A 4.33 g sample of a laboratory solution contains 1.32 g of acid. What is the concentration of the solution as a mass percentage?

1 Answer
Jul 12, 2016

Answer:

#30.5%#

Explanation:

A solution's percent concentration by mass, #"% m/m"#, tells you how many grams of solute, which in your case is an unknown acid, are present in #"100 g"# of solution.

#color(blue)(|bar(ul(color(white)(a/a)"% m/m" = "grams of solute / 100 g of solution"color(white)(a/a)|)))#

As you know, a solution contains a solute and a solvent, which more often than not is water. This means that a solution's #"% m/m"# concentration tells you how many grams of solute and grams of solvent must be mixed to get #"100 g"# of solution.

In your case, you know that you get #"1.32 g"# of acid in #"4.33 g"# of solution. To find the solution's percent concentration by mass, use this as a conversion factor to figure out how many grams of solute you'd get in #"100 g"# of solution

#100 color(red)(cancel(color(black)("g solution"))) * overbrace("1.32 g acid"/(4.33color(red)(cancel(color(black)("g solution")))))^(color(purple)("given to you")) = "30.5 g acid"#

Since #"100 g"# of this solution contain #"30.5 g"# of acid, it follows that the percent concentration by mass is

#"% m/m" = color(green)(|bar(ul(color(white)(a/a)color(black)("30.5% acid")color(white)(a/a)|)))#

The answer is rounded to three sig figs.

Notice that this is equivalent to dividing the mass of solute by the total mass of the solution and multiplying by #100#

#"% m/m" = (1.32 color(red)(cancel(color(black)("g acid"))))/(4.33color(red)(cancel(color(black)("g solution")))) * 100 = color(green)(|bar(ul(color(white)(a/a)color(black)("30.5% acid")color(white)(a/a)|)))#

As mentioned before, you can use the solution's percent concentration by mass to say that #"100 g"# of solution will contain

#"30.5 g acid"" "# and#" " "100 g " - " 30.5 g" = "69.5 g water"#

In other words, you can make this solution by adding #"30.5 g"# of acid for every #"69.5 g"# of water, which of course gets you #"30.5 g"# of acid per #"100 g"# of solution.