Final answer:
To heat 200.0g of water by 10.0°C, 6.11 millimoles of ethanol need to be burned, based on the given heat of combustion of ethanol (-1368 kJ/mol) and the specific heat capacity of water (4.18 J/g°C).
Step-by-step explanation:
To find out how many millimoles of ethanol need to be burned to generate enough energy to heat 200.0g of water by 10.0 degrees Celsius, we need to use the specific heat capacity of water and the heat of combustion of ethanol. The specific heat capacity of water is 4.18 J/g°C, which tells us that it takes 4.18 joules to raise 1 gram of water by 1 degree Celsius.
Firstly, we calculate the total energy required to heat 200.0g of water by 10.0°C: 200.0g × 10.0°C × 4.18 J/g°C = 8360 J (or 8.360 kJ).
Given that the heat of combustion of ethanol is -1368 kJ/mol, we can determine how many millimoles of ethanol are needed: 8.360 kJ / 1368 kJ/mol = 0.00611 mol. Since we are asked for millimoles, we convert this to millimoles by multiplying by 1000, giving us 6.11 millimoles of ethanol.