Melting point of ethanol = -114°c
Enthalpy of fusion = 5.02KJ/mol
Specific heat of solid ethanol = 0.97J/gk
specific heat of liquid ethanol = 2.3 j/gk.
mass of ethanol = 25.0g
moles of ethanol = mass/Molar mass = 25.0/46.07 = 0.543 moles
step 1:
solid ethanol at -135 C changing to solid ethanol at -114 C
Q1 = mass x specific heat of solid ethanol x change in Temperature
= 25.0 x 0.97 x [-114 - (-135)]
= 25.0 x 0.97 x [-114+135]
= 25.0 x 0.97 x 21
Q1 = 509.25 J
Step 2: solid ethanol at -114 C is changing to liquid ethanol at -114 C
Q2 = moles x deltaHfusion
= 0.543 x 5.02 KJ
= 2.72586 x 1000 J
Q2 = 2725.86 J
Step 3: liquid ethanol at -114 C is changing to liquid ethanol at -50 C
Q3 = mass x specific heat of liquid ethanol x change in T
= 25.0 x 2.3 x [-50 -(-114)]
= 25.0 x 2.3 x [-50+114]
= 25.0 x 2.3 x 64
Q3 = 3680J
Total heat = Q1 + Q2 + Q3
= 509.25 + 2725.86 + 3680
= 6915.11 J
Total heat = 6.915 KJ
Total heat required to convert 25.0g of solid ethanol at -135 C to liquid ethanol at -50 C is 6.9KJ.
