What volume of 0.10 M #NaOH# can be prepared from 250 mL of 0.30 M #NaOH#?

1 Answer
Jul 29, 2016

Answer:

#"750 mL"#

Explanation:

The thing to notice here is that the initial solution is #3# times more concentrated than the target solution, since

#(0.30 color(red)(cancel(color(black)("M"))))/(0.10color(red)(cancel(color(black)("M")))) = 3#

This tells you that the volume of the target solution must be #3# times greater than the volume of the initial solution.

That is the case because when you dilute a solution, you decrease its concentration by increasing its volume while keeping the number of moles of solute constant.

http://acidsandbasesfordummieschem.weebly.com/molarity.html

This implies that when the concentration of a solution decreases by a factor, which is usually called dilution factor, #"DF"#, upon dilution, the volume of the diluted solution increases by the same factor #"DF"#.

#color(blue)(|bar(ul(color(white)(a/a)"DF" = V_"final"/V_"initial" = c_"initial"/c_"final"color(white)(a/a)|)))#

You thus have

#V_"final" = 3 xx "250 mL" = color(green)(|bar(ul(color(white)(a/a)color(black)("750 mL")color(white)(a/a)|)))#

The answer is rounded to two sig figs.

So, you can decrease the concentration of #"250 mL"# of sodium hydroxide solution from #"0.30 M"# to #"0.10 M"# by adding enough water to get its final volume to #"750 mL"#.