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Difficulty: MediumMixture and Concentration

A cosmetic chemist creates a skin care product by mixing two vitamin C solutions. Solution A consists of 200200 milliliters of a liquid that is 15%15\% vitamin C by volume. Solution B is a liquid that is 25%25\% vitamin C by volume. How many milliliters of Solution B must be added to Solution A so that the resulting mixture is 21%21\% vitamin C by volume?

Answer: 300 mL

Answer

300300 milliliters of Solution B must be added.
Adding 300300 mL of Solution B contributes 300×0.25=75300 \times 0.25 = 75 mL of pure vitamin C. Combined with Solution A's 3030 mL of vitamin C, the total amount of vitamin C is 105105 mL in a total mixture volume of 200+300=500200 + 300 = 500 mL. The resulting concentration is 105500=21%\frac{105}{500} = 21\%.

Step-by-Step Solution

1
Calculate the volume of pure solute (vitamin C) contained in Solution A.
200×0.15=30200 \times 0.15 = 30 mL of pure vitamin C.
The solute volume is calculated by multiplying total volume by the percentage concentration.
2
Express the solute contribution of Solution B and set up the equation for the combined concentration.
30+0.25x200+x=0.21\frac{30 + 0.25x}{200 + x} = 0.21
The final concentration is equal to total volume of pure solute divided by the total volume of the final mixture.
3
Solve the algebraic equation for xx.
30+0.25x=42+0.21x  ⟹  0.04x=12  ⟹  x=30030 + 0.25x = 42 + 0.21x \implies 0.04x = 12 \implies x = 300
Cross-multiplying and isolating xx yields the required volume of Solution B in milliliters.

Key Concept

Weighted average concentration equation for mixing two liquids.
Estimated Time:1m 30s
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Topics

Mixture and Concentration

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