Question 1e76e

Jun 9, 2016

$0.406$

Explanation:

The mole fraction of a compound that's part of a mixture is simply the ratio between the number of moles of said compound and the total number of moles present in the mixture.

So, for a compound $i$ you will have

$\textcolor{b l u e}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \text{mole fraction of i" = "number of moles of i"/"total number of moles} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

In your case, the mixture is said to contain three ionic compounds

• sodium chloride, $\text{NaCl}$
• potassium chloride, $\text{KCl}$
• lithium chloride, $\text{LiCl}$

The first thing to do is use the molar masses of the three compounds to determine how many moles of each you have

$\text{For NaCl: " 0.564 color(red)(cancel(color(black)("g"))) * "1 mole NaCl"/(58.44color(red)(cancel(color(black)("g")))) = "0.009651 moles NaCl}$

$\text{For KCl: " 1.52 color(red)(cancel(color(black)("g"))) * "1 mole KCl"/(74.55color(red)(cancel(color(black)("g")))) = "0.02039 moles KCl}$

$\text{For LiCl: " 0.857color(red)(cancel(color(black)("g"))) * "1 mole LiCl"/(42.39color(red)(cancel(color(black)("g")))) = "0.02022 moles LiCl}$

The total number of moles present in the mixture will be

${n}_{\text{total}} = {n}_{N a C l} + {n}_{K C l} + {n}_{L i C l}$

${n}_{\text{total" = 0.009651 + 0.02039 + 0.02022 = "0.05026 moles}}$

All you have to do now in order to find the mole fraction of potassium chloride is to divide the number of moles of potassium chloride by the total number of moles present in the mixture

${\chi}_{K C l} = \left(0.02039 \textcolor{red}{\cancel{\textcolor{b l a c k}{\text{moles"))))/(0.05026color(red)(cancel(color(black)("moles}}}}\right) = \textcolor{g r e e n}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{0.406} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

The answer is rounded to three sig figs.

SIDE NOTE It's worth mentioning that the mole fractions of all the components in the mixture must add up to give $1$.

In this case, you will have

overbrace("moles of NaCl"/"total moles")^(color(blue)("mole fraction of NaCl")) + overbrace("moles of KCl"/"total moles")^(color(purple)("mole fraction of KCl")) + overbrace("moles of LiCl"/"total moles")^(color(darkgreen)("mole fraction of LiCl")) = 1#

simply because

$\text{total moles" = "moles of NaCl" + "moles of KCl" + "moles of LiCl}$