Question #cb299

1 Answer
Mar 5, 2017

Answer:

#"2 kg NaCl"#

Explanation:

Don't forget that a solution's percent concentration by mass tells you the amount of solute present for every #"100 g"# of solution.

In other words, the solution's percent concentration by mass is a measure of the number of grams of solute present for every #"100 g"# of solute and solvent.

You can replace grams with kilograms if you want and say that a #40%# by mass sodium chloride solution will contain #"40 kg"# of sodium chloride for every #"100 kg"# of solution.

#"40 kg NaCl " stackrel(color(white)(acolor(red)("for every")aaa))(->) "100 kg NaCl" + "H"_2"O"#

You already know that you have #"3 kg"# of water available. Let's assume that #x# represents the number of kilograms of sodium chloride that must be added to #"3 kg"# of water in order to make a #40%# sodium chloride solution.

You know that #x# #"kg"# of sodium chloride in

#(3 + x)color(white)(.)"kg solution"#

will be equivalent to #"40 kg"# of sodium chloride in #"100 kg"# of solution, so set up the proportion as

#(xcolor(red)(cancel(color(black)("kg NaCl"))))/((3 + x) color(red)(cancel(color(black)("kg solution"))) ) = (40 color(red)(cancel(color(black)("kg NaCl"))))/(100color(red)(cancel(color(black)("kg solution"))))#

This means that you will have

#x = 40/100 (3 + x)#

#100x = 120 + 40x#

#60x = 120 implies x= 120/60 = 2#

Therefore, you need to add #"2 kg"# of sodium chloride, the equivalent of #"2000 g"#, to #"3 kg"# of water in order to make a #40%# by mass sodium chloride solution.