Question

What is the concentration of the solution produced when 150.0 mL of water is added to 200.0 mL of 0.250 M NaCl?

Answer 1

`"0.143 M"`

Explanation:

The thing to remember about a dilution is that you can find its dilution factor by dividing either the volume of the diluted solution by the volume of the stock solution

`"DF" = V_"diluted"/V_"stock"`

or by dividing the concentration of the stock solution by the concentration of the diluted solution.

`"DF" = c_"stock"/c_"diluted"`

So you can say that for any dilution, you have

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

In your case, the volume of the diluted solution will be

`V_"diluted" = "150.0 mL + 200.0 mL" = "350.0 mL"`

This means that the dilution factor is equal to

`"DF" = (350.0 color(red)(cancel(color(black)("mL"))))/(200.0 color(red)(cancel(color(black)("mL")))) = color(blue)(1.75)`

You can thus say that the stock solution was `color(blue)(1.75)` times more concentrated than the diluted solution, since

`c_"stock" = "DF" * c_"diluted"`

This implies that the concentration of the diluted solution is equal to

`c_"diluted" = c_"stock"/"DF"`

`c_"stock" = "0.250 M"/color(blue)(1.75) = color(darkgreen)(ul(color(black)("0.143 M")))`

The answer is rounded to three sig figs.