Question

Calculate the mass of:
$\left( i \right)$ An atom of silver (atomic mass of silver $= 108\,u$ ).
$\left( {ii} \right)$ A molecule of $C{O_2}$ .

Answer 1

For this we must know the definition of atomic mass unit is the atomic mass of an element is the average mass of the atoms of an element measured in atomic mass unit (amu, also as Daltons, D). Where $1\,\,amu = 1.6605 \times {10^{ - 24}}g$ .

Complete step by step answer:
In $\left( i \right)$ , since we have to calculate the mass of silver, Let us assume that the mass of silver is $x$ grams.
Avogadro number gives us the value of the number of atoms, molecules, or ions present in one mole of a given species. The value of Avogadro number or Avogadro constant is $6.022 \times {10^{23}}$ .
Mole is a unit to determine the amount of substance. $1$ Mole $= 6.022 \times {10^{23}}$ molecules.
Therefore, $1$ mole of silver will have $6.022 \times {10^{23}}$ molecules of silver atoms. Hence, Atomic mass of silver $= 108g$ .
Atomic mass of silver $=$ Mass of $6.033 \times {10^{23}}$ silver atoms
Mass of one silver atom $=$ $\dfrac{{Atomic\,mass\,of\,silver}}{{6.022 \times {{10}^{23}}}}$ $g$.
$=$ $\dfrac{{108}}{{6.022 \times {{10}^{23}}}}$ $g$ .
Mass of silver atom $=$ $1.794 \times {10^{ - 22}}g$ .
In $\left( {ii} \right)$ , Since we have to calculate the mass of Carbon dioxide $\left( {C{O_2}} \right)$ , Let us assumed that the mass of carbon dioxide $\left( {C{O_2}} \right)$ is $x$ grams.
Therefore, $1$ mole of carbon dioxide $\left( {C{O_2}} \right)$ will have $6.022 \times {10^{23}}$ molecules of carbon dioxide $\left( {C{O_2}} \right)$ atoms. Hence, Atomic mass of carbon dioxide $= 44g$ .
Mass of one $\left( {C{O_2}} \right)$ molecules $= \dfrac{{44}}{{6.022 \times {{10}^{23}}}}g$
Mass of one $\left( {C{O_2}} \right)$ molecules $= 7.304 \times {10^{ - 24}}g$ .

Note:
An atomic mass unit (symbolized AMU or amu) is defined as precisely $\dfrac{1}{{12}}$ the mass of an atom of carbon $- 12$ . The AMU is used to express the relative masses of atoms or elements.