A mixture of O2 and O3 has vapour density 18.4 (O=16). The mixture is heated until all O3 decomposes by 2O3 -> 3O2. Find the percent increase in volume at constant temperature and pressure, to one decimal place.

JEE Advanced levelNumerical answerDifficulty 3 of 3mc106

A mixture of $O X_{2}$ and $O X_{3}$ has vapour density $18.4$ ( $O = 16$ ). The mixture is heated until all $O X_{3}$ decomposes by $2 O X_{3} 3 O X_{2}$ . Find the percent increase in volume at constant temperature and pressure, to one decimal place.

Numerical answer type, answer in %, tolerance 0.1.

Average molar mass = 36.8. For mole fraction x of

O X_{3}

: 48x + 32(1-x) = 36.8, so x = 0.30. Per mole of mixture,

O X_{3}

= 0.30 mol becomes 0.450 mol

O X_{2}

, a gain of 0.150 mol. Volume increase = 15.0%.