Respuesta :
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, [tex]Q=ms\Delta T[/tex]
where, Q is the heat energy, m is mass in grams, s is specific heat capacity in joule per gram per degree C and [tex]\Delta T[/tex] is the change in temperature.
For second step, there is a phase change so the equation used is, [tex]Q=m\Delta H_f_u_s[/tex]
where [tex]\Delta H_f_u_s[/tex] is the enthalpy of fusion.
Let's do the calculations for the first step:-
[tex]\Delta T[/tex] = -114-(-135) = 21 degree C
m = 25.0 g
s = 0.97 J per g per degree C
[tex]Q_1=25.0g(0.97\frac{J}{g.^0C})(21^0C)[/tex]
[tex]Q_1[/tex] = 509.25 J
let's convert this J to kj
[tex]509.25J(\frac{1kj}{1000J})[/tex]
= 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.
[tex]25.0g(\frac{1mol}{46.07g})[/tex]
= 0.543 mol
[tex]Q_2=0.543mol(\frac{5.02kj}{mol})[/tex]
[tex]Q_2[/tex] = 2.72 kj
For the third step, [tex]\Delta T[/tex] = -50 -(-114) = 64 degree C
[tex]Q_3=25.0g(2.3\frac{J}{g.^0C})(64^0C)[/tex]
[tex]Q_3[/tex] = 3680 J
[tex]3680J(\frac{1kj}{1000J})[/tex]
= 3.68 kj
total Q = [tex]Q_1+Q_2+Q_3[/tex]
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.
