Question

One mole of any substance contains $6.022 \times {10^{23}}$ atoms/molecules. Number of molecules of ${H_2}S{O_4}$ present in 100mL of 0.02M ${H_2}S{O_4}$ ​ solution is __________?
a.) $12.044 \times {10^{20}}$ molecules.
b.) $6.022 \times {10^{23}}$ molecules.
c.) $1 \times {10^{23}}$ molecules.
d.) $12.044 \times {10^{23}}$ molecules.

Answer 1

Hint: Start by using the definition and formula of Molarity , defined as number of moles present per litre of volume of solution. Rearrange the terms and find out the number of moles present in 100mL of 0.02M ${H_2}S{O_4}$ ​ solution by converting into desired units. Then find out the total number of molecules present in the same by multiplying Avogadro’s number or constant ${N_A} = 6.022 \times {10^{23}}$.

Complete step by step answer:
Given,
100mL of 0.02M ${H_2}S{O_4}$
1 mole = $6.022 \times {10^{23}}$ atoms/molecule………….(equation 1)
$6.022 \times {10^{23}}$ is nothing but the Avogadro’s number denoted by ${N_A}$.

Now , we know that
Molarity (M) = $\dfrac{{{\text{No}}{\text{. of moles(n)}}}}{{{\text{Volume of solution in Litres(V)}}}}$
Using the above formula we can find the number of moles present in 100mL of 0.02M ${H_2}S{O_4}$
solution
${\text{No}}{\text{. of moles(n)}} = {\text{Volume of solution in Litres(V}}) \times {\text{Molarity(M)}}$
But before that let us convert 100 ml into Litres , which will be equal to $\dfrac{{100}}{{1000}} = 0.1L$
Now substituting all the values in above discussed formula , we get
$
  {\text{No}}{\text{. of moles(n)}} = 0.1 \times 0.02 \\
  {\text{No}}{\text{. of moles(n)}} = 2 \times {10^{ - 3}}{\text{moles}} \\
$
Now from equation 1 , we get
1 mole =${N_A}$= $6.022 \times {10^{23}}$ atoms/molecule
So $2 \times {10^{ - 3}}{\text{moles}}$ = $(2 \times {10^{ - 3}}) \times (6.022 \times {10^{23}})$molecules
$ = 12.044 \times {10^{20}}$molecules.

Which means 100mL of 0.02M ${H_2}S{O_4}$ solution contains $12.044 \times {10^{20}}$molecules.
So, the correct answer is “Option A”.

Note: Students must know all the important laws and definitions related to mole concept which includes Molarity , Molality , Normality. Also one must remember Avogadro’s number(${N_A}$) i.e. $6.022 \times {10^{23}}$, which is required to solve many similar questions. Attention must be given while substituting the values and the exponents, as any mistake might lead to wrong or absurd value.