Question

A balloon containing 1 mole of air at 1 atm initially, is filled further till pressure increases to 4 atm. The initial diameter of the balloon is 1 m and the pressure at each stage is proportional to diameter of the balloon. How many moles of air are added to change the pressure from 1 atm to 4 atm?

• A. 80
• B. 257
• C. 255
• D. 256

Answer 1

The correct option is C 255

$P\propto d;P=kdandk=\frac{1atm}{1metre}PV=nRT;$
$radiusoftheballoon=\frac{d}{2}$
$kd\left(\frac{1}{6}\pi d^3\right)=nRT;$
$\frac{d_1^4}{d_2^4}=\frac{n_1}{n_2};\frac{1}{4^4}=\frac{n_1}{n_2};n_2=256$
Number of moles added = 256 - 1 = 255