Multiple choice

A mixture of $CH_4, N_2$ and $O_2$ is enclosed in a vessel of one litre capacity at $0^oC$. The ratio of pressure of gases is $1:4:2$. Total pressure of the gaseous mixture is $2660 \,mm$. The molecules of oxygen present in the vessel is

  1. $\dfrac{{0.02 \times {{10}^{23}}}}{{22.4}}$
  2. $4.02 \times 10^{23}$
  3. $22.4 \times 10^{22}$
  4. $1000$
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A Correct answer
AI explanation

Use Dalton's law to find that the partial pressure of oxygen is two sevenths of the total pressure of 2660 mm, which equals 760 mm or 1 atmosphere. Applying the ideal gas equation at this pressure and a temperature of 273.15 Kelvin reveals the volume of the gas is 0.01 liters. Since one mole of an ideal gas occupies 22.4 liters at standard conditions, the number of oxygen molecules is calculated as (0.01 / 22.4) x 6.02 x 10^23, matching the form of (0.02 x 10^23) / 22.4.

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