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Find the amount of red food coloring (in grams) necessary to add to 50 grams of water to prepare a 15% solution of red food coloring in water.

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Answer:

  • 9 grams

Explanation:

Percentage is a concentration unit that describes the amount of a solute in 100 parts of total substance (solution).

The weight percent of a solution is given by the formula:

  • % (w/w) = (mass of solute / mass of solution) × 100

Here, the red food coloring is the solute, water is the solvent, and the solution is the mixture.

You know the mass of water (50 g) and the percentage (15%), thus you can calculate the mass of red food coloring (x) in this way:

1. Mass of solution

  • Mass of solution = mass of red food coloring + mass of water

  • mass of solution = x + 50

2. Percent

  • [tex]%=x/(x+50)\times 100=15[/tex]% = x / (x + 50) × 100 = 15

3. Solve for x:

  • x / (x + 50) = 0.15
  • x = 0.15(x + 50)
  • x = 0.15x + 7.5
  • 0.85x = 7.5
  • x = 8.82 g

Round to two one significant figure, because the number 50 grams has one significant figure.

  • x = 9 grams.

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