What amount of heat (in kJ) is required to convert 19.1 g of an unknown solid (MM = 83.21 g/mol) at -5.00 °C to a liquid at 52.3 °C?

Question

(heat capacity of solid = 2.39 J/g･°C; heat capacity of liquid = 1.58 J/g･°C; ∆Hfus = 3.72 kJ/mol; Tf = 10.3°C). Please give me each step to how you came up with your answer.

Answer 1

Based on the info given for dHFus (Tf = 10.3C), I’ll assume that’s the melting point..

Step 1. Heat required to raise temp from -5 to 10.3:

q = mcdT = (19.1 g)(2.39 J/ g^o)(15.3⁰) = 698.4J

Step 2. Heat required to melt the stuff (phase change, no change in temp):

q = mdHfus = (19.1 g)(3.72 kJ/mole x 1 mole/83.21 g). = 0.8539 kJ = 853.9 Ju

Step 3. Heat required to raise temp from 10.3 to 52.3 degrees:

q = mcdT = (19.1 g)(1.58 J/g^o)(42⁰) = 1267 J

Step 4. Total all of the heats.

698.4 J + 853.9 J + 1267 J = 2819 J

Step 5. Convert to kJ and correct to 3 significant figures:

2819 J x 1 kJ/1000 J = 2.819 kJ = 2.82 kJ (final answer)