Final answer:
The molar heat of combustion of ethanol is calculated using the temperature change observed when burning ethanol and the known specific heat of water. The enthalpies of formation for ethanol, water, and carbon dioxide are used to confirm the molar heat of combustion via Hess's law. Finally, this heat is converted to determine the millimoles of ethanol required to heat 200g of water.
Step-by-step explanation:
To calculate how many millimoles of ethanol would need to be burned, we first need to determine the molar heat of combustion of ethanol using the information provided. Knowing that a 1.55 gram sample of ethanol produces a 55°C temperature increase in 200g of water, we can calculate the specific heat of water (4.18 J/g°C) and then use it to find the total heat in joules. This heat divided by the mass of ethanol gives us the heat of combustion per gram of ethanol.
Using the enthalpies of formation provided for ethanol, water, and carbon dioxide, we can calculate the molar heat of combustion of ethanol by applying Hess's law and subtracting the sum of the enthalpies of formation of the products from the sum of the enthalpies of formation of the reactants.
Lastly, knowing that ethanol has a molar mass of 46 g/mol, we can convert the energy required to heat 200g of water into moles and then millimoles of ethanol required for combustion, considering the molar heat of combustion we have calculated.