Question

The total number of electrons present in 18ml of water is:
(Avogadro’s number is \[{N_A}\] )
A.18 \[{N_A}\]
B.10 \[{N_A}\]
C.9 \[{N_A}\]
D.1 \[{N_A}\]

Answer 1

Hint: When we divide the given mass by the atomic mass of an element, we get the number of moles present of that particular element. We are familiar with the fact that the number of molecules present in one mole of water are equal to the Avogadro’s number i.e. \[6.023 \times {10^{23}}\] .
Formulas used:
 \[{M_w} = volume \times density\] and
\[number\,of\,moles = \dfrac{{given\,mass}}{{molar\,mass}}\]

Complete step by step answer:
We are given the volume of the water as 18ml. Density of water is known to us as 1g/ml. Also, we know that the formula for getting the mass if we are provided with volume and density i.e. \[density = \dfrac{{mass}}{{volume}}\] . Therefore, mass will be equal to the product of density and volume.
Now, we have the same formula in terms of water as, \[{M_w} = volume \times density\]
Thus, the mass of the water is 18g. This is the same as the molecular mass of water.
Now we can calculate the moles of water present using the below formula.
 \[number\,of\,moles = \dfrac{{given\,mass}}{{molar\,mass}}\]
So, the number of moles of water will be \[\dfrac{{18}}{{18}} = 1\] mole. The number of water molecules in 18 grams mass of water or in 1 mole of water will be the Avogadro’s number i.e. \[6.023 \times {10^{23}}\] .
Now, let us count the number of electrons in one molecule of water such that two hydrogen atoms will contribute 2 electrons and one oxygen atom will contribute 8 electrons. In total, there are 10 electrons in water molecules.
So, we can say that the number of electrons in \[6.023 \times {10^{23}}\] molecules of water will be ten times of it i.e. \[10 \times 6.023 \times {10^{23}}\] or 10 \[{N_A}\] .

Hence, the correct option is (B).

Note:
Avogadro number is the measurement of the number of atoms, molecules or ions present in 1 mole of a substance. It is a constant of proportionality factor which relates the amount of substance in a sample with the number of constituent particles. Therefore, its SI unit is the reciprocal of the mole, represented as \[{N_A}\] which is equal to \[6.023 \times {10^{23}}\].