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?

- 6.91 kj of heat is needed.

Solution:- We have solid ethanol at -135 degree C and wants to calculate the heat required to convert it to -50 degree C liquid ethanol.

Melting point of ethanol is -114 degree C. So, it is a three step process. In the first step, -135 degree C solid ethanol changes to -114 degree C solid ethanol.

In second step, -114 degree C solid ethanol melts to -114 degree C liquid ethanol. In third step, -114 degree C liquid changes to -50 degree C liquid.

for the first and third step, there is a change in temperature and so we use the equation,

where, Q is the heat energy, m is mass in grams, s is specific heat capacity in joule per gram per degree C and is the change in temperature.

For second step, there is a phase change so the equation used is,

where is the enthalpy of fusion.

Let's do the calculations for the first step:-

= -114-(-135) = 21 degree C

m = 25.0 g

s = 0.97 J per g per degree C

= 509.25 J

let's convert this J to kj

= 0.509 kj

For the second step we need the moles of ethanol as the enthalpy of fusion is given in kj per mol. Molar mass of ethanol is 46.07 g per mol.

= 0.543 mol

= 2.72 kj

For the third step, = -50 -(-114) = 64 degree C

= 3680 J

= 3.68 kj

total Q =

total Q = 0.509 kj + 2.72 kj + 3.68 kj

total Q = 6.909 kj

this could be round to 6.91 kj.

So, 6.91 kj of heat is needed to convert -135 degree C solid ethanol to -50 degree C ethanol.