ANAND CLASSES Study Material and Notes to learn the Molarity on Dilution Equation 𝑀₁𝑉₁ = 𝑀₂𝑉₂ with detailed explanations, solved examples, conceptual questions, and MCQs for JEE, NEET, and CBSE Class 11 Chemistry.

📚 Topic: Molarity and Dilution — $M_1V_1 = M_2V_2$

🔹 What is Molarity (M)?

Molarity is the most common unit of concentration used in chemistry. It tells you how many moles of solute are present in 1 litre of solution. $$\text{Molarity (M)} = \frac{\text{Moles of solute}}{\text{Volume of solution in litres}}$$

💡 For example:

1 M solution of NaCl means 1 mole of NaCl is dissolved in 1 litre of water.

🔹 What is Dilution?

Dilution is the process of adding more solvent (usually water) to a solution to reduce its concentration, without changing the amount of solute.

🔁 Key idea:

The amount of solute (in moles) remains constant during dilution. Only the volume increases.

🔹 Derivation of the Dilution Formula: $M_1V_1 = M_2V_2$

Let’s say:

Initial solution has molarity $M_1$ and volume $V_1$
After dilution, it becomes molarity $M_2$ and volume $V_2$

Since moles of solute don’t change:

$$\text{Initial moles} = M_1 \times V_1 $$

$$\text{Final moles} = M_2 \times V_2$$

$$\Rightarrow M_1 \times V_1 = M_2 \times V_2$$

This is the dilution formula.

🔹 Understanding Through Example

Let’s say we have a beaker with 100 mL of 2 M HCl.

Now we add 300 mL of water to it. The total volume becomes 400 mL.

Before:
Molarity = 2 M
Volume = 100 mL
Moles = $2 \times 0.1 = 0.2 \text{ mol}$
After:
Volume = 400 mL = 0.4 L
Moles = still 0.2 mol (solute didn’t change)

$$\text{New Molarity} = \frac{0.2}{0.4} = 0.5 \text{ M}$$

✅ So the concentration has decreased from 2 M → 0.5 M due to dilution.

🔹 Important Points to Remember

✅ Units of volume (V) must be the same on both sides (either mL or L).
✅ Use this formula only when there’s no chemical reaction, just dilution.
✅ Moles of solute remain constant before and after dilution.

📘 Real-Life Application

Preparing IV fluids in hospitals.
Making standard solutions in labs.
Reducing concentration of acids for safe handling.

📝 Practice Questions

Q1.

How much water should be added to 200 mL of 3 M HNO₃ to dilute it to 1 M?

Solution:

Given:
$M_1 = 3$, $V_1 = 200$, $M_2 = 1$, $V_2 = ?$

Use: $$3 \times 200 = 1 \times V_2$$

$$\Rightarrow V_2 = 600 \text{ mL}$$

🧠 So, add 400 mL of water to get 600 mL of 1 M HNO₃.

📌 FAQs

❓What happens to the number of moles during dilution?

They remain the same. Only volume increases and molarity decreases.

❓Why can’t we use this formula for reactions?

Because in a chemical reaction, moles change due to reaction. This formula assumes no reaction.

❓Can this be used for all concentration units?

No. This formula works only for molarity (M).

✅ Conceptual Questions – Molarity and Dilution

🧠 Q1. Why does the molarity of a solution decrease on dilution?

Answer:
Because volume increases while the amount (moles) of solute remains constant, so the concentration (moles per litre) becomes less.

🧠 Q2. If you double the volume of a solution without adding more solute, what happens to the molarity?

Answer:
The molarity becomes half.
Since $M \propto \frac{1}{V}$, doubling volume halves the molarity.

🧠 Q3. Can the dilution equation $M_1V_1 = M_2V_2$ be used for mixtures of different solutions?

Answer:
❌ No. It is valid only for a single solute in a solution being diluted. Not for mixing different solutes.

🧠 Q4. What stays the same during dilution?

Answer:
✅ Number of moles of solute
Only solvent is added, so solute amount stays constant.

🧠 Q5. What are the limitations of the $M_1V_1 = M_2V_2$ formula?

Answer:

Applicable only when no chemical reaction takes place.
Only valid for dilutions, not for reactions or mixtures of different solutions.
Volumes must be in the same unit.

🎯 MCQs on Molarity and Dilution

❓ Q1. What volume of 5 M NaOH should be diluted to prepare 500 mL of 1 M NaOH?

A) 50 mL
B) 100 mL
C) 200 mL
D) 400 mL

✅ Answer: B) 100 mL

Solution: $$M_1V_1 = M_2V_2$$

$$\Rightarrow 5 \times V_1 = 1 \times 500$$

$$\Rightarrow V_1 = 100 \text{ mL}$$

❓ Q2. A solution is diluted by adding 3 times its volume of water. The final molarity will be:

A) 1/2 of original
B) 1/3 of original
C) 1/4 of original
D) Same as original

✅ Answer: C) 1/4 of original

Explanation:
Final volume = original + 3 × original = 4 × original

$$M_2 = \frac{M_1}{4}$$

❓ Q3. Which of the following remains constant during dilution?

A) Molarity
B) Volume
C) Solute mass
D) Solvent amount

✅ Answer: C) Solute mass

Explanation:
Dilution does not affect the amount of solute; only solvent is added.

❓ Q4. What is the molarity of a solution formed by diluting 250 mL of 4 M HCl to 1 L?

A) 0.5 M
B) 1 M
C) 2 M
D) 4 M

✅ Answer: A) 1 M