Question

If the molecular mass of $C{O_2}$ is ${\text{44amu}}$ and Avogadro's number is $6.022 \times {10^{23}}$. Therefore, what is the mass of one molecule of $C{O_2}$?
(A)$7.31 \times {10^{ - 23}}$
(B) $3.65 \times {10^{ - 23}}$
(C) $1.01 \times {10^{ - 23}}$
(D) $2.01 \times {10^{ - 23}}$

Answer 1

Hint:
The mass of a given molecule is termed as molecular mass, It is expressed in units Dalton \[\left( {Da} \right)\] or \[u\]. Different Molecules have different masses. The molecules are mass of the, generally represent the mass of one mole of that substance, it can also be calculated for a single molecule.

Complete step by step answer:
In this question, we are provided with the molecular mass of $C{O_2}$ that is ${\text{44amu}}$(atomic mass unit).
It implies that the mass of one mole $C{O_2}$ molecules is ${\text{44amu}}$.
We are also provided with the Avogadro number that is $6.022 \times {10^{23}}$
It implies the total number of particles are entities present in the mole of a substance $6.022 \times {10^{23}}$. Therefore, if we want to calculate the mass of one molecule of $C{O_2}$, we need to divide the mass of one more $C{O_2}$ by the number of particles present in one mole, that is Avogadro's number.
Therefore,
Mass of one molecule of
$C{O_2} = \dfrac{{{\text{molecular mass of C}}{{\text{O}}_{\text{2}}}}}{{{\text{Avogadro's number}}}}$.
$ = \dfrac{{44}}{{6 \times {{10}^{23}}}}$
$ = 7.31 \times {10^{ - 23}}$
Hence the mass of one molecule of $C{O_2}$ is $7.31 \times {10^{ - 23}}$.

Hence the correct option is (A) $7.31 \times {10^{ - 23}}$.

Additional information:
Avogadro’s number is named so in the honour Of Amedeo Avogadro. He discovered the number of particles (atoms or molecules or ions) of substance have proportional relationship with the mass of that substance.
As one dozen means \[12,\] one gross means \[144\], in the same way Avogadro's number means $6.022 \times {10^{23}}$ particles. Avogadro’s number is represented as ${N_A}$.
The Avogadro's number is related to many constants such as gas constant($R$ ),Boltzmann constant (${K_B}$), Faraday constant $(F)$, molar mass constant $({M_u})$. etc.

Note: The mass of the molecule is calculated with the help of Avogadro’s number. In the same way if mass of one molecule is given and we are asked to calculate the molar mass of the substance. Then, In that case we would simply multiply the mass of the molecule with Avogadro number to obtain the molecular mass of the substance.
molecular mass $ = $ mass of one molecule $ \times $ avogadro's number