Question

A gaseous mixture contains oxygen and sulphur dioxide in the ratio of 1:4 by mass. Therefore the ratio of their respective number of molecules is:
A.1:2
B.1:4
C.2:1
D.4:1

Answer 1

It is worth remembering that mass of one mole of atoms of an element or a molecule (which contains $6.022\times {{10}^{23}}$ atoms or molecules per mole) has mass equal to molecular mass of the compound but in grams. This is the mole concept.
Thus, value of molar mass in amu (atomic mass unit, $\mu$) = molecular mass in grams

Complete step by step answer:
Option (A) 1:2 is the correct answer.
We will solve by assuming some mass to the gas mixture.
Let the mass of oxygen ${{O}_{2}}$ be 1g in the mixture, then according to question, mass of sulphur dioxide $S{{O}_{2}}$ is 4g.
Now, for ${{O}_{2}}$
1 mole of ${{O}_{2}}$ atoms = $6.022\times {{10}^{23}}$atoms
Now, as we know, molecular mass of ${{O}_{2}}$=32 $\mu$
(mass number of oxygen is 16 $\mu$, thus molecular mass = $16+16=32$)
Thus, molar mass of ${{O}_{2}}$= 32 g
According to mole concept,
1 mole of${{O}_{2}}$ atoms = $6.022\times {{10}^{23}}$ atoms ${{\equiv }_{{}}}$32 g
Thus 32 g of ${{O}_{2}}$ gas contains $6.022\times {{10}^{23}}$ atoms,
Then 1g of ${{O}_{2}}$ gas contains = $\dfrac{6.022\times {{10}^{23}}}{32}$ atoms.
Now for$S{{O}_{2}}$,
1 mole of $S{{O}_{2}}$ atoms = $6.022\times {{10}^{23}}$atoms
Now, as we know, molecular mass of $S{{O}_{2}}$= 64 $\mu$
Thus, molar mass of $S{{O}_{2}}$= 64 g
According to mole concept,
1 mole of $S{{O}_{2}}$ atoms = $6.022\times {{10}^{23}}$ atoms ${{\equiv }_{{}}}$64g
Thus 64 g of $S{{O}_{2}}$ gas contains $6.022\times {{10}^{23}}$ atoms,
Then 4 g of $S{{O}_{2}}$ gas contains = $1:2$ atoms.
Hence, ratio of number of molecules of to the number of molecules of is:
=$\left( \dfrac{6.022\times {{10}^{23}}}{32} \right):\left( \dfrac{6.022\times {{10}^{23}}}{64}\times 4 \right)$
=$\left( \dfrac{1}{32} \right):\left( \dfrac{4}{64} \right)$
=$\left( \dfrac{1}{32} \right)\times \left( \dfrac{64}{4} \right)$
=$\left( \dfrac{1}{2} \right)$=$1:2$
Thus option (A) is correct.

Additional information: Mass number of an atom is the sum of the total number of protons and neutrons in its nucleus. 1 mass number unit is roughly equal to 1 atomic mass unit. Hence the atomic mass of oxygen $O$ is 16 atomic mass units as its mass number is 16 (8 protons+8 neutrons).

Note: The constant $6.022\times {{10}^{23}}$ is known as Avogadro Number and is denoted by ${{N}_{A}}$.
In many elements, mass number is twice the atomic number (number of protons in an atom). But this is not the case in a few elements and isotopes.