Question

Statement - I:
Two vessels A and B of equal capacity are connected to each other by a stopcock. Vessel A contains a gas at $0^{0}C$ and 1 atmosphere pressure and vessel B is evacuated. If the stopcock is suddenly opened, the final pressure in A and B will be 0.5 atmosphere.
Statement - 2:
If the temperature is kept constant, the pressure of a gas is inversely proportional to its volume

• A. Statement - I is true, Statement - II is true; statement - II is a correct explanation for statement - I
• B. Statement - I is true, Statement - II is true; statement - II is NOT a correct explanation for statement - I
• C. Statement - I is true, Statement - II is false
• D. Statement - I is false, Statement - II is true

Answer 1

The correct option is A Statement - I is true, Statement - II is true; statement - II is a correct explanation for statement - I

As per the ideal gas law, we have

$PV=nRT$

where,

P is pressure of gas

V is volume of gas

n is number of moles of gas

R is universal gas constant

T is temperature of gas

When the temperature of gas is kept constant we can write

$PV=constant$

$P\propto \frac{1}{V}$

Thus, pressure is inversely proportional to volume.

When the stopcock is suddenly opened, the gas will be occupied in both vessels. As the volume becomes double and the pressure will decrease to one half of its original value. The initial pressure of gas was 1 atm, hence the final pressure in both vessels will be 0.5 atm.

Hence, option A is correct, i.e. statement - I is true, statement - II is true; statement - II is correct explanation for statement - I.