Question

What amount of thermal energy (in kJ) is required to convert 27.0 g of ethanol at -158 °C completely to gaseous ethanol at 85 °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

The total heat required for the transfer of ethanol from the solid state to the gaseous state could be expressed as:

$Q_t=Q_s+Q_m+Q_L+Q_b+Q_g;$

,or

$Q_t=mC_s(t_{-114}-t_{-158})+\lambda_mm+mC_L(t_{78}-t_{-114})+\lambda_bm+mC_g(t_{85}-t_{78});$

,finally

$Q_t=27.0g(1.05\frac{J}{g^0C}*44^0C+5.0\frac {kJ}{mol}*\frac{1}{46g/mol}+2.44\frac{J}{g^0C}*192^0C+35.0\frac{kJ}{mol}*\frac{1}{46g/mol}+1.01\frac{J}{g^0C}*7^0C)=37.6kJ.$