Concentration Examples in Chemistry

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

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 quantity of solute dissolved per unit volume of solution, most commonly expressed as molarity ( $M$ ) in units of moles per liter (mol/L).

How 'strong' a solution is—more solute in the same volume = more concentrated.

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: Concentration starts by identifying solute, solvent, amount, volume, and the concentration unit.

Common stuck point: Students often know a formula related to concentration 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

Calculate the molarity of a solution made by dissolving

5.85

g of NaCl in water to make

500\,\text{mL}

of solution. (NaCl molar mass =

58.44\,\text{g/mol}

)

Answer

0.200\,\text{M}

First step

Moles of NaCl

= \frac{5.85}{58.44} = 0.100\,\text{mol}

Full solution

2
Volume in liters $= 500\,\text{mL} = 0.500\,\text{L}$ .
3
Molarity $= \frac{n}{V} = \frac{0.100}{0.500} = 0.200\,\text{M}$ .

Molarity (

M

) is the most common concentration unit in chemistry. It measures moles of solute per liter of solution, not per liter of solvent.

Example 2

medium

How many grams of KOH are needed to prepare

250\,\text{mL}

of a

0.40\,\text{M}

solution? (KOH =

56.11\,\text{g/mol}

)

Example 3

medium

Calculate the molarity of a solution made by dissolving 5.85 g of NaCl (molar mass 58.5 g/mol) in enough water to make 500 mL.

Example 4

easy

Compute the molarity when

0.040

mol of

\text{AgNO}_3

is dissolved in enough water to make

250\,\text{mL}

of solution.

Example 5

medium

How many grams of

\text{KCl}

(molar mass

74.55\,\text{g/mol}

) are needed to prepare

500\,\text{mL}

of a

0.20\,\text{M}

solution?

Example 6

medium

What volume of

16\,\text{M}

nitric acid stock is needed to make

250\,\text{mL}

0.80\,\text{M}

HNO

_3

Example 7

medium

A titration uses

30.0\,\text{mL}

0.250\,\text{M}

NaOH to neutralize HCl. How many moles of HCl reacted?

Example 8

hard

Calculate the molarity when

4.00\,\text{g}

\text{NaOH}

(molar mass

40.0\,\text{g/mol}

) is dissolved to make

250\,\text{mL}

of solution.

Example 9

hard

What mass of glucose (

\text{C}_6\text{H}_{12}\text{O}_6

, molar mass

180\,\text{g/mol}

) must be dissolved to prepare

2.0\,\text{L}

of a

0.25\,\text{M}

solution?

Practice Problems

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

Example 1

easy

What is the molarity of a solution containing

0.50

mol of solute in

2.0

Example 2

easy

What is the molarity of a solution made by dissolving

0.750

mol of

\text{KNO}_3

in enough water to make

2.50

L of solution?

Example 3

easy

What is the molarity of 2 mol of solute in 1 L of solution?

Example 4

easy

Molarity of 0.5 mol solute in 2 L solution?

Example 5

easy

How many moles of solute are in 2 L of a 3 M solution?

Example 6

easy

Convert 250 mL to liters.

Example 7

easy

Molarity of 1 mol solute in 500 mL solution?

Example 8

easy

Does molarity use the volume of solvent or of solution?

Example 9

easy

How many moles in 0.5 L of 0.2 M solution?

Example 10

easy

What volume (L) of 2 M solution contains 4 mol of solute?

Example 11

medium

What mass of NaOH (

M=40

) is needed for 0.5 L of 2 M solution?

Example 12

medium

Molarity of 117 g NaCl (

M=58.5

) dissolved to 2 L solution?

Example 13

medium

Dilution: 100 mL of 6 M is diluted to 300 mL. New molarity?

Example 14

medium

How much water to add to 100 mL of 6 M to make 2 M?

Example 15

medium

Molarity of 0.25 mol solute in 250 mL solution?

