Imagine your frozen lemonade is sold as a 4X concentrated (stock) solution that must be diluted in water. How would you make 36 ml of 1X lemonade?

Question

Imagine your frozen lemonade is sold as a 4X concentrated (stock) solution that must be diluted in water. How would you make 36 ml of 1X lemonade?

A. Combine 9 mL of concentrate with 27 mL of water

B. Combine 9 mL of concentrate with 36 mL of water

C. Combine 1 mL of concentrate with 35 mL of water

D. Combine 27 mL of concentrate with 9 mL of water

Answer 1

Hi Jas,

We can use the equation M₁V₁=M₂V₂, where M is the concentration (most often expressed in molarity, but the "4x,3x,2x,... etc" relative concentration definition works fine) and V is volume.

So, we want our final volume (V₂) to be 36 mL. We also want the concentration of this final solution (M₂) to be 1x

V₂ = 36 mL

M₂ = 1x

M₁ = 4x (as implied by the problem)

So now, we solve for V₁, which represents the volume of the stock solution that we should take

M₁V₁=M₂V₂

(4x)V₁ = (1x)(36 mL)

V₁ = (1x / 4x) (36 mL) = (1/4) (36 mL) = 9 mL

So V₁ = 9 mL. So, we first take this 9 mL from the stock 4x bottle and put it in our beaker. Then, to get to the final requested volume of 36 mL, we just add water (dilution). How much water do we add?

36 mL - 9 mL = 27 mL water

So we combine 9 mL of concentrate with 27 mL water