Sankalp NEET Full Test-5 Question-89 Solution

Question: 89: A vessel contains 3.2 g of dioxygen gas at STP ( 273.15 K and 1 atm pressure). The gas is now transferred to another vessel at constant temperature, where pressure becomes one third of the original pressure. The volume of new vessel in L is :

(Given – molar volume at STP is 22.4 L )

(1) 6.72

(2) 2.24

(3) 22.4

(4) 67.2

Answer: Option (1)

Explanation:

First, calculate the number of moles of dioxygen gas.

Molar mass of \mathrm{O_2} is 32 \ \mathrm{g \ mol^{-1}}.

\text{Number of moles} = \frac{3.2}{32} = 0.1 \ \mathrm{mol}

At STP, 1 mole of any gas occupies 22.4 \ \mathrm{L}.

So, volume of 0.1 \ \mathrm{mol} of gas at STP is:

V_1 = 0.1 \times 22.4 = 2.24 \ \mathrm{L}

The gas is transferred to another vessel at constant temperature, so Boyle’s law applies:

P_1 V_1 = P_2 V_2

Given that the final pressure is one third of the original pressure:

P_2 = \frac{P_1}{3}

Substituting in Boyle’s law:

P_1 \times 2.24 = \frac{P_1}{3} \times V_2

Canceling P_1:

2.24 = \frac{V_2}{3} V_2 = 3 \times 2.24 = 6.72 \ \mathrm{L}

Therefore, the volume of the new vessel is 6.72 \ \mathrm{L}.