Question

Calculate the number of particles in $8\;gram$ of ${O_2}$ molecule.

Answer 1

Hint: We know that, $1mole = {N_A} particles$. The number of units in one mole of a substance is known as Avogadro Number. Here, ${N_A} = $Avogadro number, ${N_A} = 6.022 \times {10^{23}}$. No of the moles of a substance can be found out by dividing the given mass of the substance by molar mass. $No.{\text{ of moles = }}\dfrac{{given\,{{mass}}}}{{molar{{ mass}}}}$

Complete step by step answer:
To find the number of particles in $8\;gram$ of ${O_2}$ molecule, we first need to find the number of moles of particles in $8\;gram$ of ${O_2}$ molecule.
Given, the weight of the sample $ = 8\;gram$
 Also, we know that the atomic weight of O molecule $ = 16g/mol$
The atomic weight of ${O_2}$ molecule $ = 2(16)g/mol$
The atomic weight of ${O_2}$ molecule $ = 32g/mol$
Number of moles of particles in $8\;gram$ of ${O_2}$ molecule $ = \dfrac{{weight\;of\;the\;given\;sample}}{{atomic{\text{ mass of }}{{{O}}_2}}}$
Thus, the number of moles of particles in $8\;gram$ of ${O_2}$ molecule $ = \dfrac{{8g}}{{32g/mol}}$
Thus, The number of moles of particles in $8\;gram$ of ${O_2}$ molecule $ = 0.25moles$.
Now, we know the number of moles of particles in $8\;gram$ of ${O_2}$ molecule.
Let’s find out the number of particles in $8\;gram$ of ${O_2}$ molecule.
For this, we use the cross multiplication technique as mentioned in the hint.
We know that $1\;mole \to 6.022 \times {10^{23}}particles$
$0.25\;mole \to x\;particles$
Here, $x$ denotes the number of particles in 8 grams of ${O_2}$ molecule.
Now, we cross multiply to find the value of $x$
$ \Rightarrow x = \left( {6.022 \times {{10}^{23}}} \right)\left( {0.25} \right)$
$ \Rightarrow x = 1.5055 \times {10^{23}}particles$
Hence, the number of particles in 8 grams of ${O_2}$ the molecule is $1.5055 \times {10^{23}}particles$.

Note:
Knowing the number of moles, the colligative properties such as osmotic pressure, molality, molarity can be calculated. To find the elevation in boiling point, depression in freezing point, number of moles are to be found out. Avogadro’s number can also be defined as the number of atoms in 12 g of Carbon-12.