Question

Children bought some balloons each of two litre capacity to a chemist and asked him to fill them with hydrogen gas. The chemist possessed eight litre cylinders containing hydrogen at $10$ atmospheric pressure at room temperature. How many balloons could he fill with hydrogen gas at normal atmospheric pressure at the same temperature?
A. $28$
B. $36$
C. $32$
D. $28$

Answer 1

Hint: To find out the solution of this question, consider the ideal gas equation. Find out the amount of gas required at the given pressure and volume and then find out the number of balloons he filled with hydrogen gas.

Complete step by step solution:
Let us consider the ideal gas equation:
$PV=nRT$ where,
P is the pressure,
V is the volume,
n is the amount,
R is the universal gas constant and
T is the temperature.
-So, here we have to consider temperature as constant. R is already a constant.
-Initial pressure in the cylinder (consider P) is given as $10\text{ atm}$.
-Initial volume in the cylinder (consider V) is given as $8$ litres.
-Final pressure in the balloons (consider $P'$) is given as $1\text{ atm}$.
So, the final volume in the balloons will be $V'$. At the same temperature, $PV=P'V'$.
Placing the values, we will get:
$10\times 8=1\times V'$
So, $V'=80$
Thus, the final volume in the balloons will be $80$ litres. We see that one balloon has two litres of volume. So, how many balloons will have $80$ litres. So, the number of balloons (each of two litres capacity) that the chemist can fill will be $=\dfrac{80}{2}=40$

Hence, the correct option is A.

Note: Ideal gas equation can be used for any gases. It is important to note that, at constant temperature the pressure is inversely proportional to that of the volume while the pressure and volume are directly proportional to the amount of gas.