Question 0a460

Sep 4, 2017

$1.5 \cdot {10}^{18}$

Explanation:

The first thing that you need to do here is to convert the mass of the crystal to moles by using the molar mass of sodium chloride.

Notice that the mass of the crystal is given to you in milligrams, $\text{mg}$. To convert the mass to grams, use the fact that

$\textcolor{b l u e}{\underline{\textcolor{b l a c k}{\text{1 g" = 10^3color(white)(.)"mL}}}}$

You will have

overbrace(0.15 color(red)(cancel(color(black)("mg"))) * (1color(red)(cancel(color(black)("g"))))/(10^3color(red)(cancel(color(black)("mg")))))^(color(blue)("mg to g")) * overbrace("1 mole NaCl"/(58.44color(red)(cancel(color(black)("g")))))^(color(blue)("the molar mass of NaCl")) = 2.567 * 10^(-6)color(white)(.)"moles NaCl"

Now, to find the number of formula units present in the crystal, you must use the fact that in order to have $1$ mole of sodium chloride, you need to have $6.022 \cdot {10}^{23}$ formula units of sodium chloride $\to$ this is given by Avogadro's constant, which acts as the definition of a mole.

You can thus say that your sample will contain

2.567 * 10^(-6) color(red)(cancel(color(black)("moles NaCl"))) * overbrace((6.022 * 10^(23)color(white)(.)"formula units NaCl")/(1color(red)(cancel(color(black)("mole NaCl")))))^(color(blue)("Avogadro's constant"))#

$= \textcolor{\mathrm{da} r k g r e e n}{\underline{\textcolor{b l a c k}{1.5 \cdot {10}^{18} \textcolor{w h i t e}{.} \text{formula units NaCl}}}}$

The answer is rounded to two sig figs, the number of sig figs you have for the mass of the salt crystal.