Question

Question #04705

Answer 1

`DeltaH_"fus" = -"6.005 kJ/mol"`

Explanation:

As you know, the molar enthalpy change of fusion, `DeltaH_"fus"`, is defined as the change in enthalpy when one mole of a substance undergoes a liquid to solid or a solid to liquid phase change at its melting / freezing point.

More specifically, the molar enthalpy change of fusion will tell you

• how much heat must be added to one mole of a substance at its melting point in order for a solid `->` liquid phase change to take place

• how much heat must be given off by one mole of a substance at its freezing point in order for a liquid `->` solid phase change to take place

In your case, you are interested in finding out the molar enthalpy change of fusion for the freezing of `"30.00 g"` of water at `0^@"C"`. This means that the molar enthalpy change of fusion must carry a negative sign, since it represents heat lost.

The equation you'll use here looks like this

`color(blue)(q = n * DeltaH_"fus")" "`, where

`q` - heat lost / absorbed
`n` - the number of moles of the substance
`DeltaH_"fus"` - the molar enthalpy change of fusion

Use water's molar mass to determine how many moles you have in that `"30.00-g"` sample

`30.00 color(red)(cancel(color(black)("g"))) * ("1 mole H"_2"O")/(18.015color(red)(cancel(color(black)("g")))) = "1.6653 moles H"_2"O"`

No,w you know that `"10.00 kJ"` of heat are given off when this sample of water goes from liquid water at `0^@"C"` to ice at `0^@"C"`.

This means that the value of `q` will be

`q = -"10.00 kJ"`

Again, the negative sign is used to symbolize heat lost.

This means that you have

`DeltaH_"fus" = q/n`

`DeltaH_"fus" = (-"10.00 kJ")/"1.6653 moles" = color(green)(-"6.005 kJ/mol")`

The answer is rounded to four sig figs.

So, you can say that the molar enthalpy change of fusion for water will be equal to

• `DeltaH_"fus" = +"6.005 kJ/mol" ->` when ice at `0^@"C"` melts to liquid water at `0^@"C"`
• `DeltaH_"fus" = -"6.005 kJ/mol" ->` when liquid water at `0^@"C"` freezes to ice at `0^@"C"`