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How much 100% active ingredient powder would you need to add to 4 mL
of multivitamin powder that is 20% active ingredient powder in order to
strengthen the mixture to 50% active ingredient powder?

Respuesta :

oladayoademosu

We need to add 2.4 mL of 100 % active ingredient powder to strengthen the mixture to 50% active ingredient powder

How to calculate the amount of active ingredient?

The amount of each volume m = CV where

  • C = concentration and
  • V = volume

The amount of 50 % mixture, m = amount of 100 % powder + amount of 20 % powder.

M = m + m'

CV = C'V' + C"V" where

  • C = 50% concentration = 0.5,
  • V = 50 % Volume,
  • C' = 100 % concentration = 1,
  • V' = 100 % volume,
  • C" = 20 % concentration  = 0.2
  • and V" = 20 % volume = 4 mL

So, CV = C'V' + C"V"

0.5V = 1 × V' + 0.2 × 4

0.5V = V' + 0.8  (1)

Also, we have that the total volume V = V' + V"

V = V' + 4 (2)

Substituting equation (2)into (1), we have

0.5V = V' + 0.8

0.5(V' + 4) = V' + 0.8

0.5V' + 0.5 × 4 = V' + 0.8

0.5V' + 2 = V' + 0.8

0.5V' - V' = 0.8 - 2

-0.5V' = -1.2

V' = -1.2/-0.5

V' = 2.4 mL

So, we need to add 2.4 mL of 100 % active ingredient powder to strengthen the mixture to 50% active ingredient powder

Learn more about active ingredient here:

https://brainly.com/question/12414597

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