Question

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

Answer 1

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 `"NaCl"` in the original solution.
2. Calculate the new masses of `"NaCl"` and solution after adding `"NaCl"`.
3. Calculate the percent of `"NaCl"` in the new solution.

1. Mass of `bb"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

`"Mass of component" = ("mass of mixture" × 100 %)/"mass %"`

∴ `"Mass of NaCl" = ("180 g" × 8 color(red)(cancel(color(black)(%))))/(100 color(red)(cancel(color(black)(%)))) = "14.4 g"`

2. New masses

`"Mass of NaCl" = "14.4 g + 20 g" = "34.4 g"`

`"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 %`

Answer 2

`17%`

Explanation:

The idea here is that adding the `"20 g"` of sodium chloride, `"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, `"% m/m"`, essentially tells you how many grams of solute, which in your case is sodium chloride, you get per `"100 g"` of solution.

Initially, your solution has a mass of `"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_"NaCl" = "14.4 g" + "20 g" = "34.4 g NaCl"`

The total mass of the solution will now be

`m_"solution" = "180 g" + "20 g" = "200 g"`

Since `"200 g"` of solution contain `"34.4 g"` of sodium chloride, it follows that `"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.