# 20g of NaCl were added to an 8% 180g of NaCl solution. What is the mass percent of NaCl in the solution now?

Jun 19, 2016

The new solution is 17 % ("w/w")color(white)(l) "NaCl".

#### Explanation:

It seems we should have a three-part strategy:

1. Calculate the mass of $\text{NaCl}$ in the original solution.
2. Calculate the new masses of $\text{NaCl}$ and solution after adding $\text{NaCl}$.
3. Calculate the percent of $\text{NaCl}$ in the new solution.

1. Mass of $\boldsymbol{\text{NaCl}}$ in original solution

The formula for percent composition is

color(blue)(|bar(ul(color(white)(a/a) "Mass %" = "mass of component"/"mass of mixture" × "100 %"color(white)(a/a)|)))" "

We can rearrange this to

$\text{Mass of component" = ("mass of mixture" × 100 %)/"mass %}$

$\text{Mass of NaCl" = ("180 g" × 8 color(red)(cancel(color(black)(%))))/(100 color(red)(cancel(color(black)(%)))) = "14.4 g}$

2. New masses

$\text{Mass of NaCl" = "14.4 g + 20 g" = "34.4 g}$

$\text{Mass of solution" = "180 g + 20 g" = "200 g}$

3. New percent composition

"Mass %" = "mass of NaCl"/"mass of solution" × "100 %" = (34.4 color(red)(cancel(color(black)("g"))))/(200 color(red)(cancel(color(black)("g")))) × 100 % = 17 %

Jun 20, 2016

17%

#### Explanation:

The idea here is that adding the $\text{20 g}$ of sodium chloride, $\text{NaCl}$, will increase the percent concentration by mass of the solution, so right from the start you should expect the concentration of the target solution to be higher than 8%.

A solution's percent concentration by mass, $\text{% m/m}$, essentially tells you how many grams of solute, which in your case is sodium chloride, you get per $\text{100 g}$ of solution.

Initially, your solution has a mass of $\text{180 g}$ and a percent concentration by mass equal to 8%. This implies that the initial solution contains

180 color(red)(cancel(color(black)("g solution"))) * overbrace("8 g NaCl"/(100color(red)(cancel(color(black)("g solution")))))^(color(blue)("= 8% m/m NaCl")) = "14.4 g NaCl"

The target solution will contain a total of

${m}_{\text{NaCl" = "14.4 g" + "20 g" = "34.4 g NaCl}}$

The total mass of the solution will now be

${m}_{\text{solution" = "180 g" + "20 g" = "200 g}}$

Since $\text{200 g}$ of solution contain $\text{34.4 g}$ of sodium chloride, it follows that $\text{100 g}$ will contain

100color(red)(cancel(color(black)("g solution"))) * "34.4 g NaCl"/(200color(red)(cancel(color(black)("g solution")))) = "17.2 g NaCl"

Therefore, the target solution's percent concentration by mass is

"% m/m" = color(green)(|bar(ul(color(white)(a/a)color(black)("17% NaCl")color(white)(a/a)|)))

I'll leave the answer rounded to two sig figs.

As predicted, the percent concentration of the solution increased upon the addition of more solute.