Ethanol (c2h5oh) melts at -114â°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 -135â°c to liquid ethanol at -50â°c?

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.

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