Question

A weather balloon is inflated with helium. The balloon has a volume of 100 m^3 and it must be inflated to a pressure of 0.10 atm. If we use 50-L cylinders of compressed helium gas at a pressure of 100.0 atm. how many cylinders do we need? Assume the temperature remains constant

Answer 1

If the cylinders were at 1.00 atm, they would contain 50.00 L each, so at 100.0 atm they contain 5000. L each.

1 m³ = 1000 L, so 100.0 m³ = 1.000 × 10⁵ L. Since the pressure in the balloon is only 0.10 atm, though, the gas volume equals only 1.000 × 10⁴ L at 1 atm.
(1.000 × 10⁴ L) / (5000. L/cylinder) = 2.00 cylinders.

Answer 2

Answer : The number cylinders needed will be, 2

Solution :

According to Boyle's law, the volume of gas is inversely proportional to the pressure of the gas.

$P\propto \frac{1}{V}$

or,

$\frac{P_1}{P_2}=\frac{V_2}{V_1}$

where,

$P_1$ = pressure of balloon = 0.10 atm

$P_2$ = pressure of helium gas = 100 atm

$V_1$ =  volume of balloon = $100m^3=10^5L$

$V_2$ = volume of helium gas

Now put all the given values in the above formula, we get

$\frac{0.10atm}{100atm}=\frac{V_2}{10^5L}$

$V_2=100L$

Now we have to calculate the number of cylinders needed.

$\text{Number of cylinders needed}=\frac{100}{50}=2$

Therefore, the number cylinders needed will be, 2