Multiple choice

When $10$ mL of ethyl alcohol (density $=0.7893: g: mL^{-1})$ is mixed with $20$ mL of water (density $0.9971: g: mL^{-1})$ at $25^oC$, the final solution has a density of $0.9571 :g :mL^{-1}$. The percentage change in total volume on mixing is :

  1. $3.1\%$
  2. $2.4\%$
  3. $1\%$

  4. none of these
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A Correct answer
Explanation

Initial mass = (10 * 0.7893) + (20 * 0.9971) = 7.893 + 19.942 = 27.835 g. Final volume = Mass / Density = 27.835 / 0.9571 = 29.083 mL. Initial volume = 30 mL. Change = 30 - 29.083 = 0.917 mL. Percentage change = (0.917 / 30) * 100 = 3.056%, which rounds to 3.1%.

AI explanation

The mass of ethyl alcohol is its volume multiplied by its density, which is 10 milliliters multiplied by 0.7893 grams per milliliter to equal 7.893 grams. The mass of water is 20 milliliters multiplied by 0.9971 grams per milliliter to equal 19.942 grams, making the total mass of the mixture 27.835 grams. The final volume of the mixture is the total mass divided by the final density, calculated as 27.835 divided by 0.9571 to equal 29.08 milliliters, whereas the initial volume was 30 milliliters. The percentage change in total volume on mixing is calculated as the initial volume minus the final volume, all divided by the initial volume and multiplied by 100, which is (30 minus 29.08) divided by 30 and then multiplied by 100 to give a result of 3.1%.

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