Question

The mass of one molecule of carbon dioxide is:
(A)- $26.49\times {{10}^{24}}g$
(B)- $44g$
(C)- $7.30\times {{10}^{-23}}g$
(D)- $22g$

Answer 1

Hint: The mass of the substance is obtained by the sum of its constituent atoms and it is equal to its molecular weight in grams per mole of the substance. The substance may be atoms, ions or molecules.

Complete step by step answer:
One molecule of carbon-dioxide has a carbon atom covalently bonded to the two adjacent oxygen atoms. Hence, its molecular formula is given as $C{{O}_{2}}$, with a linear geometry.
So, we can get the molecular mass of $C{{O}_{2}}$ equal to the sum of the atomic mass units of the constituent atoms multiplied by the number of their occurrence in the formula and measured in SI units as atomic mass units (amu).
Then, the molecular mass of $C{{O}_{2}}$ molecule is
$=$ atomic mass of carbon $+$ (2 $\times $atomic mass of oxygen)
$=12+(2\times 16)$
$=44\,u$
Now, in order to know the mass of the compound (in grams), we take its molar mass which is the mass of one mole of molecules of the given compound. It is measured in grams per mole, where one mole of the substance has $6.022\times {{10}^{23}}$ molecules of the substance.
Then, in $C{{O}_{2}}$ compound, its molar mass will be 44 g, that is, mass of 1 mole of given compound having $6.022\times {{10}^{23}}$molecules of $C{{O}_{2}}$.
Thus, we have, the number of grams in 1 mol of $C{{O}_{2}}$ is the same as the number of its atomic mass units.
So, if 1mole of the compound having $6.022\times {{10}^{23}}$ molecules have mass equal to 44g, then one molecule of carbon-dioxide will have mass$=\dfrac{44}{6.022\times {{10}^{23}}}=7.306\times {{10}^{-23}}g$.

Therefore, the mass of one molecule of $C{{O}_{2}}$ is option (C)- $7.30\times {{10}^{-23}}g$.

Note: The number $6.022\times {{10}^{23}}$is a dimensionless number, known as the Avogadro constant, given as ${{N}_{A}}$, which acts as the proportionality constant and unit is $mo{{l}^{-1}}$. Thereby, relating the amount of the substance to its constituent atoms or molecules.