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7.5 grams of a gas occupies 5.6 litres of volume at STP. The gas is (atomic weights of C, N and O are 12, 14, and 16 respectively):
A) $NO$
B) ${N_2}O$
C) $CO$
D) $C{O_2}$

Last updated date: 13th Jun 2024
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Hint: Gaseous state is the less ordered state. The molecules in gases are separated from each other by large distances. The intermolecular forces are the weakest in them. The gases have all three types of motion i.e. the translatory, rotatory, and vibratory and possess high kinetic energy. Various laws are there to explain the properties of gases (Boyle’s law, Charlie’s law, Gay-Lussac’s law, Avogadro’s law).

Complete step by step solution:
In the question, we have to calculate the molecular mass of the gas and see if the calculated molecular mass is equal to the molecular mass of one of the compounds in the given options.
Mass of the gas $ = 7.5$litres
The volume occupied by the gas at STP $ = 5.6$ liters
We know,
At STP 1 mole of gas occupies 22.4 liters
Now, Number of moles of the gas $ = \dfrac{{5.6}}{{22.4}}$
$ = 0.25$ mole
(As we have calculated the number of moles of the gas by the given values so that we can use it when we will find the molecular mass of the gas).
We know,
Number of moles $ = \dfrac{{mass}}{{molecular\,mass}}$
Molecular mass $ = \dfrac{{mass}}{{No.\,of\,moles}}$
(Now we will put given values in the above equation to calculate the molecular mass of the gas).
Molecular mass $ = \dfrac{{7.5}}{{0.25}}$
$ = 30$ gm/moles
Now we will see which of the compounds in the given options have a molecular mass of 30 gm/mol.
$NO$$ = 14 + 16 = 30$gm/moles
${N_2}O$$ = 2 \times 14 + 16 = 44$gm/moles
$CO$$ = 12 + 16 = 28$ gm/moles
$C{O_2}$ $ = 12 + 2 \times 16 = 44$ gm/moles

After calculating, we can see that NO has a molecular mass of 30 gm/moles. So the gas is NO (nitric oxide).

Hence, the correct answer is Option A.

Note: Properties of gases.
Shape and Volume: - Since particles of gases are not held in fixed positions and move freely gases neither have definite shapes nor volumes. They fill the whole space available to them and take up the shape and volume of the vessel in which they are enclosed.
Homogeneous nature: - All the parts of a gas or a gaseous mixture composition throughout.
Compressibility: - On increasing pressure, gases can be readily compressed due to the presence of large empty spaces.
Random motion: - The molecules or atoms of a gas are in a state of continuous zig-zag motion in all directions.
Pressure: - Due to their random motion, the molecules of the gas collide on the walls of the container and thus exert a certain force on the walls of the container.
Diffusion: - Gases mix (diffuse) with each other freely due to the free movement of their molecules.
Density: - Due to the large separation of molecules, gases have a large volume and thus low densities.