How much energy is required to heat 87.1 g acetone (molar mass=58.08 g/mol) from a solid at -154.0°C to a liquid at -42.0°C? The following physical data may be useful.
ΔH_fus = 7.27 kJ/mol
C_liq = 2.16 J/g°C
C_gas= 1.29 J/g°C
C_sol = 1.65 J/g°C
T_melting= -95.0°C

Question

Quizplus · Accepted Answer

The heating process can be divided into two steps: solid to liquid and liquid to a higher temperature. We can use the following equations: Q1 = nΔH_fus Q2 = m × C_liq × ΔT where Q1 is the heat required to melt the solid, Q2 is the heat required to heat the liquid to the desired temperature, n is the number of moles of acetone, m is the mass of acetone, ΔH_fus is the molar enthalpy of fusion, C_liq is the specific heat capacity of liquid acetone, and ΔT is the change in temperature. For the first step: n = 87.1 g / 58.08 g/mol = 1.50 mol Q1 = 1.50 mol × 7.27 kJ/mol = 10.9 kJ For the second step: ΔT = (-42.0°C) - (-154.0°C) = 112.0°C Q2 = 87.1 g × 2.16 J/g°C × 112.0°C = 21.3 kJ Therefore, the total heat required is: QT = Q1 + Q2 = 10.9 kJ + 21.3 kJ = 29.4 kJ The best choice is D, as it matches the calculated value.

How Much Energy Is Required to Heat 87