.008 + 16.00 = 46.068 grams.
In other words, the molar mass of ethanol = 46.068 g/mol.
0.08322794 moles of ethanol = 0.08322794 x 46.068 = 3.8341 grams of ethanol.
Finally, if 50% of the heat from burning the ethanol is lost to the surroundings, then you will need to burn twice as much ethanol in order to heat the water. 2 x 3.8341 = 7.668 grams.
Please note that I have gone overboard with the number of significant figures in the first bit of this answer in order to eliminate roundoff error.
Hope this helps.
