Q.One mole of any substance contains $6.022 \times 10^{23}$ atoms/molecules. Number of molecules of $H_2SO_4$ present in 100 mL of 0.02M $H_2SO_4$ solution is ______.

Concept: Relating molarity, volume, and Avogadro's number to find the number of molecules.

The molarity tells us moles of solute per liter of solution. For a 0.02 M $H_2SO_4$ solution, we have 0.02 moles in 1000 mL.

Step 1: Find moles in 100 mL.

Step 2: Convert moles to molecules using Avogadro's number ($N_A = 6.022 \times 10^{23}$). …

The question asks for the number of molecules, not the amount in moles. Whenever you need to count individual particles—atoms, molecules, ions—you bridge from the macroscopic world (moles, concentration, volume) to the microscopic one using Avogadro's number, $N_A = 6.022 \times 10^{23} \, \text{mol}^{-1}$.

The strategy is straightforward: first calculate how many moles of $H_2SO_4$ are present in the given volume of solution, then convert that amount to molecules.

Step-by-step calculation

1. Identify what you know.

   The solution is 0.02 M (molarity), meaning there are 0.02 moles of $H_2SO_4$ per litre of solution. The volume given is 100 mL, which is $\frac{100}{1000} = 0.1$ L.

2. Calculate the number of moles.

   Molarity is defined as moles per litre:

Substituting the values:

So the solution contains $2 \times 10^{-3}$ moles of $H_2SO_4$.

3. Convert moles to molecules. …

Concept: Molarity and Avogadro's Number

Molarity ($M$) = number of moles of solute per litre of solution.

Avogadro's Number = $6.022 \times 10^{23}$ particles per mole.

Method: Mole–Molarity–Particle Conversion

Steps

1. Write the given data

   • Volume of solution = $100 \text{ mL} = 0.1 \text{ L}$
   • Molarity = $0.02 \text{ M}$
   • Avogadro’s number = $6.022 \times 10^{23} \text{ molecules/mol}$

2. Find moles of $H_2SO_4$

3. Convert moles to molecules …

🧠 Concept Recap

We are given:

• Volume = 100 mL = 0.1 L
• Molarity = 0.02 M = 0.02 mol/L
• Avogadro’s number = $6.022 \times 10^{23}$ molecules/mol

Correct approach:

1. Find moles of $H_2SO_4$:

2. Find number of molecules:

Which equals $12.044 \times 10^{20}$ molecules → Option (i).

✗ Common Mistake #1: Forgetting to convert mL to L

What students do:

They plug in 100 mL directly:

Then multiply by Avogadro’s number → huge wrong answer like $12.044 \times 10^{23}$ (option (iv)).

Why it’s wrong:

Molarity is mol/L, so volume must be in litres.

✓ How to avoid:

Always write the unit:

Make it a habit — never skip this step.

✗ Common Mistake #2: Confusing atoms with molecules

What students do:

They calculate molecules correctly but then multiply by the number of atoms per molecule (e.g., 7 atoms in $H_2SO_4$) and give an answer for atoms, not molecules.

Why it’s wrong:

The question explicitly asks for number of molecules, not atoms.

✓ How to avoid:

Read the question carefully — underline “molecules” or “atoms”. If it says molecules, stop after multiplying moles by Avogadro’s number.

✗ Common Mistake #3: Misplacing the decimal in scientific notation

What students do:

They compute $0.002 \times 6.022 \times 10^{23}$ and write $1.2044 \times 10^{21}$ but then match it to $12.044 \times 10^{20}$ incorrectly, thinking it’s a different number.

Why it’s wrong:

$12.044 \times 10^{20}$ is exactly equal to $1.2044 \times 10^{21}$ — just a different notation.

✓ How to avoid:

Practice converting between forms: …