Question

Balloons of $4L$ capacity are to be filled with hydrogen at a pressure of $1atm$ and 27$^\circ$C from an $8L$cylinder containing hydrogen at $10atm$ at the same temperature. Find the number of balloons that can be filled.

Answer 1

We need to know the relationship between Pressure, Volume, temperature and the amount of hydrogen each balloon will require. This relationship is given by the Ideal Gas Law. It is a combination of various gas laws such as Boyle’s Law, Charles’s Law, Gay Lussac’s Law and Avogadro’s Law. The equation for the Ideal Gas Law is $PV = nRT$,where $P$ is the pressure ,$V$ is the Volume, $n$ is the number of moles ,$R$ is the Gas Constant and $T$ is the temperature.

Complete step by step answer:
Given in the question:
Volume of each balloon= $4L$
Pressure of hydrogen inside each balloon = $1atm$
Volume of the cylinder containing hydrogen = $8L$
Pressure of cylinder containing hydrogen = $10atm$
Temperature is constant for both the cylinder and balloons.
The ideal gas equation states:
$PV = nRT$
Since the temperature is constant,
$n = PV$
Now we calculate the number of moles of hydrogen inside the $8L$ cylinder as:
${n_c} = 10atm \times 8L$
On multiplication we get,
$\Rightarrow {n_c} = 80moles$
We also calculate the number of moles of hydrogen each $4L$ balloon requires as:
${n_b} = 1atm \times 4L$
On multiplication we get,
$\Rightarrow {n_b} = 4moles$
Thus the number of $4L$ balloons containing $4moles$ of hydrogen that can be filled by $80moles$ of hydrogen are $\dfrac{{80}}{4} = 20$

Hence, the number of balloons that can be filled are $20$ balloons.

Note: We must be noted that there is an alternative method for solving these type of problems by using the Boyle’s law equation which is ${P_1}{V_1} = {P_2}{V_2}$ . ${V_2}$ calculated as the total volume of hydrogen gas the 8L cylinder can hold having pressure of 1atm inside. This total volume will be divided by the volume capacity of each balloon to give us the number of balloons that can be filled.