Question

Calculate the number of molecules of Sulphur (\[{S_8}\]) present in $128g$ of Sulphur (${S_2}$).

Answer 1

Hint: As we have already learnt that a mole is the definite amount of a substance expressed in terms of weight, volume and number of particles. One mole contains a fixed number of particles as present in $12g$ of Carbon-12 atoms.

Formula used:
$moles = \dfrac{{mass}}{{molecular{\text{ mass}}}} = \dfrac{{no.{\text{ }}of{\text{ molecules}}}}{{6.022 \times {{10}^{23}}}}$

Complete step by step answer:
So, to calculate the number of molecules, we can first identify the moles and then using the formula given below we can calculate the molecules without any difficulties. Moles can be easily calculated by dividing the given mass of the substance with the molecular mass of the given substance. Then, with the calculated moles, the number of molecules can be calculated by multiplying the moles with Avogadro’s number.
For that let us first write the values given in the question-$mass = 128g$, the molecular mass of \[{S_8}\]=$8 \times 32g = 256g$.
Now, we can use this below written formula to calculate the number of molecules:
$moles = \dfrac{{mass}}{{molecular{\text{ mass}}}} = \dfrac{{no.{\text{ }}of{\text{ molecules}}}}{{6.022 \times {{10}^{23}}}}$
When we put the given values in the formula we get:
$
  moles = \dfrac{{128}}{{256}} \\
  {\text{ = 0}}{\text{.5 moles}}
$
$
\Rightarrow 0.5 = \dfrac{{no.{\text{ of molecules}}}}{{6.022 \times {{10}^{23}}}} \\
\Rightarrow {\text{No}}{\text{. of molecules = 0}}{\text{.5 }} \times {\text{6}}{\text{.022}} \times {\text{1}}{{\text{0}}^{23}} \\
{\text{ = 3}}{\text{.011}} \times {\text{1}}{{\text{0}}^{23}}{\text{ molecules}}
 $

Therefore, the number of molecules of Sulphur (\[{S_8}\]) is $3.011 \times {10^{23}}$.

Additional information:
Similarly, the number of atoms can be calculated by first calculating the moles and then multiplying those calculated moles with Avogadro’s number. If volume is given and we are asked to calculate the number of atoms or number of molecules then we can apply the formula $\dfrac{{given{\text{ volume in litres }}}}{{22.4{\text{ }}litres}}$and then multiply the calculated value with the Avogadro’s number.

Note:
Students should learn this formula to calculate anything given in the question so that you do not get any answer wrong. $moles = \dfrac{{mass}}{{molecular{\text{ mass}}}} = \dfrac{{no.{\text{ }}of{\text{ molecules}}}}{{6.022 \times {{10}^{23}}}} = \dfrac{{no.{\text{ of atoms}}}}{{6.022 \times {{10}^{23}}}} = \dfrac{{given{\text{ volume in litres}}}}{{22.4{\text{ litres}}}}$
This is the easiest formula to learn and from an entrance exams point of view it takes less time to calculate the answers.