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:- 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,
`Q=ms\Delta T`

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

For second step, there is a phase change so the equation used is,
`Q=m\Delta H_f_u_s`

where
`\Delta H_f_u_s` is the enthalpy of fusion.

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

`\Delta T` = -114-(-135) = 21 degree C

m = 25.0 g

s = 0.97 J per g per degree C

`Q_1=25.0g(0.97(J)/(g.^0C))(21^0C)`

`Q_1` = 509.25 J

let's convert this J to kj

`509.25J((1kj)/(1000J))`

= 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.

`25.0g((1mol)/(46.07g))`

= 0.543 mol

`Q_2=0.543mol((5.02kj)/(mol))`

`Q_2` = 2.72 kj

For the third step,
`\Delta T` = -50 -(-114) = 64 degree C

`Q_3=25.0g(2.3(J)/(g.^0C))(64^0C)`

`Q_3` = 3680 J

`3680J((1kj)/(1000J))`

= 3.68 kj

total Q =
`Q_1+Q_2+Q_3`

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.