Respuesta :
Answer: The heat required is 6.88 kJ.
Explanation:
The conversions involved in this process are :
[tex](1):ethanol(s)(-135^0C)\rightarrow ethanol(s)(-114^0C)\\\\(2):ethanol(s)(-114^0C)\rightarrow ethanol(l)(-114^0C)\\\\(3):ethanol(l)(-114^0C)\rightarrow ethanol(l)(-50^0C)[/tex]
Now we have to calculate the enthalpy change.
[tex]\Delta H=[m\times c_{p,s}\times (T_{final}-T_{initial})]+n\times \Delta H_{fusion}+[m\times c_{p,l}\times (T_{final}-T_{initial})]+n\times \Delta H_{vap}+[m\times c_{p,g}\times (T_{final}-T_{initial})][/tex]
where,
[tex]\Delta H[/tex] = enthalpy change = ?
m = mass of ethanol = 25.0 g
[tex]c_{p,s}[/tex] = specific heat of solid ethanol= 0.97 J/gK
[tex]c_{p,l}[/tex] = specific heat of liquid ethanol = 2.31 J/gK
n = number of moles of ethanol = [tex]\frac{\text{Mass of ethanol}}{\text{Molar mass of ethanol}}=\frac{25.0g}{46g/mole}=0.543mole[/tex]
[tex]\Delta H_{fusion}[/tex] = enthalpy change for fusion = 5.02 KJ/mole = 5020 J/mole
[tex]T_{final}-T_{initial}=\Delta T[/tex] = change in temperature
The value of change in temperature always same in Kelvin and degree Celsius.
Now put all the given values in the above expression, we get
[tex]\Delta H=[25.0 g\times 0.97J/gK\times (-114-(-135)K]+0.534mole\times 5020J/mole+[25.0g\times 2.31J/gK\times (-50-(-114))K][/tex]
[tex]\Delta H=6885.93J=6.88kJ[/tex] (1 KJ = 1000 J)
Therefore, the heat required is 6.88 kJ
