Question

My weight is $80kg$. I want to fly in the sky with the help of balloons each containing $50$ moles of $H_2$ gas at $0.05atm$ pressure and ${27}^{o}C$ temperature. If the density of air at the given condition is $1.25gm{L}^{-1}$, how many such types of balloons do I need to attach with myself to fly in the sky? [Mass of balloon can be neglected]

• A. $2$
• B. $3$
• C. $7$
• D. $9$

Answer 1

The correct option is B $3$

Given data for one balloon:

$n=50$

$P=0.05atm$
mass of $H_2$ in the one balloon, $m_{H_2}=50\times 2=100g$

$T={27}^{0}C=300K$

Mass lift for payload by one balloon, $m_1$

Using Ideal gas equation

$PV=nRT$

Finding volume of displaced air because of one balloon, $V$

$V=\frac{50\times 0.0821\times 300}{0.05}=24630L$

Finding the mass of air displaced by one balloon, $Mass=Massliftgenerated$

Given the density of air,$=1.25gm/L$

According to the formula:

$Density=\frac{Mass}{Volume}$

$Mass=1.25\times 24630=30787g$
As we know,
$themassliftgenerated=massofballoons+massof{H}_2+MassliftforPayload$
$\Rightarrow 30787=0+m_{H_2}+Massliftforpayload$

$\Rightarrow 30787=100+m_1$
$\Rightarrow m_1=30687g$

To lift the weight of mine that is $80Kg=80000g$

No. of balloons required $>=\frac{80000}{m_1}=\frac{80000}{30687}=2.6$
So, the least integer to satisfy the condtion $=$ No. of balloons required $=3$
Hence, the correct option is $\left(B\right)$