Question #59b26

1 Answer
Dec 20, 2017

Answer:

#"0.05 M"#

Explanation:

The trick here is to realize that diluting a solution will cause its concentration to decrease by the factor as its volume increases.

#"DF" = V_"diluted"/V_"stock" = c_"stock"/c_"diluted"#

Here #"DF"# is the dilution factor.

In your case, the volume of the stock solution increases by #"875 mL"# to a total value of

#V_"diluted" = "125 mL" + "875 mL"#

#V_"diluted" = "1,000 mL"#

This means that the dilution factor is equal to--remember, we're using the volume of the diluted solution and the volume of the stock solution here!

#"DF" = ("1,000" color(red)(cancel(color(black)("mL"))))/(125color(red)(cancel(color(black)("mL")))) = color(blue)(8)#

So if the volume increased by factor of #color(blue)(8)#, it follows that the concentration must have decreased by a factor of #color(blue)(8)#.

#color(blue)(8) = c_"stock"/c_"diluted"#

You will thus have

#c_"diluted" = c_"stock"/color(blue)(8)#

#c_"diluted" = "0.400 M"/color(blue)(8) = color(darkgreen)(ul(color(black)("0.05 M")))#

The answer is rounded to one significat figure because when you're adding the two volumes, the answer, i.e. #"1,000 mL"#, has one significant figure and no decimal places.