How much heat is needed?

Question

Ethanol (C₂H₅OH) melts at -114°C. The enthalpy of fusion is 5.02 kJ/mol. The specific heats of solid and liquid ethanol are 0.97 J/gK and 2.3 J/gK, respectively. How much heat (kJ) is needed to convert 25.0 g of solid ethanol at -125°C to liquid ethanol at -40°C?

Answer 1

Hello, Chris,

The total amount of energy(heat) can be calculated by taking each step of the process separately.

[Note: Since the temperature changes are in increments, we can use the differerence of the Centigrade readings and Kelvin will have the identical value].

1. Warm The Solid
2. The specific heat for solid ethanol is 0.97 J/gK. This is telling us the we need to add 0.97 Joules to raise 1 gram of solid ethanol by 1 degree Kelvin. In this case we are raising the temperature by 11K (-114-(-125)) = 11K. The total heat required is the specific heat, times the temperature change, times the mass in grams:
3. (0.97 J/gK)*(25.0g)*(11K) = 266.8 Joules
4. Melt the Solid
5. The heat of fusion for this is 5.02 kJ/mole. The transition from solid to liquid requires 5.02 kJ for every mole. 25.0 grams of ethanol is (25.0 grams/46.0 g/mole) = 0.5432 moles
6. (5.02 kJ/mole)*(0.5432 moles) = 2.73 kJ
7. Note that this step does not involve any warming. The temperature remains at -114C.
8. Warm the Liquid
9. The specific heat for the liquid phase is 2.3 J/gK The temperature rise is (-40 - (-114))= 74K
10. (2.3 J/gK)*(25.0 g)*(74K) = 4255 Joules

Now all we need is to add the heats required for all three steps. Be careful about units. The heat of fusion was provided as kJ, whereas the others were all just Joules. I converted the first and last to kJ and then added all three to get 7.25 kJ to warm 25.0 grams of ethanol at - 125 through melting and up to -40C.

Bob