Multiple choice

A vessel is filled with a mixture of oxygen and nitrogen. At what ratio of partial pressures will the mass of gases be identical?

  1. $P(O_2)=0.785$ $P(N_2)$
  2. $P(O_2)=8.75$ $P(N_2)$
  3. $P(O_2)=11.4$ $P(N_2)$
  4. $P(O_2)=0.875$ $P(N_2)$
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D Correct answer
Explanation

For the masses of oxygen and nitrogen to be equal, the number of moles must be inversely proportional to their molar masses. Since molar mass of O2 is 32 and N2 is 28, the ratio of moles n(O2)/n(N2) = 28/32 = 0.875. By Dalton's Law, the ratio of partial pressures equals the ratio of moles in a mixture.

AI explanation

According to the ideal gas law, the ratio of partial pressures is equal to the ratio of moles, so P(O2) divided by P(N2) equals n(O2) divided by n(N2). Because the masses of the two gases are identical, the ratio of their moles is the inverse of the ratio of their molar masses. Therefore, P(O2)/P(N2) equals 28 divided by 32, which equals 0.875, establishing that P(O2) equals 0.875 P(N2).

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