What amount of heat (in kJ) is required to convert 10.1 g of an unknown solid (MM = 83.21 g/mol) at -5.00 °C to a liquid at 52.3 °C?

Question

What amount of heat (in kJ) is required to convert 10.1 g of an unknown solid (MM = 83.21 g/mol) at -5.00 °C to a liquid at 52.3 °C? (specific heat capacity of solid = 2.39 J/g･°C; specific heat capacity of liquid = 1.58 J/g･°C; ∆Hfus = 3.72 kJ/mol; normal freezing point, Tf = 10.3°C)

Answer 1

q = mass x specific heat x change in temperature

q = mass x ∆H

Step 1: increase temp of solid from -5.00º to the freezing point at 10.3º

q = mC∆T = (10.1 g)(2.39 J/gº)(15.3º) = 369.3 J

Step 2: melt the material at 10.3º

q = (10.1 g)(3.72 kJ/mol x 1 mol/83.21g) = 0.452 J

Step 3: raise temp of liquid from 10.3 to 52.3º

q = (10.1 g)( 1.58 J/gº)(42º) = 670.2 J (assuming the boiling point is greater than 52.3º)

Total heat needed = 369.3 + 0.452 + 670.2 = 1040 J