Question

The helium in the cylinder has a volume of $6.0\times {10}^{-3}{m}^3\left(0.0060m^3\right)$ and is at a pressure of$2.75\times {10}^{6}Pa$. (1) The pressure of helium in each balloon is $1.1\times {10}^5$ Pa. The volume of helium in an inflated
balloon is $3.0\times {10}^{-3}\left(0.0030m^3\right).$ The temperature of the helium does not change. Calculate the number of balloons that were inflated.

Answer 1

Given that,

in the cylinder ( containing $He$) :-

$V=6.0\times {10}^{-3}{m}^{3}P=2.75\times {10}^{6}Pa$.

So, net moles of $He$ in cylinder ( using Ideal gas law):-

$PV=nRT\Rightarrow n$ ( net no. of moles)$=\frac{PV}{RT}$

$\Rightarrow n=\frac{(6.0\times {10}^{-3})\times (2.75\times {10}^6)}{RT}=\frac{1.65\times {10}^4}{RT}$

in each balloon,

$v=3.0\times {10}^{-3}{m}^{3}P=1.1\times {10}^{5}Pa$

So, moles of $He$ in one balloon, ( $T$) remains constant )

$n_1=\frac{(3.0\times {10}^{-3})\times (1.1\times {10}^5)}{RT}=\frac{3.3\times {10}^2}{RT}$

so, If $N$ balloons are filled, we get from conservation of matter,

$\Rightarrow n=N.n_1$

$\Rightarrow N=\frac{n}{n_1}=\frac{1.65\times {10}^4}{3.3\times {10}^2}=50$ (Ans)