Respuesta :
Answer : The amount of heat required is, 639.3 KJ
Solution :
The conversions involved in this process are :
[tex](1):Cr(s)(1760^oC)\rightarrow Cr(s)(1860^oC)\\\\(2):Cr(s)(1860^oC)\rightarrow Cr(l)(1860^oC)\\\\(3):Cr(l)(1860^oC)\rightarrow Cr(l)(2060^oC)[/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})][/tex]
where,
[tex]\Delta H[/tex] = enthalpy change or heat required = ?
m = mass of Cr = 126.3 g
[tex]c_{p,s}[/tex] = specific heat of solid Cr = [tex]44.8J/g^oC[/tex]
[tex]c_{p,l}[/tex] = specific heat of liquid Cr = [tex]0.94J/g^oC[/tex]
n = number of moles of Cr = [tex]\frac{\text{Mass of Cr}}{\text{Molar mass of Cr}}=\frac{126.3g}{52g/mole}=2.428mole[/tex]
[tex]\Delta H_{fusion}[/tex] = enthalpy change for fusion = 20.5 KJ/mole = 20500 J/mole
Now put all the given values in the above expression, we get
[tex]\Delta H=[126.3g\times 44.8J/g^oC\times (1860-(1760))^oC]+2.428mole\times 20500J/mole+[126.3g\times 0.94J/g^oC\times (2060-1860)^oC][/tex]
[tex]\Delta H=639342.4J=639.3KJ[/tex] Â Â (1 KJ = 1000 J)
Therefore, the amount of heat required is, 639.3 KJ
