Question

A vessel has $6g$ of hydrogen at pressure $P$ and temperature $500K$ . A small hole is made in it so that hydrogen leaks out. How much hydrogen leaks out if the final pressure is $P/2$ and temperature falls to $300K$ ?
a) $2g$
b) $3g$
c) $4g$
d) $1g$

Answer 1

Hydrogen is the first chemical element of the periodic table and has the symbol $H$ and atomic number $1$ . It has a standard atomic weight of 1.008,hence hydrogen is the lightest element in the periodic table. Hydrogen is also the most abundant chemical substance in the universe.It has various physical phases of existence with each phase having its own chemical property.Some of its physical phases are Gaseous,Solid,Liquid and slush hydrogen.

Complete answer: T
The above experiment has been carried out with hydrogen which exists in the Gaseous phase.The molecules of gas have very high energy and they tend to occupy the entire volume of the closed container in which they are put.Hence the volume of closed container is equivalent to the volume of the gas.
According to the ideal gas law,
$PV = nRT$
By definition of number of moles $n$
$PV = \dfrac{m}{M}RT$ …………………(1)
Initially the weight of gas is $6g$ and temperature is $500K$ .Let us substitute this value in equation 1 and call the equation as equation 2
$PV = \dfrac{6}{M}R \times 500$ ………………….(2)
After this a small hole was made in the container which caused the gas to leak.The final pressure was noted as $P/2$ and the temperature dropped to $300K$ hence substituting these values in equation number 1.Let the weight of gas which leaked be $x$
$\dfrac{P}{2}V = \dfrac{{(6 - x)}}{M}R \times 300$ ……………….(3)
Let us divide equation (2) by equation (3) to get,
$2 = \dfrac{6}{{6 - x}} \times \dfrac{5}{3}$
Solving the above equation we get $x = 1g$ .Hence the correct option is (d) $1g$ .

Note:
Hydrogen has a variety of industrial applications.It is the main source of energy in rockets used for space exploration missions.Due to their negligible levels of pollution,hydrogen powered cars are gaining popularity.Industrial refining of petroleum products also use hydrogen.