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
Jun 19, 2016

Answer:

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 %#

Jun 20, 2016

Answer:

#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.