Physics Q34 – JEE-MAIN 2026

Home Physics Kinetic TheoryQuestion #205

A mixture of carbon dioxide and oxygen has volume

8310 {cm}^{3}

, temperature

300 K

, pressure

100 kPa

and mass

13.2 g

. The number of moles of carbon dioxide and oxygen gases in the mixture respectively are _______. (Assume both carbon dioxide and oxygen gases behave like ideal gases) [

R = 8.31 J/molK

]

Clue 1 of 3: Ideal Gas Law and Mixture Properties

For an ideal gas mixture, the total number of moles can be determined using the ideal gas law with the total pressure, volume, and temperature. The total mass of the mixture is the sum of the masses of individual components.

🧠 Full Solution Path

Step 1: Calculate Total Moles✦ Active

Use the Ideal Gas Law, $P V = n_{total} R T$ , to find the total moles of the gas mixture. Convert units to SI: $V = 8310 {cm}^{3} = 8.31 \times 10^{- 3} m^{3}$ , $P = 100 kPa = 10^{5} Pa$ .

n_{total} = \frac{P V}{R T} = \frac{(10^{5} Pa) (8.31 \times 10^{- 3} m^{3})}{(8.31 J/molK) (300 K)} = \frac{100}{300} = \frac{1}{3} mol

Step 2: Set up Mass Balance Equation○ Expand

Let $n_{{CO}_{2}}$ be the moles of carbon dioxide and $n_{O_{2}}$ be the moles of oxygen. The molar mass of ${CO}_{2}$ is $44 g/mol$ and $O_{2}$ is $32 g/mol$ . The total mass is $13.2 g$ . This gives us a system of two linear equations:

n_{{CO}_{2}} + n_{O_{2}} = \frac{1}{3} (Equation 1)

44 n_{{CO}_{2}} + 32 n_{O_{2}} = 13.2 (Equation 2)

Step 3: Solve the System of Equations○ Expand

From Equation 1, $n_{O_{2}} = \frac{1}{3} - n_{{CO}_{2}}$ . Substitute this into Equation 2:

44 n_{{CO}_{2}} + 32 (\frac{1}{3} - n_{{CO}_{2}}) = 13.2

44 n_{{CO}_{2}} + \frac{32}{3} - 32 n_{{CO}_{2}} = 13.2

12 n_{{CO}_{2}} = 13.2 - \frac{32}{3} = \frac{39.6 - 32}{3} = \frac{7.6}{3}

n_{{CO}_{2}} = \frac{7.6}{36} \approx 0.211 mol

Then, calculate $n_{O_{2}}$ :

n_{O_{2}} = \frac{1}{3} - n_{{CO}_{2}} = \frac{1}{3} - 0.211 = 0.333 - 0.211 = 0.122 mol

Rounding to two decimal places, $n_{{CO}_{2}} = 0.21 mol$ and $n_{O_{2}} = 0.12 mol$ . This matches option 3.

💡 Teacher's Secret Hint

Ensure consistent units throughout the calculation, especially when using the ideal gas law.

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Physics Question 34 – JEE-MAIN 2026

Clue 1 of 3: Ideal Gas Law and Mixture Properties

🧠 Full Solution Path