Question

Equal volume of oxygen and an unknown gas weight $3.00g$ and $7.50g$, respectively. Which of the following is the unknown gas?
(A) $C{O_2}$
(B) $NO$
(C) $N{O_2}$
(D) $S{O_3}$

Answer 1

As both the gases have equal volume and the weight is given, we will assume that both are measured at the same temperature and pressure. Hence, we will calculate the molar mass of unknown gas keeping in mind Avogadro’s law.

Complete step by step answer:
According to Avogadro’s Law or Avogadro’s principle, it states that the total number of atoms/molecules of a gas is directly proportional to the volume occupied by the gas at constant temperature and pressure.
Formula for Avogadro’s law is:
$V \times n$ or
$\dfrac{V}{n} = K$
Where, $V$ is volume of gas
$n$ is amount of gas (moles)
$K$ is constant
This means that whenever, the volume of two gases is equal then, moles of two gases will also be equal.
According to the question, the volume of ${O_2}$ and an unknown gas is the same.
So, ${V_1} = K\,{n_1}$ and ${V_2} = K\,{n_2}$
Where ${V_1}$ and ${V_2}$ are the volume of ${O_2}$ and unknown gas and ${n_1}$ and ${n_2}$ are number of moles respectively.
As, ${V_1} = {V_2}$
Comparing the two equations:
${n_1} = {n_2}$
Number of moles of ${O_2}$, {n_1}$$$$ = \dfrac{{3.00}}{{32}} = 0.09375\,\,moles
As ${n_1} = {n_2}$, ${n_2} = 0.09375\,\,moles$
As Molar mass $= \dfrac{{{\text{given weight}}}}{{{\text{number of moles}}}}$
So, molar mass $= \dfrac{{7.50}}{{0.09375}} = 80\,g\,\,mol$
The molar mass $S{O_3}$ gas is $80\,g\,\,mol$.

Additional information: Avogadro's law is closely related to the ideal gas equation since it links the temperature, pressure, volume, and amount of substance for a given gas. This law is named after the Italian scientist Amedeo Carlo Avogadro, who even suggested that the two dissimilar ideal gases occupying the same volume at a constant temperature and pressure must contain an equal number of molecules. The process of respiration is one of the examples of Avogadro's law.

Note: Remember that Avogadro’s law holds true at the constant or standard conditions of temperature and pressure only. Avogadro’s law is perfectly applicable to ideal gases but it provides only an approximate relationship for real gases. This deviation of real gases from ideal gases increases at low temperature and high pressure.