MCQEasyJEE 2023Stoichiometry & Calculations

JEE Chemistry 2023 Question with Solution

When a hydrocarbon A undergoes complete combustion it requires 1111 equivalents of oxygen and produces 44 equivalents of water. What is the molecular formula of A?

  • A

    C9H8C_9H_8

  • B

    C11H4C_{11}H_4

  • C

    C5H8C_5H_8

  • D

    C11H8C_{11}H_8

Answer

Correct answer:A

Step-by-step solution

Standard Method

Given: A hydrocarbon AA undergoes complete combustion, requires 1111 equivalents of oxygen, and produces 44 equivalents of water.

Find: The molecular formula of the hydrocarbon.

Let the molecular formula of the hydrocarbon be CxHyC_xH_y. The balanced combustion reaction is:

CxHy+(x+y4)O2xCO2+y2H2OC_xH_y + \left(x + \frac{y}{4}\right) O_2 \rightarrow x \, CO_2 + \frac{y}{2} \, H_2O

From the amount of water produced:

y2=4\frac{y}{2} = 4

So,

y=8y = 8

Using the oxygen requirement:

x+y4=11x + \frac{y}{4} = 11

Substitute y=8y = 8:

x+84=11x + \frac{8}{4} = 11 x+2=11x + 2 = 11 x=9x = 9

Therefore, the hydrocarbon is C9H8C_9H_8. The correct option is A.

The solution marks option D, but the working clearly gives C9H8C_9H_8, which matches option A in the listed options.

Using combustion stoichiometry carefully

Given: Hydrocarbon CxHyC_xH_y, oxygen required =11= 11 equivalents, water formed =4= 4 equivalents.

Find: Values of xx and yy.

For complete combustion of a hydrocarbon:

CxHyxCO2+y2H2OC_xH_y \rightarrow x \, CO_2 + \frac{y}{2} \, H_2O

Hence, the coefficient of water is y2\frac{y}{2}.

Since water produced is 44 equivalents:

y2=4\frac{y}{2} = 4 y=8y = 8

Now the oxygen coefficient in complete combustion is:

x+y4x + \frac{y}{4}

Given this is 1111, we get:

x+84=11x + \frac{8}{4} = 11 x+2=11x + 2 = 11 x=9x = 9

Thus the molecular formula is C9H8C_9H_8.

Common mistakes

  • Using the water coefficient as y4\frac{y}{4} instead of y2\frac{y}{2} is incorrect because each molecule of H2OH_2O contains two hydrogen atoms. Match hydrogen atoms properly, then use y2\frac{y}{2} for water.

  • Writing the oxygen coefficient as x+y/42\frac{x + y/4}{2} is wrong for the balanced combustion equation of CxHyC_xH_y. The correct coefficient of O2O_2 is x+y4x + \frac{y}{4} because the oxygen atoms needed are 2x+y22x + \frac{y}{2}, which correspond to x+y4x + \frac{y}{4} molecules of O2O_2.

  • Accepting the printed option label from the solution without checking the algebra is a mistake. The working gives C9H8C_9H_8, so the defensible answer must be the option containing that formula, which is A here.

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