Question

Give an estimate of the number of electrons in $100g$ of water. How much are the total negative charges on these electrons?

Answer 1

Hint: First, we have to learn the idea of ‘mol’. Then we will figure out the relation between ‘Molecular Weight’ and ‘Mole’. Once this concept gets clear, then we can proceed to find out the number of electrons. Finally, we can arrive at our final answer, i.e., the total charge of these electrons.

Complete step by step solution:
By definition, Mole is the standard unit for measuring small quantities of the physical world, such as atoms, electrons, and other subatomic particles. According to Avogadro, $1mol$ of a substance contains $6.02214 \times {10^{23}}$ atoms, often denoted by ${N_A}$. The weight of $1mol$ of a substance is called the Molecular Weight of that substance.
Weight of $1mol$ water $ = 18g$
Therefore, the molecular weight of water $ = 18g/mol$
Given weight of the water $ = 100g$
Hence, the molecular weight of the given water $ = \left( {\dfrac{{100}}{{18}}} \right) = 5.55g$
Now for one atom of ${H_2}O$ we have $10$ electrons, $2$ electrons from two $H$-atoms, and $8$ electrons from one $O$-atom.
So $5.55$ moles water contains $\left( {10 \times 5.55} \right) = 55.5$ moles electrons.
Now we know,
Number of electrons = number of moles of electrons $ \times $ Avogadro’s Number
Hence, the number of electrons = $55.5 \times 6.0214 \times {10^{23}}$
$\Rightarrow {\text{334}}{\text{.1877}} \times {10^{23}}$
We know the charge of an electron = $ - 1.6 \times {10^{ - 19}}C$.
Now, The total charge carried by the electrons = Total number of electrons $ \times $ Charge of an electron
$\Rightarrow \left( {334.1877 \times {{10}^{23}}} \right) \times \left( { - 1.6 \times {{10}^{ - 19}}} \right)C$
$\Rightarrow - 5.347 \times {10^6}C$

Therefore, the total negative charge carried by the electrons = $5.347 \times {10^6}C$.

Note: Avogadro’s Number is instrumental in science. Besides, the concept of a mole is very crucial in the field of chemistry. It is vital to measure all the substances in the mole unit to perform a good chemistry experiment.