# Question 7e12c

Apr 25, 2017

$\Delta {H}_{\text{rxn" = -"2.9 kJ}}$

#### 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 $\textcolor{\mathrm{da} r k \mathmr{and} a n \ge}{\text{1 mole}}$ of potassium hydroxide is dissolved in water at constant pressure and to an infinite dilution, $\textcolor{b l u e}{\text{58.5 kJ}}$ of heat are being 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.

${M}_{\text{M KOH") = M_ ("M K") + M_ ("M O") + M_ ("M H}}$

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 $1$ mole of potassium hydroxide has a mass of $\text{56 g}$. You can thus say that the molar heat of solution will be equivalent to

$- 58.6 {\text{kJ" /color(red)(cancel(color(black)("mol"))) * (1 color(red)(cancel(color(black)("mole KOH"))))/"56 g" = -"1.0464 kJ g}}^{- 1}$

You now know that when $\text{1 g}$ of potassium hydroxide is dissolved in water, $\text{1.0464 kJ}$ of heat are being 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 $\text{2.8 g}$ of potassium hydroxide in water is equal to

$\textcolor{\mathrm{da} r k g r e e n}{\underline{\textcolor{b l a c k}{\Delta {H}_{\text{rxn" = - "2.9 kJ}}}}}$

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.