Final answer:
To determine the amount of heat required to convert 36.0 g of ethanol from 39 °C to vapor at 78 °C, we calculate the heat needed for the temperature increase and the heat needed for the phase change, considering ethanol's specific heat capacity and enthalpy of vaporization.
Step-by-step explanation:
The question asks how much heat is required to convert 36.0 g of ethanol at 39 °C to the vapor phase at 78 °C. To compute this, we need to calculate the heat needed to raise the temperature of the ethanol from 39 °C to its boiling point, and then the heat required to vaporize it at that temperature.
To find the total heat (q) required, we use the formula q = mcΔT for the temperature change and q = nΔHvap for the phase change, where:
- m = mass of ethanol
- c = specific heat capacity of ethanol (2.44 J/g°C)
- ΔT = temperature change (78 °C - 39 °C)
- n = moles of ethanol
- ΔHvap = enthalpy of vaporization of ethanol (38.56 kJ/mol)
First, calculate the heat required to raise the temperature:
q = (36.0 g) × (2.44 J/g°C) × (78 °C - 39 °C)
Then, calculate the number of moles of ethanol using its molar mass (46.07 g/mol) and use this to find the heat required to vaporize the ethanol:
Moles of ethanol (n) = 36.0 g / 46.07 g/mol
Vaporization heat (qvap) = n × ΔHvap
Finally, add both heat quantities for the total heat required.