Question

A balloon containing 1 mole air at 1 $atm$ initially is filled further with air till pressure increases to 4 $atm$. The initial diameter of the balloon is 1 $m$ and the pressure at each stage is proportion to diameter of the balloon. How many no.of moles of air 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

Pis directly proportional to d; P=kd

and k=1atm/1metre

$PV=nRT;kd\left(\frac{1}{6}\pi d^3\right)=nRT$

$\frac{d_1^4}{d_2^4}=\frac{n_1}{n_2}$

$\frac{1}{4^4}=\frac{n_1}{n_2}$

$n_2=256$

No.of moles added=256−1=255.