What volumes of a 2 % solution and a 6 % solution must I mix to get 300 mL of a 5 % solution?

1 Answer
Jul 4, 2017

Answer:

You must mix #"75 cm"^3# of the 2% solution and #"225 cm"^3# of the 6 % solution.

Explanation:

We can use a modification of the dilution formula to solve this problem:

#color(blue)(bar(ul(|color(white)(a/a)V_1c_1 + V_2c_2 = V_3c_3color(white)(a/a)|)))" "#

Let #x# = the volume of 2 %.
Then #300 - x# = the volume of 6 %.

Then

#x × 2color(red)(cancel(color(black)(%))) + (300-x) × 6color(red)(cancel(color(black)(%))) = 300 × 5color(red)(cancel(color(black)(%)))#

#2x + 1800 - 6x = 1500#

#4x = 300#

#x = 300/4 = 75#

∴ You must use #"75 cm"^3# of 2% and #"225 cm"^3# of 6 %.

Check:

#75 × 0.02 + 225 × 0.06 = 300 × 0.05#

#1.5 + 13.5 = 15#

#15 = 15#

It checks!