Multiple choice

Vapour density of mixture of ${ NO }{ 2 }$ and ${ N }{ 2 }{ O }{ 4 }$ is 34.5, then percentage abundance of ${ NO }{ 2 }$ in mixture is:

  1. 50%

  2. 25%

  3. 40%

  4. 60%
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A Correct answer
Explanation

Vapour density = M_mix / 2. M_mix = 34.5 * 2 = 69. Let x be the mole fraction of NO2 (M=46) and (1-x) be the mole fraction of N2O4 (M=92). 46x + 92(1-x) = 69. 46x + 92 - 92x = 69. -46x = -23. x = 0.5. So 50%.

AI explanation

The molecular mass of NO2 is 46 and that of N2O4 is 92, meaning their respective vapour densities are 23 and 46. Using the method of mixture and alligation on these vapour densities against the mixture average of 34.5 gives a ratio of (34.5 minus 23) to (46 minus 34.5), which is 11.5 to 11.5 or 1 to 1. This 1 to 1 ratio means the percentage abundance of NO2 in the mixture is 50%.

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