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 -135°c to liquid ethanol at -50°c?

Answer 1

Answer: 4.18925 kJ heat is needed to convert 25.0 g of solid ethanol at -135 °C to liquid ethanol at -50°C.

Explanation:

Temperature of Solid $C_2H_5OH=-135^oC=138 K(0^oC=273K)$

Melting temperature of Solid $C_2H_5OH=114^oC=159 K$

Temperature of liquid $C_2H_5OH=-50^oC=223K$

Specific heats of solid  ethanol = 0.97 J/gK

Specific heats of liquid ethanol = 2.3 J/gK

Heat required to melt the the 25 g solid $C_2H_5OH$ at 159 K

$\Delta T_1$ = 159 K - 138 K = 21 K

$Q_1=mc\Delta T= 25\times 0.97J/gK\times 21 K=509.25 J$

Heat required to melt and raise the temperature of $C_2H_5OH$ upto 223 K

$\Delta T_2$ = 223 K - 159 K  = 64 K

$Q_2=mc\Delta T= 25\times 2.3J/gK\times 64 K=3680 J$

Total heat to convert solid ethanol to liquid ethanol at given temperature :

$Q_1+Q_2=509.25 J+3680 J=4189.25 J=4.18925 kJ$ (1kJ=1000J)

Hence, 4.18925 kJ of heat will be required to convert 25.0 g of solid ethanol at -135 °C to liquid ethanol at -50°C.