Dilution Examples in Chemistry

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Dilution.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Chemistry.

Concept Recap

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.

Read the full concept explanation →

How to Use These Examples

Read the first worked example with the solution open so the structure is clear.
Try the practice problems before revealing each solution.
Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Dilution starts by identifying solute, solvent, amount, volume, and the concentration unit.

Common stuck point: 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.

Sense of Study hint: Ask: Am I tracking solute, solvent, total solution, concentration, dissolving, or dilution rather than just naming a mixture?

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

Example 4

medium

A 0.150 M K

_2

_2

_7

solution is diluted from 25.0 mL to 250 mL. Find new concentration and moles of solute.

Example 5

hard

How would you prepare 1.00 L of 0.100 M NaCl from solid NaCl (M = 58.5)?

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy

You dilute

50\,\text{mL}

4.0\,\text{M NaOH}

to a final volume of

200\,\text{mL}

. What is the new concentration?

Example 2

easy

How much

6.0\,\text{M}

hydrochloric acid is needed to prepare

250

mL of

1.5\,\text{M}

HCl?

Example 3

easy

A solution is diluted by adding water. Does its concentration increase or decrease?

Example 4

easy

Using M1V1 = M2V2 with M1 = 2 M, V1 = 1 L, V2 = 4 L, find M2.

Example 5

easy

M1 = 6 M, V1 = 2 L, M2 = 3 M. Find V2.

Example 6

easy

To dilute 100 mL of 1 M solution to 0.5 M, what final volume is needed?

Example 7

easy

In dilution, does the number of moles of solute change?

Example 8

easy

M1 = 4 M, V1 = 250 mL, V2 = 1000 mL. Find M2.

Example 9

easy

If V2 is the total final volume, how much water do you add to dilute 50 mL up to 200 mL?

Example 10

easy

M1 = 10 M, V1 = 5 mL, M2 = 1 M. Find V2.

Example 11

medium

How much of a 12 M stock acid is needed to make 600 mL of 2 M acid?

Example 12

medium

100 mL of 3 M solution is diluted to 500 mL. What is the new concentration?

Example 13

medium

You have 250 mL of 0.8 M solution. How much water must be added to make it 0.2 M?

Example 14

medium

Convert units: M1 = 5 M, V1 = 0.2 L, V2 = 500 mL. Find M2.

Example 15

medium

A 0.5 M solution is concentrated by evaporating water from 800 mL down to 200 mL. Find the new concentration.

Example 16

medium

How many mL of 4 M stock are needed to make 2 L of 0.5 M solution?

Example 17

medium

A solution is diluted from 2 M to 0.25 M. By what factor did the volume increase?

Example 18

medium

A 0.25 M solution of 400 mL is diluted to 1000 mL. Find the new concentration.

Example 19

medium

How much 5 M stock is needed to make 400 mL of 1.25 M solution?

Example 20

challenge

You need 500 mL of 0.3 M HCl but only have 2 M stock. Describe the volumes: stock needed and water added.

Example 21

challenge

Stock is 18 M. After diluting 10 mL of stock to a final 0.6 M, what is the final volume, and how much water was added?

Example 22

challenge

Two dilutions in series: 50 mL of 1.2 M is diluted to 300 mL, then 100 mL of that is diluted to 500 mL. Find the final concentration.

Example 23

easy

Dilute 200 mL of 2 M solution to 800 mL. Find new concentration.

Example 24

easy

_1

= 8 M, V

_1

= 50 mL, V

_2

= 400 mL. Find M

_2

Example 25

easy

How much water do you add to dilute 100 mL up to a final 500 mL?

Example 26

easy

Why is concentrated acid added to water (not water to acid)?

Example 27

easy

Diluting by a factor of 10 means concentration becomes:

Example 28

medium

_1

= 0.75 M, V

_1

= 200 mL, M

_2

= 0.15 M. Find V

_2

Example 29

medium

Mix 100 mL of 1.0 M NaCl with 100 mL of water. Find final concentration. (Assume volumes add.)

Example 30

medium

100 mL of 0.20 M KCl is mixed with 300 mL of 0.40 M KCl. Find the final concentration (additive volumes).

Example 31

medium

How much water must be added to 200 mL of 3.0 M HCl to dilute it to 1.0 M?

Example 32

medium

Express the volume of water to add when diluting V

_1

of stock at M

_1

to final M

_2

Example 33

medium

You have 250 mL of 1.0 M solution. What is the maximum factor you can dilute by if you can only make a 1.0 L final volume?

Example 34

medium

How many mL of 0.50 M NaOH are needed to provide 0.025 mol NaOH?

Example 35

medium

_1

= 1.50 M, V

_1

= 100 mL, M

_2

= 0.250 M. Water to add?

Example 36

hard

A serial dilution: take 10 mL of 2.0 M and dilute to 100 mL. Then take 10 mL of that solution and dilute to 100 mL. Find the final concentration.

Example 37

hard

A student wants 250 mL of 0.40 M HCl from 12.0 M stock. How many mL of stock and how much water?

Example 38

hard

500 mL of 0.20 M H

_2

_4

is concentrated by evaporating water until the volume is 100 mL. Find the final concentration.

Example 39

hard

You have 100 mL of 0.50 M HCl. How much 2.0 M HCl must be added to raise its concentration to 1.0 M? (Assume volumes add.)

Example 40

hard

Three dilutions in series: 25 mL of 0.80 M → 100 mL → take 50 mL → 250 mL → take 20 mL → 200 mL. Final M?

Example 41

challenge

How much pure water must be added to 500 mL of 18.0 M H

_2

_4

to give 3.00 M H

_2

_4

? (Assume volumes simply add.)

Example 42

challenge

To make 1.00 L of 0.200 M HCl, you mix 6.00 M and 1.00 M HCl solutions (volumes add). Find each volume.

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Related Concepts

Concentration Titration

Background Knowledge

These ideas may be useful before you work through the harder examples.

concentration