Example 16

medium

How many grams of glucose (

M=180

) in 0.5 L of 0.1 M solution?

Example 17

medium

Mixing 1 L of 2 M with 1 L of 4 M (same solute). Final molarity?

Example 18

medium

A titration uses 25 mL of 0.1 M HCl. How many moles of HCl is that?

Example 19

medium

Dilution: what volume of 12 M stock makes 600 mL of 2 M solution?

Example 20

challenge

How many grams of

CaCl_2

(

M=111

) are in 250 mL of a 0.4 M solution?

Example 21

challenge

Mixing 200 mL of 0.5 M NaCl with 300 mL of 1 M NaCl. Final molarity?

Example 22

challenge

2NaOH + H_2SO_4 \rightarrow Na_2SO_4 + 2H_2O

, what volume of 0.5 M

H_2SO_4

neutralizes 0.02 mol NaOH?

Example 23

easy

A solution contains

0.80

mol of

\text{KBr}

4.0\,\text{L}

of solution. What is its molarity?

Example 24

easy

How many moles of solute are in

400\,\text{mL}

of a

0.50\,\text{M}

solution?

Example 25

easy

What is the molarity of a solution that contains

0.10

mol of HCl in

200\,\text{mL}

of solution?

Example 26

easy

1.5\,\text{L}

solution contains

3.0

mol of

\text{NaNO}_3

. What is its molarity?

Example 27

medium

What volume (in mL) of

2.0\,\text{M}

NaOH provides

0.040

mol of NaOH?

Example 28

medium

Dissolving

9.8\,\text{g}

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

(molar mass

98\,\text{g/mol}

) to make

200\,\text{mL}

of solution gives what molarity?

Example 29

medium

Dilute

50\,\text{mL}

4.0\,\text{M}

HCl to a final volume of

500\,\text{mL}

. What is the new molarity?

Example 30

medium

Mix

100\,\text{mL}

0.20\,\text{M}

KCl with

400\,\text{mL}

of water. What is the new molarity?

Example 31

medium

Mix

300\,\text{mL}

0.40\,\text{M}

NaCl with

200\,\text{mL}

0.90\,\text{M}

NaCl. Find the final molarity.

Example 32

medium

A bottle reads

0.150\,\text{M}

\text{Ca(NO}_3)_2

. How many moles of nitrate ion are in

200\,\text{mL}

of this solution?

Example 33

medium

0.500\,\text{L}

solution is

0.300\,\text{M}

\text{Na}_2\text{SO}_4

. Find the molarity of

\text{Na}^+

Example 34

hard

How many mL of

6.0\,\text{M}

HCl are needed to provide

0.030

mol of HCl?

Example 35

hard

In the reaction

2\text{HCl} + \text{Ca(OH)}_2 \rightarrow \text{CaCl}_2 + 2\text{H}_2\text{O}

, what volume of

0.200\,\text{M}

HCl neutralizes

25.0\,\text{mL}

0.150\,\text{M}

\text{Ca(OH)}_2

Example 36

hard

A student mixes

250\,\text{mL}

0.100\,\text{M}

AgNO

_3

with

250\,\text{mL}

0.100\,\text{M}

NaCl. If AgCl precipitates completely, what is

[\text{NO}_3^-]

in the final solution?

Example 37

challenge

0.500\,\text{L}

sample of

0.200\,\text{M}

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

is fully neutralized by

\text{NaOH}

via

\text{H}_2\text{SO}_4 + 2\text{NaOH} \rightarrow \text{Na}_2\text{SO}_4 + 2\text{H}_2\text{O}

. What mass of NaOH (

40.0\,\text{g/mol}

) is consumed?

Example 38

challenge

200\,\text{mL}

sample of

0.50\,\text{M}

NaCl is evaporated to

50\,\text{mL}

. Assuming no NaCl is lost, find the new molarity.

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Related Concepts

Mole Solution Dilution Titration

Background Knowledge

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

molesolution