Question

A balloon is filled with hydrogen at room temperature. It will burst if pressure exceeds 0.2 bar. If at 1 bar pressure, the gas occupies 2.27L Volume, then up to what volume can the balloon be expanded?
A. 11.35 L
B. >11.35 L
C. <11.35 L
D. None of these

Answer 1

We know the ideal gas equation $PV = nRT$ , in the given question there are only 2 variables Pressure and Volume.
And we know from Boyle’s Law that pressure and volume are inversely proportional.
So, we can derive relation between Pressure and Volume as
$\dfrac{{{P_1}}}{{{P_2}}} = \dfrac{{{V_2}}}{{{V_1}}}$
The Volume will be less than the value at 0.2 bar pressure, so that it does not burst.

Complete step by step answer:
Ideal gas equation can be written as $PV = nRT$
And we know from Boyle’s Law that pressure and volume are inversely proportional at constant temperature.
So, we can derive relation between Pressure and Volume as
$\dfrac{{{P_1}}}{{{P_2}}} = \dfrac{{{V_2}}}{{{V_1}}}$ at constant Temperature(Isothermal Condition).
Given Data:
The hydrogen gas at the pressure of 1 bar occupy the volume of 2.27 Litres.
$\therefore {P_1} = 1bar \\\ {V_1} = 2.27L \\\$
The balloon will burst at pressure exceeding 0.2 bar, so we can calculate corresponding volume:
${P_2} = 0.2bar$
Using Equation
$\dfrac{{{P_1}}}{{{P_2}}} = \dfrac{{{V_2}}}{{{V_1}}}$
Now substitute the given value in above equation:
$\dfrac{1}{{0.2}} = \dfrac{{{V_2}}}{{2.27}}$
Cross multiplying, and finding value of unknown variable volume,
$\Rightarrow {V_2} = \dfrac{{2.27}}{{0.2}} \\\ \Rightarrow {V_2} = 11.35L \\\$
Now if pressure is increasing, then volume has to be less than limiting value, as Pressure and volume are inversely proportional.
This limiting value means, below which the balloon will burst, so in order for the balloon not to burst, the volume should be less than the limiting value of 11.35L.
Thus Option (C) <11.35 L is the right answer.

Additional Information:
The Ideal Gas equation is derived from different gas laws like Boyle’s Law, Charles's Law, Gaylussac’s Law and Avogadro Law. They denote the relationship between pressure, Volume, temperature and number of moles of gases.

Note: Remember that pressure and volume are inversely proportional, so when one increases the other decreases. And when you are increasing pressure so the volume will decrease, and thus when it is less than 11.35 L, then the balloon will burst.