# Question a4544

Mar 14, 2016

$\text{119.991 u}$

#### Explanation:

The first thing to note here is that you're dealing with an ionic compound, which means that you're actually looking for the mass of $3$ formula units o sodium hydroxide, $\text{NaOH}$.

Now, the unified atomic mass unit, $u$, is defined as the mass of $\frac{1}{12} \text{th}$ of the mass of a single, unbound, neutral carbon-12 atom in its electronic ground state.

More importantly, it's worth remembering that one unified atomic mass unit is approximately equal to the mass of one proton or of one neutron, i.e. of one nucleon.

In simple terms, one unified atomic mass unit is equivalent to ${\text{1 g mol}}^{- 1}$

$\textcolor{b l u e}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} {\text{1 u " = " 1 g mol}}^{- 1} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

Use the molar mass of sodium hydroxide to find how many unified atomic mass units you get per formula unit

39.997color(red)(cancel(color(black)("g mol"^(-1)))) * "1 u"/(1color(red)(cancel(color(black)("g mol"^(-1))))) = "39.997 u"

This means that three formula units of sodium hydroxide will have a mass of

$3 \textcolor{red}{\cancel{\textcolor{b l a c k}{\text{formula units"))) * "39.997 u"/(1color(red)(cancel(color(black)("formula unit")))) = color(green)(|bar(ul(color(white)(a/a)"119.991 u} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

The calculation you did in your suggested solution gives you the mass of three formula units of sodium hydroxide expressed in grams, not in unified atomic mass units.

Since the molar mass of a compound tells you the mass of one mole of said compound, you can use Avogadro's number to determine the mass of a single formula unit of sodium hydroxide.

$\textcolor{b l u e}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \text{1 mole" = 6.022 * 10^(23)"formula units} \textcolor{w h i t e}{\frac{a}{a}} |}}} \to$ Avogadro's number

In this case, you would have

$39.997 \text{g"/color(red)(cancel(color(black)("mol"))) * overbrace((1color(red)(cancel(color(black)("mol"))))/(6.022 * 10^(23)"f. units"))^color(purple)("Avogadro's number") = 6.642 * 10^(-23)"g/f. unit}$

This means that three formula units will have a mass of

3color(red)(cancel(color(black)("f. units"))) * (6.642 * 10^(-23)"g")/(1color(red)(cancel(color(black)("f. unit")))) = 1.993 * 10^(-22)"g"#