Multiple choice

A gaseous mixture contains $\displaystyle CO_{2}\left ( g \right )$ and $\displaystyle N_{2}O\left ( g \right )$ in a $2:5$ ratio by mass. Find the ratio of the number of molecules of $\displaystyle CO_{2}\left ( g \right )$ and $\displaystyle N_{2}O\left ( g \right )$.

  1. $2 : 5$
  2. $5 : 2$
  3. $3 : 5$
  4. $5 : 3$
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A Correct answer
Explanation

Mass ratio CO2 : N2O = 2 : 5. Molar mass CO2 = 44, N2O = 44. Ratio of moles = (2/44) : (5/44) = 2 : 5. Since number of molecules is proportional to moles, the ratio is 2 : 5.

AI explanation

Assume the total mass of the mixture is 7 grams, consisting of 2 grams of carbon dioxide and 5 grams of nitrous oxide. The number of moles is the mass divided by the molar mass, so the moles of carbon dioxide are 2 divided by 44, which equals 1 divided by 22. The moles of nitrous oxide are 5 divided by 44. Because equal volumes of gases at the same conditions contain equal numbers of molecules, the ratio of the number of molecules is the same as the ratio of moles. The ratio is (1 divided by 22) to (5 divided by 44), which simplifies to 2 to 5.

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