# A sample of substance X that has a mass of 326.0 g releases 4325.8 cal when it freezes at its freezing point. If substance X has a molar mass of 58.45 g/mol, what is the molar heat of fusion for substance X?

##### 1 Answer

#### Answer:

#### Explanation:

For a given substance, the **molar enthalpy of fusion**, **mole** of said substance.

This implies that the molar enthalpy of fusion will almost always have a **positive value**, since heat is usually **needed** in order for a substance to go from solid at its melting point to liquid at its melting point.

Now, your goal here is to figure out the enthalpy change that occurs when **mole** of substance *liquid to solid* at its freezing point.

You already know that the substance **gives off** energy when it freezes, so right from the start, you know that this enthalpy change will carry a **negative sign**.

#DeltaH_ ("liquid " -> " solid") = -"(a value) mol "^(-1)#

The minus sign symbolizes heatgiven offand#"mol"^(-1)# symbolizes that this enthalpy change occursper moleof substance

So start by making a note that you must have

#overbrace(DeltaH_"fus")^(color(blue)("must be positive")) = - overbrace(DeltaH_ ("liquid " -> " solid"))^(color(purple)("will be negative"))#

Next, use the **molar mass** of substance *moles*.

#326.0 color(red)(cancel(color(black)("g"))) * "1 mole X"/(58.45color(red)(cancel(color(black)("g")))) = "5.5774 moles X"#

So, you know that when **moles** of **given off**. Use this information to find the heat given off when **mole** of

#1 color(red)(cancel(color(black)("mole X"))) * "4325.8 cal"/(5.5774color(red)(cancel(color(black)("mole X")))) = "775.6 cal"#

You can thus say that the enthalpy change that occurs when **mole** of

#DeltaH_ ("liquid " -> " solid") = - "775.6 cal mol"^(-1)#

Therefore, the molar enthalpy of fusion will be equal to

#DeltaH_"fus" = - (-"775.6 cal mol"^(-1))#

#color(darkgreen)(ul(color(black)(DeltaH_"fus" = +"775.6 cal mol"^(-1))))#

The answer is rounded to four **sig figs**, the number of sig figs you have for the mass of the sample.