The molar heat of fusion for water is 6.01 kJ/mol. How much energy is released when 36.8 g of water freezes at its freezing point?
For a given substance, the molar heat of fusion basically tells you one thing from two perspectives
- how much heat is needed in order to melt one mole of that substance at its melting point
- how much heat must be removed in order to freeze one mole of that substance at its freezing point
It is very important to realize that the molar enthalpy of fusion will carry a positive sign when you're dealing with melting and a negative sign when you're dealing with freezing.
That is the case because heat released carries a negative sign, while heat absorbed carries a positive sign. So, for water, you can say that
#DeltaH_"fus" = +"6.01 kJ/mol" ->#heat needed for melting
#DeltaH_"fus" = -"6.01 kJ/mol" ->#heat released when freezing
You're interested in finding out how much heat is released when
#36.8 color(red)(cancel(color(black)("g"))) * ("1 mole H"_2"O")/(18.015color(red)(cancel(color(black)("g")))) = "2.043 moles H"_2"O"#
The heat released can be calculated using the equation
#color(blue)(q = n * DeltaH_"fus")" "#, where
Since you're dealing with freezing, you will have
#q = 2.043 color(red)(cancel(color(black)("moles"))) * (-6.01"kJ"/color(red)(cancel(color(black)("mol")))) = -"12.3 kJ"#
What this means is that when
Remember, the negative sign symbolizes heat released.
#q = -"12.3 kJ"#
is equivalent to saying that