Question

The helium in the cylinder has a volume of $6\cdot 0\times {{10}^{-3}}{{m}^{3}}(0\cdot 0060{{m}^{3}})$ and is at a pressure of $2\cdot 75\times {{10}^{6}}Pa$. The pressure of helium in each balloon is $1.1\times {{10}^{5}}Pa$. The volume of helium in an inflated balloon is $3\cdot 0\times {{10}^{-3}}{{m}^{3}}(0\cdot 0030{{m}^{3}})$. The temperature of the helium does not change. Calculate the number of balloons that were inflated.

Answer 1

Hint : Here we use the ideal gas equation to calculate the number of moles which are further used to calculate the number of balloons the gas van inflate.
The ideal gas equation is given by:
$PV=nRT$
The ideal particles are equally sized and do not have intermolecular forces(attraction or repulsion) with other gas particles. The gas particles move randomly in agreement with Newton's laws of motion. The gas particles have perfect elastic collisions with no energy loss.

Complete step by step answer
In this question we are given that in a cylinder containing He gas has:
$V=6\cdot 0\times {{10}^{-3}}{{m}^{3}}(0\cdot 0060{{m}^{3}})$
$P=2\cdot 75\times {{10}^{6}}Pa$
Using ideal gas equation;
$PV=nRT$
$n=\dfrac{PV}{RT}$
$=\dfrac{(6\cdot 0\times {{10}^{-3}})(2\cdot 75\times {{10}^{6}})}{RT}$
$n=\dfrac{1\cdot 65\times {{10}^{4}}}{RT}$
For each balloon;
${{V}_{1}}=3\cdot 0\times {{10}^{-3}}{{m}^{3}}(0\cdot 0030{{m}^{3}})$
${{P}_{1}}=1\cdot 1\times {{10}^{5}}Pa$
As the temperature (T) remains constant for He in the balloon.
So, using ideal gas equation again we get;
${{n}_{1}}=\dfrac{{{P}_{1}}{{V}_{1}}}{RT}$
${{n}_{1}}=\dfrac{(3\cdot 0\times {{10}^{-3}})(1\cdot 1\times {{10}^{5}})}{RT}$
${{n}_{1}}=\dfrac{3\cdot 3\times {{10}^{2}}}{RT}$
Let N number of balloons are filled. With the conservation of matter, we get;
$n=N\cdot {{n}_{1}}$
$N=\dfrac{n}{{{n}_{1}}}$
$=\dfrac{\dfrac{1\cdot 65\times {{10}^{4}}}{RT}}{\dfrac{3\cdot 3\times {{10}^{2}}}{RT}}$
$\begin{aligned} & =\dfrac{1\cdot 65\times {{10}^{4}}}{RT}\times \dfrac{RT}{3\cdot 3\times {{10}^{2}}} \\\ & N=0\cdot 5\times {{10}^{2}} \\\ & N=50 \\\ \end{aligned}$
Therefore, 50 balloons can be filled from the given amount of He gas in the cylinder.

Note One should remember that this ideal gas law makes no comment as to whether a gas heats or cools during compression or expansion. An ideal gas may not change temperature, but most gases like air are not ideal and follow the Joule-Thomson effect. The ideal gas law suggests that the volume of a given quantity of gas and the number of moles in a given volume of gas vary with changes in pressure and temperature.