The calculations involve finding the temperature change, converting mass to moles, determining the heat of vaporization, and then calculating the heat needed using the specific heat formula. The final answer is approximately 111.50 kJ.
Certainly, let's go through the detailed calculations step by step.
Calculate Temperature Change (ΔT):
ΔT = T_final - T_initial = 78.4°C - (-60.8°C) = 139.2°C
Convert Mass to Moles:
n = 133 g / 46.07 g/mol ≈ 2.889 mol
Use the Specific Heat Formula:
Q = n * ΔH
Find Heat of Vaporization (ΔH) for Ethanol:
The heat of vaporization for ethanol is approximately 38.56 kJ/mol.
Calculate Heat (Q):
Q = 2.889 mol * 38.56 kJ/mol ≈ 111.50 kJ
So, the amount of heat needed to boil 133 g of ethanol from -60.8°C to its boiling point of 78.4°C is approximately 111.50 kJ.