Question #53829

1 Answer
Feb 28, 2017

Answer:

#"1.67% m/v"#

Explanation:

The idea here is that when a solution undergoes a #1:3# dilution, its final volume increases by a factor of #3#.

This is done by adding enough solvent to ensure that the total volume of the solution increases by a factor of #3#. As a result, the concentration of the solution will decrease by a factor of #3#.

In your case, the starting solution has a #"5% m/v"# concentration and a volume of #"250 mL"#. The total volume of the solution after the dilution will be

#V_"final" = 3 xx "250 mL" = "750 mL"#

The concentration of the solution after the dilution will be

#"% m/v" = "5%"/3 = color(darkgreen)(ul(color(black)(1.67%)))#

You can double-check this result by working with the mass of solute present in the solution. In the initial solution, you have

#250 color(red)(cancel(color(black)("mL solution"))) * overbrace("5 g NaCl"/(100color(red)(cancel(color(black)("mL solution")))))^(color(blue)("= 5% m/v NaCl")) = "12.5 g NaCl"#

Remember, the solution is diluted by adding solvent, so you know for a fact that the diluted solution will contain #"12.5 g"# of sodium chloride.

In order to find the diluted solution's mass by volume percent concentration, you must determine how many grams of solute you have in #"100 mL"# of solution. The diluted solution has a volume of #"750 mL"# and contains #"12.5 g"# of sodium chloride, which means that #"100 mL"# of this solution will contain

#100 color(red)(cancel(color(black)("mL solution"))) * "12.5 g NaCl"/(750 color(red)(cancel(color(black)("mL solution")))) = "1.67 g NaCl"#

This means that the mass by volume percent concentration of the diluted solution will be

#color(darkgreen)(ul(color(black)("% m/v = 1.67% NaCl")))#

I'll leave the answer rounded to three sig figs, but keep in mind that you only have one significant figure for the concentration of the initial solution.