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 [tex]C_2H_5OH=-135^oC=138 K(0^oC=273K)[/tex]
Melting temperature of Solid [tex]C_2H_5OH=114^oC=159 K[/tex]
Temperature of liquid [tex]C_2H_5OH=-50^oC=223K[/tex]
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 [tex]C_2H_5OH[/tex] at 159 K
[tex]\Delta T_1[/tex] = 159 K - 138 K = 21 K
[tex]Q_1=mc\Delta T= 25\times 0.97J/gK\times 21 K=509.25 J[/tex]
Heat required to melt and raise the temperature of [tex]C_2H_5OH[/tex] upto 223 K
[tex]\Delta T_2[/tex] = 223 K - 159 K = 64 K
[tex]Q_2=mc\Delta T= 25\times 2.3J/gK\times 64 K=3680 J[/tex]
Total heat to convert solid ethanol to liquid ethanol at given temperature :
[tex]Q_1+Q_2=509.25 J+3680 J=4189.25 J=4.18925 kJ[/tex] (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.
