Dilution Formula

Dilution is the process of decreasing the concentration of a solution by adding more solvent while keeping the total amount of solute constant.

The Formula

M_1V_1 = M_2V_2

(molarity × volume before = molarity × volume after)

When to use: Watering down a drink—same amount of flavor, more liquid, weaker taste.

Quick Example

Dilute 100 mL of 2M HCl with water to 200 mL total → resulting concentration is 1M.

Notation

M_1

and

M_2

are the initial and final molarities (mol/L),

V_1

and

V_2

are the initial and final volumes. The product

MV

equals total moles of solute.

What This Formula Means

The process of decreasing the concentration of a solution by adding more solvent while keeping the total amount of solute constant.

Watering down a drink—same amount of flavor, more liquid, weaker taste.

Formal View

Dilution conserves the moles of solute:

n_1 = n_2

, therefore

c_1V_1 = c_2V_2

, where

c

is molar concentration and

V

is volume. This assumes ideal mixing with no volume change upon mixing (valid for dilute solutions).

Worked Examples

Example 1

easy

How much water must be added to

100\,\text{mL}

6.0\,\text{M HCl}

to make a

1.0\,\text{M}

solution?

Answer

500\,\text{mL of water}

First step

Use

M_1V_1 = M_2V_2

6.0 \times 100 = 1.0 \times V_2

Full solution

2
$V_2 = 600\,\text{mL}$ .
3
Water to add $= 600 - 100 = 500\,\text{mL}$ .

Dilution does not change the number of moles of solute — it only increases the total volume. The dilution equation

M_1V_1 = M_2V_2

reflects this conservation.

Example 2

medium

A stock solution of

\text{H}_2\text{SO}_4

12.0\,\text{M}

. What volume is needed to prepare

500\,\text{mL}

0.60\,\text{M}

solution?

Example 3

medium

How many mL of 16 M HNO

_3

are needed to prepare 2.0 L of 0.50 M HNO

_3

Common Mistakes

Using the volume of solvent added instead of the total final volume — $V_2$ is the total volume of the final solution, not just the amount of solvent added - Fix this by naming the substances or sample, checking "Am I tracking solute, solvent, total solution, concentration, dissolving, or dilution rather than just naming a mixture?", and attaching units, formulas, states, or evidence to the final statement. - Fix this by naming the substances or sample, checking "Am I tracking solute, solvent, total solution, concentration, dissolving, or dilution rather than just naming a mixture?", and attaching units, formulas, states, or evidence to the final statement.
Forgetting to match units — both volumes must be in the same unit (both mL or both L) for the equation to work - Fix this by naming the substances or sample, checking "Am I tracking solute, solvent, total solution, concentration, dissolving, or dilution rather than just naming a mixture?", and attaching units, formulas, states, or evidence to the final statement. - Fix this by naming the substances or sample, checking "Am I tracking solute, solvent, total solution, concentration, dissolving, or dilution rather than just naming a mixture?", and attaching units, formulas, states, or evidence to the final statement.
Adding water to concentrated acid instead of acid to water — this is a safety hazard because the exothermic mixing can cause violent boiling and splashing - Fix this by naming the substances or sample, checking "Am I tracking solute, solvent, total solution, concentration, dissolving, or dilution rather than just naming a mixture?", and attaching units, formulas, states, or evidence to the final statement. - Fix this by naming the substances or sample, checking "Am I tracking solute, solvent, total solution, concentration, dissolving, or dilution rather than just naming a mixture?", and attaching units, formulas, states, or evidence to the final statement.
Using dilution from a keyword alone - Signal words like solution, solute, solvent only point to a possible model; the substances and evidence must match too. - Fix this by naming the substances or sample, checking "Am I tracking solute, solvent, total solution, concentration, dissolving, or dilution rather than just naming a mixture?", and attaching units, formulas, states, or evidence to the final statement.

Why This Formula Matters

Dilution connects particle thinking to lab preparation. It is essential for titrations, dilution, solubility, electrolytes, and any reaction that happens in solution.

Frequently Asked Questions

What is the Dilution formula?

The process of decreasing the concentration of a solution by adding more solvent while keeping the total amount of solute constant.

How do you use the Dilution formula?

Watering down a drink—same amount of flavor, more liquid, weaker taste.

What do the symbols mean in the Dilution formula?

$M_1$ and $M_2$ are the initial and final molarities (mol/L), $V_1$ and $V_2$ are the initial and final volumes. The product $MV$ equals total moles of solute.

Why is the Dilution formula important in Chemistry?

Dilution connects particle thinking to lab preparation. It is essential for titrations, dilution, solubility, electrolytes, and any reaction that happens in solution.

What do students get wrong about Dilution?

Students often know a formula related to dilution but skip the recognition step: Am I tracking solute, solvent, total solution, concentration, dissolving, or dilution rather than just naming a mixture? That leads to a correct-looking substitution attached to the wrong chemical model.

What should I learn before the Dilution formula?

Before studying the Dilution formula, you should understand: concentration.

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Related Concepts

Concentration Titration

Related Formulas

Concentration Formula Titration Formula