Multiple choice

A gas mixture of $3$ litres of propane $(C_{3}H_{8})$ and butane $(C_{4}H_{10})$ on complete combustion at $250^{0}C$ produced $10$ litres of $CO_{2}$. Find out the composition of the gas mixture (Propane: Butane).

  1. $2:1$
  2. $1: 2$
  3. $1.5:1.5$
  4. $0.5: 2.5$
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A Correct answer
Explanation

Let x be volume of propane and y be volume of butane. x + y = 3. Combustion: C3H8 + 5O2 -> 3CO2 + 4H2O; C4H10 + 6.5O2 -> 4CO2 + 5H2O. So, 3x + 4y = 10. Solving the system: 3x + 3y = 9 and 3x + 4y = 10 gives y = 1, x = 2. Ratio is 2:1.

AI explanation

Assume the 3 litres of the mixture contains x litres of propane and (3 - x) litres of butane. The combustion reactions are C3H8 + 5O2 -> 3CO2 + 4H2O and C4H10 + 6.5O2 -> 4CO2 + 5H2O. By Gay-Lussac's law of gaseous volumes, x litres of propane yields 3x litres of CO2, and (3 - x) litres of butane yields 4(3 - x) litres of CO2. Setting the total carbon dioxide produced as 3x + 12 - 4x = 10, we find x = 2. The composition is 2 litres of propane to 1 litre of butane, making the ratio 2:1.

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