Question

The number of sulphur atoms present in $200ml$ of $1N$ ${H_2}S{O_4}$, given that Avogadro’s number is ${A_o}$.
A. $\dfrac{{{A_o}}}{5}$
B. $\dfrac{{{A_o}}}{2}$
C. $\dfrac{{{A_o}}}{{10}}$
D. ${A_o}$

Answer 1

Hint: One mole of any substance contains exactly $$6.02214076 \times {\text{ }}{10^{23}}$$ atoms or molecules. This number is Avogadro’s number. Avogadro's number is the number of atoms, per mole of a substance. According to the question, this value is represented by ${A_o}$. Normality is defined as equivalent moles of solute in a given volume of solution. Normality is always a multiple of molarity. After calculating Molarity from the given information, we can calculate the number of atoms of sulphur.

Formula used:
We will use the formula,
$N = M \times x$
$M = $ Molarity of ${H_2}S{O_4}$
$x = $ Number of ${H^ + }$ ions
$M = \dfrac{{mol}}{V}$
$mol = $Number of moles of solute
$V = $ Volume of the solution.

Complete answer:
One mole of any substance contains exactly $$6.02214076 \times {\text{ }}{10^{23}}$$ atoms or molecules. This number is the value of the Avogadro constant ${N_A}$ . Here we are given Avogadro number ${A_o}$ . Normality is defined as equivalent moles of solute in a given volume of solution. Normality is always a multiple of molarity and its $SI$ unit is $N$ . It is given by the formula
$N = M \times x$……$\left( 1 \right)$
$M = $ Molarity of ${H_2}S{O_4}$
$x = $ Number of ${H^ + }$ ions
We know that dissociation of ${H_2}S{O_4}$ can be written as
$H_2SO_4 \, \rightleftharpoons 2H^+ + {SO_4}^{2-}$
Therefore, $x = 2$
Putting $N = 1$ and $x = 2$ in the equation $\left( 1 \right)$
$N = M \times x$
$
\Rightarrow 1 = M \times 2 \\
\Rightarrow \dfrac{1}{2} = M $
From here, we get Molarity $\left( M \right) = 0.5M$. Molarity is the number of moles of the given substance in the given volume of solution. It is given by the formula
$M = \dfrac{{mol}}{V}$……$\left( 2 \right)$
$mol = $Number of moles of solute
$V = $ The volume of solution. It is expressed in liters. We are given $200ml$ of volume. We will first convert it into liters.
We have calculated Molarity and volume is given. Putting these values in the equation $\left( 2 \right)$ , we can calculate the number of moles
$M = \dfrac{{mol}}{V}$
$ \Rightarrow 0.5 = \dfrac{{mol \times 1000}}{{200}}$
$ \Rightarrow mol = \dfrac{1}{{10}}$$mol$
From here we can calculate the number of atoms. Avogadro's number is the number of atoms, per mole of a substance. Therefore
Number of atoms of Sulphur = $\dfrac{1}{{10}} \times $ ${A_o}$ $ = \dfrac{{{A_o}}}{{10}}$

Thus the correct option is C.

Note:
Here we have used the concept of both Molarity and Normality, so it is important to know the difference between them. Molarity describes moles of the substance in the given volume of solution whereas Normality describes only reactive moles of the substance in the given volume of solution.