Enthalpy of a Phase Change

Question

How many grams of ice at -13.4 ∘C can be completely converted to liquid at 19.1 ∘C if the available heat for this process is 4.17×103 kJ? For ice, use a specific heat of 2.01 J g−1 ∘C−1 and ΔfusH=6.01kJ mol−1.

Express your answer to three significant figures and include the appropriate units.

Answer 1

m grams of ice @ -13.4ºC to m grams of liquid @ 19.1ºC, given 4.17x10³ kJ of heat energy?

Step 1: raise temp of ice to 0º. q = mC∆T = (m)(2.01 J/gº)(13.4º)

Step 2: melt the ice @ 0º. q = m∆Hfus = (m)(6.01 kJ/mol)(1mol/18g = (m)(334 J/g)

Step 3: raise temp of liquid @0º to 19.1º. q = mC∆T = (m)(4.184 J/gº)(19.1º)

The sum of these steps is ...

(m)(2.01 J/gº)(13.4º) + (m)(334 J/g) + (m)(4.184 J/gº)(19.1º)

26.9m + 334m + 79.9m = 440.8m J/g

4170 J are provided, so we an solve for m (mass)...

4170 J = 440.8m J/g

m = 9.46 g of ice