# Question #7e12c

##### 1 Answer

#### Answer:

#### Explanation:

You know that the *molar* heat of solution of potassium hydroxide is equal to

#DeltaH_"sol" = - color(blue)("58.5 kJ") color(white)(.)color(darkorange)("mol"^(-1))#

This means that when *infinite dilution*, **given off**, hence the *minus sign* used in the expression of the molar heat of solution.

You can actually convert this value to *kilojoules per gram* by using the **molar mass** of potassium hydroxide.

#M_ ("M KOH") = M_ ("M K") + M_ ("M O") + M_ ("M H")#

You will have

#M_ ("M KOH") = "39 g mol"^(-1) + "16 g mol"^(-1) + "1 g mol"^(-1)#

#M_ ("M KOH") = "56 g mol"^(-1)#

This tells you that **mole** of potassium hydroxide has a mass of

#-58.6 "kJ" /color(red)(cancel(color(black)("mol"))) * (1 color(red)(cancel(color(black)("mole KOH"))))/"56 g" = -"1.0464 kJ g"^(-1)#

You now know that when **given off**.

Therefore, your sample of potassium hydroxide will give off

#2.8 color(red)(cancel(color(black)("g"))) * "1.0464 kJ given off"/(1color(red)(cancel(color(black)("g")))) = "2.9 kJ given off"#

This is equivalent to saying that the *enthalpy change* that occurs when you dissolve

#color(darkgreen)(ul(color(black)(DeltaH_"rxn" = - "2.9 kJ")))#

The answer is rounded to two **sig figs**, the number of sig figs you have for the mass of potassium hydroxide.

Remember, the minus sign is used to denote **heat given off**.