Multiple choice

A sample of an ethanol-water solution has a volume of $55.0\ cm^{3}$ and mass of $50.0\ g$. What is the percentage of ethanol (by mass) in the solution ? Assume that there is no change in volume when the pure compounds are mixed. The density of ethanol is $0.80\ g/cm^{3}$ and that of water is $1.00\ g/cm^{3}$

  1. $20\%$
  2. $40\%$
  3. $60\%$
  4. $45.45\%$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let E be mass of ethanol, W be mass of water. E + W = 50. E/0.8 + W/1.0 = 55. Substitute W = 50 - E: E/0.8 + (50-E) = 55. 1.25E - E = 5, 0.25E = 5, E = 20. Percentage = 20/50 = 40%.

AI explanation

Let the volume of ethanol be x cubic centimeters; then the volume of water is (55 minus x) cubic centimeters. Using the given densities, the total mass equation is 0.8x plus 1 times (55 minus x) equals 50. Solving this gives x as 25 cubic centimeters, so the mass of ethanol is 20 g, which makes the mass percentage 20 divided by 50, or 40%.

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