Question

Calculate the number of molecules of $NaOH$ present in $25c{{m}^{3}}$ of $0.15M$$NaOH$.
A.$3.75\times {{10}^{-3}}$ molecules
B.$2.258\times {{10}^{21}}$ molecules
C.$6.022\times {{10}^{23}}$ molecules
D.$3.75\times {{10}^{23}}$ molecules

Answer 1

Hint: Here, you should know the calculation of number of molecules through number of moles and you should also know the value of Avogadro’s number.
Avogadro’s number$({{N}_{A}})=6.022\times {{10}^{23}}$
Here, molarity is defined as the amount of substance present in the volume of the solution.
Formula Used:
$M=\dfrac{n}{V}$
where, $M$ is the molarity of $NaOH$ , $n$ is the number of moles and $V$ is the volume of the solution.

Complete step by step answer:
Here, it is given that volume of solution $=25c{{m}^{3}}$
Molarity of $NaOH=0.15M$
As we know,
$M=\dfrac{n}{V}$
where, $M$ is the molarity of $NaOH$ , $n$ is the number of moles and $V$ is the volume of the solution.
Substituting the values in the above formula, we get,
\[
M=\dfrac{n}{V}\Rightarrow 0.15=\dfrac{n}{0.025} \\
\Rightarrow n=0.15\times 0.025=0.00375 \\
\]
So therefore, the number of moles of $NaOH=0.00375$ .
To calculate the molecules of $NaOH$ ,
Molecules of $NaOH$$=$ Moles of $NaOH$$\times $ Avogadro’s number
Molecules of $NaOH=0.00375\times 6.022\times {{10}^{23}}=2.2\times {{10}^{21}}$
Hence, the correct option is B.$2.258\times {{10}^{21}}$ molecules.

Additional information:
Molarity Is defined as a measure to calculate the amount of concentration in solution in terms of moles per unit volume.
$M=\dfrac{n}{V}$
A molecule is used to name a combination of atoms, which are chemically bonded, whereas the mole is a term used to measure the number of atoms, ions. It is used to measure quantity of substance.
Avogadro’s number: It is defined as the number of units in one mole of any substance. Avogadro’s number is denoted with ${{N}_{A}}$ , where ${{N}_{A}}=6.022\times {{10}^{23}}$
The units can be electrons, ions, molecules that depend on the nature of the substance.

Note: The SI unit of Avogadro’s number is $mo{{l}^{-1}}$.You should convert the number of moles into the number of molecules using Avogadro’s number otherwise you will get an incorrect answer.SI unit of molarity is moles per litre