Question

Calculate the mass of a single atom of sulfur and a single molecule of carbon dioxide.

Answer 1

Hint: Atomic weight of sulfur atom is 32$gmmo{l^{ - 1}}$ and molecular weight of carbon dioxide is 44$gmmo{l^{ - 1}}$. Avogadro number shows the number of species present in one mole and is equal to $6.022 \times {10^{23}}$ $mo{l^{ - 1}}$.

Complete step by step solution:
- First we will calculate the mass of a single atom of sulfur.
We know that the atomic weight of sulfur atoms is 32$gmmo{l^{ - 1}}$ but as the unit of this value suggests, it is the weight of one mole of sulfur atoms. So, atomic mass of sulfur means the mass of $6.022 \times {10^{23}}$ atoms of sulfur. Now, we can easily divide the atomic mass by the number of atoms present in one mole to obtain the weight of one sulfur atom.

So, we can write that Mass of single atom of sulfur = $\dfrac{{{\text{Atomic mass of Sulfur}}}}{{6.022 \times {{10}^{23}}}}$
Mass of single atom of sulfur = $\dfrac{{32}}{{6.022 \times {{10}^{23}}}}$
Mass of single atom of sulfur = $5.31 \times {10^{ - 23}}$gm
Now, we will find the weight of a single molecule of Carbon dioxide.
First let’s find the molecular weight of Carbon dioxide.
Molecular weight of carbon dioxide = Atomic weight of C + 2(Atomic weight of O)
Molecular weight of carbon dioxide = 12 + 2(16)
Molecular weight of Carbon dioxide = 12 + 32
Molecular weight of Carbon dioxide = 44$gmmo{l^{ - 1}}$
Now, we know that $6.022 \times {10^{23}}$ molecules will be present in one mole of carbon dioxide. So, 44gm is the weight of $6.022 \times {10^{23}}$ molecules of carbon dioxide. So, we can find the weight of a single molecule of carbon dioxide by following the formula.
Weight of single ${\text{C}}{{\text{O}}_2}$ molecule = $\dfrac{{{\text{Molecular weight of C}}{{\text{O}}_2}}}{{6.022 \times {{10}^{23}}}}$
Weight of single ${\text{C}}{{\text{O}}_2}$ molecule= $\dfrac{{44}}{{6.022 \times {{10}^{23}}}}$
Weight of single ${\text{C}}{{\text{O}}_2}$ molecule = $7.31 \times {10^{ - 23}}$gm
Thus, we have found that weight of single atom of sulfur is $5.31 \times {10^{ - 23}}$gm and weight of single carbon dioxide molecule is $7.31 \times {10^{ - 23}}$gm.

Note: Do not consider atomic mass of atoms as the mass of their single atom. Same way, the molecular mass of the compound is the mass of one mole molecule and not of a single molecule.