Multiple choice

Equal weight of $CO$ and ${CH}{4}$ are mixed together in an empty container at $300K$. The fraction of total pressure exerted by ${CH}{4}$ is:

  1. $\cfrac{16}{17}$
  2. $\cfrac{7}{11}$
  3. $\cfrac{8}{9}$
  4. $\cfrac{5}{16}$
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B Correct answer
Explanation

Equal weights means equal moles of CO (MW=28) and CH4 (MW=16). Let mass be w. Moles of CO = w/28, Moles of CH4 = w/16. Total moles = w(1/28 + 1/16) = w(4+7)/112 = 11w/112. Mole fraction of CH4 = (w/16) / (11w/112) = (1/16) * (112/11) = 7/11.

AI explanation

Let us assume 16 grams of each gas are mixed, which corresponds to 1 mole of CH4 and 16 divided by 28, or 4 divided by 7, moles of CO. The mole fraction of CH4 is its moles divided by the total moles in the container: 1 divided by (1 plus 4 divided by 7). This simplifies to 1 divided by (11 divided by 7), resulting in a mole fraction of 7 divided by 11. By Dalton's law of partial pressures, the fraction of the total pressure exerted by a gas is equal to its mole fraction. The result is 7/11.

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