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

##### 2 Answers

The new solution is

#### Explanation:

It seems we should have a three-part strategy:

- Calculate the mass of
#"NaCl"# in the original solution. - Calculate the new masses of
#"NaCl"# and solution after adding#"NaCl"# . - 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

∴

**2. New masses**

**3. New percent composition**

#### Explanation:

The idea here is that adding the **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

A solution's **percent concentration by mass**, **per** **of solution**.

Initially, your solution has a mass of

#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

#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.