Question

Details of some gases taken at $273K$ temperature and $1atm$ pressure are given in the table.

Gas	Volume (L)	Number of moles
Hydrogen	224	10
Helium	112	5
Oxygen	224	10
Ammonia	56	2.5

A. On the basis of which gas law, the volume, and the number of moles are given in the table?
B. Represent this gas law in mathematical form.
C. Among these, if the pressure of hydrogen gas is changed to $2atm$. Calculate the new volume.

Answer 1

Hint: At the standard condition of temperature $273K$ and pressure$1atm$ , a substance that exists as gas is known as a pure gas. It may be made up of elemental molecules made from one type of atom $\left( {{O_2}} \right)$, individual atoms $\left( {Ne} \right)$ or compound molecules made from a variety of atoms $C{O_2}$.

Complete step by step answer:
According to the question, if we increase the volume of helium by 2 times and ammonia by 4 times then all given gases have an equal volume which contains the same number of moles.

A.It follows Avogadro's law. It states that equal volumes of different gases at the same temperature and pressure contain the same number of molecules.

B.Avogadro’s law is stated in mathematical form:
$\dfrac{V}{n} = k$ $ \Rightarrow V \propto n$ (PT constant)
Where, $V$ is the volume of the gas
$n$= number of moles of the gas
$k$= proportionality constant

C.$V \propto P$
${V_1} = 224L$, ${P_1} = 1atm$
$\Rightarrow$ ${V_2} = ?$, ${P_2} = 2atm$
$\Rightarrow$ ${P_1}{V_I} = {P_2}{V_2}$
${V_2} = {P_1}{V_1}/{P_2}$= $1atm \times 224L/2atm = 112L$

Note:
Pressure is inversely proportional to the volume of the gas at a constant temperature. This law is known as Boyle’s law where if we increase the volume, the pressure gets decreased and vice versa. Mathematical formula is $P \propto 1/V$ .