Question

Calculate the total number of electrons present in $1.8g$ of water.
A. $N_A$
B. ${\displaystyle \frac{N_A}{2}}$
C. ${\displaystyle \frac{N_A}{10}}$
D. ${\displaystyle \frac{3N_A}{10}}$

Answer 1

Hint: Firstly, with our knowledge of the molar mass of water, we can find the number of moles of the mass of water given to us. Then we can calculate the number of electrons in one molecule of water, by counting the individual electrons of the hydrogen and oxygen atoms. Multiplying the number of moles with the avogadro number and the number of electrons in a single molecule will give us our answer.
Formulas used: $n={\displaystyle \frac{W}{M}}$ where $n$ is the number of moles, $W$ is the given mass and $M$ is the molar mass

Complete step by step answer:
First, we have to find out the number of electrons present in a single molecule of water.
For that we have to know that a single molecule of water contains two hydrogen atoms and a single oxygen atom. The hydrogen atoms each contain a single electron and the oxygen atom has eight electrons. So, in total a single molecule of water contains $10$ electrons in it.
Now the molecular weight of water is calculated by adding the molecular weights of two hydrogen and an oxygen atom and the answer is $(1\times 2)+16=18$.
Next, we find out how many moles are present in $1.8g$ of water,
$n={\displaystyle \frac{W}{M}}$ where $n$ is the number of moles, $W$ is the given mass and $M$ is the molar mass
Substituting values as $w=1.8g$ and $M=18g$, we get:
$\Rightarrow n={\displaystyle \frac{1.8}{18}}$ where $n$ is the number of moles present in $1.8g$ of water.
$\Rightarrow n=0.1$
Therefore $0.1moles$ are present in $1.8g$ of water.
One molecule of water contains $N_A$ molecules.
Now multiplying the $0.1moles$ with the Avogadro’s number $\left(N_A\right)$and then by the number of electrons in a single molecule of water $\left(10\right)$, we get
$\Rightarrow 0.1\times N_A\times 10=N^A$
Therefore, there are $N_A$ of electrons present in $1.8g$ of water.
The correct option is option A.

Note:The number of electrons and number of molecules should not be confused with each other. The number of electrons in a single water molecule is $10$ while the number of moles in one mole water is $N_A$. Note that the molar mass of water is the mass of water which will have its number of water molecules equal to the Avogadro’s number. In other words, in $18g$ of water, there will be exactly $6.022\times {10}^{23}$ molecules of water.