Question

The total number of electrons present in 18 mL water (density $1$g/ml) is: a.) $6.023 \times {10^{23}}$
b.) $6.023 \times {10^{24}}$
c.) $6.023 \times {10^{25}}$
d.) $6.023 \times {10^{21}}$

Answer 1

Hint: On dividing the given mass by the atomic mass of the element we will get the number of moles present of that element. Also, we know that the number of molecules that the one mole of the water will contain will be equal to the Avogadro’s number that is equal to $6.023 \times {10^{23}}$.

Complete step by step solution: Given, volume of the water ${\text{ = V = 18ml}}$
Density of water ${\text{ = d}}$ $= 1$ g/ml
As we all know the formula for getting the mass if the volume and density is given.
That is, ${\text{density}}$ =$\dfrac{{{\text{mass}}}}{{{\text{volume}}}}$
Since the density is equal to the mass divided by the volume, so the mass will be equal to the multiplication of the density and mass.
So ${\text{mass = volume \times density}}$
So, mass of the water${\text{ = }}{{\text{m}}_{\text{w}}}{\text{ = V \times d}}$
$\Rightarrow {{\text{m}}_{\text{w}}}{\text{ = (18 \times 1)g = 18g}}$
As we know that
the mass of the one molecule of water ${\text{ = }}\left( {{\text{1 \times 2}}} \right){\text{ + 16 = 18g}}$
So, the number of the mole=$\dfrac{{{{\text{m}}_{\text{w}}}}}{{{{\text{m}}_{{\text{atomic}}}}}}$
So, the number of moles $= \dfrac{{18}}{{18}} = 1$ mole
The number of molecules of the ${{\text{H}}_{\text{2}}}{\text{O}}$in ${\text{18g}}$mass of the water that means the number of molecules in 1 mole of the water $= 6.023 \times {10^{23}}$ molecules
Hence, we have given the one mole of the water in the problem.
And also, the number of electrons in one molecule of the water $= (1 \times 2) + 8 = 10$ electron
So, the number of electrons in $6.023 \times {10^{23}}$molecule of the water$= 6.023 \times {10^{23}} \times 10$
$= 6.023 \times {10^{24}}$ electron.
Hence the total number of electrons present in 18mL water is $6.023 \times {10^{24}}$.

So, the option (B) is the correct answer.

Note: Avogadro number is actually the measurement of the number of units (atoms, molecules or ions) contained by the 1 mole of a substance. Avogadro number is basically a constant of proportionality factor that relates the amount of substance in a sample with the number of constituent particles. The SI unit of the Avogadro number is the reciprocal of the mole, and represented by ${{\text{N}}_{\text{A}}}$.
Hence the Avogadro number is $6.023 \times {10^{23}}$