Question

The density of helium gas is $\dfrac{1}{8}th$ density of oxygen gas.
The average atomic mass of helium if $4.00\,g/mol$ and the average atomic mass of oxygen is $16.00\,g/mol$
${\text{A}}{\text{. Statement I is true, Statement II is true}}$
${\text{B}}{\text{. Statement I is true, Statement II is false}}$
${\text{C}}{\text{. Statement I is false, Statement II is true}}$
${\text{D}}{\text{. Statement I is false, Statement II is false}}$

Answer 1

The density is used as one of its most important and easily measured physical properties. Densities are used for the identification of a pure substance; it is also used to characterize the compound and estimation of the composition of many types of mixtures. The purpose of this lesson is to show how densities are defined, measured and used and to ensure that you understand the closely related concepts of buoyancy and specific gravity and the role they play in our lives and the environment.

Complete step-by-step answer:
Helium is a monatomic gas;
$Density\,of\,He\, = \,\dfrac{{mass}}{{volume}}$
$= \,\dfrac{4}{{volume}}$
Oxygen is a diatomic gas;
Therefore, one oxygen contains $16.00\,g/mol$ . So, the two oxygen contains $32.00\,g/mol$

$\Rightarrow Density\,of\,oxygen\, = \,\dfrac{{mass}}{{volume}}$ $= \,\dfrac{{32}}{{volume}}$
$\Rightarrow \dfrac{4}{{Density\,of\,He}}\,\, = \,\dfrac{{32}}{{Density\,of\,oxygen}}\,\,$
$\Rightarrow Density\,of\,He\, = \,\dfrac{1}{8}th\,Density\,of\,oxygen\,$

Additional information:
Helium is an element which is denoted the symbol $He$ having atomic number $2$ and the atomic mass is $4.00\,g/mol$ . It is an odourless, colourless, non-toxic, tasteless, inert and monatomic gas. It is the first noble gas in the group in the periodic table. It is having the lowest boiling point among all the elements. $He$ is the second lightest and second most abundant element in the observable universe.

Oxygen is an element which is denoted with the symbol $O$ and atomic number $8$ and the atomic mass is $16.00\,g/mol$ . Oxygen is a highly reactive nonmetal and also an oxidizing agent which readily reacts and forms oxides with most elements. It is a member of the chalcogen group on the periodic table.

As we know that oxygen is one of the abundant elements after the hydrogen and helium in the universe by mass. At standard temperature and pressure, the two oxygen atoms form a double bond which results in dioxygen in nature. The dioxygen is a colourless and odourless diatomic gas with the formula ${O_2}$ . This diatomic oxygen gas constitutes $20.95\%$ of the Earth's atmosphere.

So, the answer is ${\text{A}}{\text{. Statement I is true, Statement II is true}}$

Note: Density is denoted as mass by volume. Suppose if there is 2 insoluble liquid mixtures like oil and water, in that case we observe that the denser liquid will be in the bottom and less dense liquid in the top. The density is denoted as $\rho$ (rho) or $D$ symbol.
$\rho \, = \,\dfrac{{mass}}{{volume}}$