Question

The following information is given for benzene at 1 atm:boiling point = 80.10 °CHvap(80.10 °C) = 393.3 J/gmelting point = 5.50 °CHfus(5.50 °C) = 127.4 J/gspecific heat gas = 1.040 J/g°Cspecific heat liquid = 1.740 J/g°CA 24.90 g sample of liquid benzene is initially at 45.70 °C. If the sample is heated at constant pressure (P = 1 atm), ____ kJ of energy are needed to raise the temperature of the sample to 103.00 °C.

Answer 1

11.87 kJ

Step-by-step explanation:

First, the temperature must rise till the boiling point, with a gain of sensitive heat (without change of physical state). So the heat can be calculated by:

Q = mxClxΔT, where Q is the heat, m the mass, Cl the specific heat of the liquid, and ΔT the temperature variation:

Q1 = 24.90x1.740x(80.10 - 45.70)

Q1 = 1490.4 J = 1.49 kJ

Then, the liquid will be boiled, with a gain of latent heat, and the temperature must be constant. It will be:

Q = mxHv, where Hv is the heat of vaporization, so:

Q2 = 24.90x393.3

Q2 = 9793.17 J = 9.79 kJ

Then the temperature must increase to the final temperature, with a gain of sensitive heat:

Q3 = mxCgxΔT

Q3 = 24.9x1.040x(103.00 - 80.10)

Q3 = 593 J = 0.59 kJ

The total heat needes is: Q1 + Q2 + Q3 = 11.87 kJ