CHEMISTRY QUESTION

Question

I've tried this question again and again but my solution is incorrect... can someone pls help me?

What amount of thermal energy (in kJ) is required to convert 40.7 g of ethanol at -158 °C completely to gaseous ethanol at 108 °C? The melting point of ethanol is -114 °C and its normal boiling point is 78 °C.

The heat of fusion of ethanol is 5.0 kJ mol^-1

The heat of vaporization of ethanol at its normal boiling point is 35.0 kJ mol^-1

The specific heat capacity of solid ethanol is 1.05 J g^-1 °C^-1

The specific heat capacity of liquid ethanol is 2.44 J g^-1 °C^-1

The specific heat capacity of gaseous ethanol is 1.01 J g^-1 °C^-1

Answer 1

I'll set up the steps for you, but you can do the actual calculations.

NOTE: some values are given in J and some in kJ. Also, some are in kJ/mole and others in J/g, etc. Be sure all your units agree. I've chosen to work in Joules and grams, instead of kJ and moles, but you can do either.

Step 1: heat required to raise temp of solid ethanol from -158º to -114º

q = mC_solid∆T = (40.7 g)(1.05 J/g/deg)(44 deg) = J

Step 2: heat required melt 40.7 g of solid ethanol.

q = m∆H_fusion = (40.7 g)(5.0 kJ/mol x 1 mol/46 g)(1000 J/kJ) = J

Step 3: heat required to raise temp of 40.7 g of liquid ethanol from -114ºC to +78º

q = mC_liquid∆H = (40.7 g)(2.44 J/g/deg)(192 deg) = J

Step 4: heat required to convert 40.7 g liquid to gas at 78º

q = m∆H_vaporization = (40.7 g)(35.0 kJ/mol)(1 mol/46 g)(1000 J/kJ) = J

Step 5: heat required to raise temp of 40.7 g of gas from 78º to 108º

q = mC_gas∆T = (40.7 g)(1.01 J/g/deg)(30 deg) = J

Add up all the joules calculated in steps 1-5 to get the total number of joules. If you want the answer in kJ, simply divide by 1000.

Hope this helps you understand the process. Remember that during any phase change (solid ->liquid->gas), there is not change in temperature.