Solution Chemistry Calculator: Molarity, Dilution and pH

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dilution calculator c1v1 = c2v2

Dilution calculator C1V1 = C2V2 and serial dilution

Diluting does not change the amount of solute, only the volume it sits in. That gives C1V1 = C2V2: fill in three values and the fourth follows, with the dilution factor and the solvent to add.

Solute conservation, final volume and serial dilution

Before and after diluting there is the same number of moles, n = C1 × V1 = C2 × V2. Concentration units cancel as long as C1 and C2 share one (mol/L, g/L, % or ppm), and the same goes for V1 and V2. To make 500 mL of 1 mol/L HCl from 12.08 mol/L: V1 = 1 × 500 ÷ 12.08 = 41.4 mL. For 250 mL of 0.5 mol/L NaOH from 2 mol/L: V1 = 0.5 × 250 ÷ 2 = 62.5 mL. For 1 L of 1 mol/L H2SO4 from 18.39 mol/L: V1 = 54.4 mL.
V2 is the final volume of the solution, not the solvent volume. Taking 41.4 mL of acid and adding 500 mL of water would give 541 mL at 0.92 mol/L. The right way is to put the concentrate in the 500 mL flask and fill to the mark. The solvent to add, V2 − V1 = 458.6 mL, only holds as an estimate when volumes add, which is not true of strong sulfuric acid, which contracts on mixing. The tool also warns when the result would require concentrating (C2 above C1 or V2 below V1).
In serial dilution the same step repeats. With a factor of 10 per tube, moving 1 mL into 9 mL of diluent (10 mL total), a 1 mol/L solution becomes 0.1, 0.01, 0.001 and so on, and tube 6 reaches 1 × 10⁻⁶ mol/L, a total dilution of 1,000,000. The 1:10 notation usually means 1 part plus 9 of diluent (factor 10), but some protocols mean 1 plus 10 (factor 11); read the protocol. Enter a target concentration and the table marks the tube that reaches it.

Dilutions solved

Concentrated HCl to 1 mol/L

Input: C1 = 12.08; C2 = 1; V2 = 500 mL
Expected output: V1 = 41.4 mL

Top up with water to 500 mL.

NaOH 2 to 0.5 mol/L

Input: C1 = 2; C2 = 0.5; V2 = 250 mL
Expected output: V1 = 62.5 mL

Dilution factor 4.

98 % H2SO4 to 1 mol/L

Input: C1 = 18.39; C2 = 1; V2 = 1000 mL
Expected output: V1 = 54.4 mL

Add the acid to the water.

100 mg/L stock to 5 mg/L

Input: C1 = 100; C2 = 5; V2 = 250 mL
Expected output: V1 = 12.5 mL

Factor 20.

Concentration after diluting

Input: C1 = 2; V1 = 25 mL; V2 = 250 mL
Expected output: C2 = 0.2

25 mL at 2 mol/L topped up to 250 mL.

1:10 serial, 6 tubes, from 1 mol/L

Input: C0 = 1; fator 10; 6 etapas
Expected output: 1e-6 mol/L

Each tube: 1 mL + 9 mL of diluent.

Full tool FAQ

How do I calculate the molarity of a solution?

Molarity is moles of solute per liter of solution: c = m ÷ (M × V). For 5.844 g of NaCl (58.44 g/mol) in 1 L of solution: 5.844 ÷ 58.44 = 0.1000 mol, so 0.1000 mol/L. V is the final solution volume, measured to the mark of the flask, not the volume of water used.

What is the difference between molarity and molality?

How do I convert % w/w to mol/L?

How much should I weigh to prepare a solution, with hydrate and purity?

How do I use C1V1 = C2V2 and what does a 1:10 dilution mean?

How do I calculate the pH of a weak acid and when does the 5 % approximation hold?

Why is the pH of 1e-8 mol/L HCl not 8?

How does a buffer work and when does Henderson-Hasselbalch fail?

How do I read a titration curve and choose the indicator?

What are the limits of the calculations and what should the tool not be used for?

Frequently asked questions

Can I use C1V1 = C2V2 with percent and ppm?

Yes, as long as C1 and C2 use the same unit and so do V1 and V2. The relation only requires the amount of solute to be conserved.

Why do volumes not always add up to the final volume?

Mixtures like ethanol and water or sulfuric acid and water contract because the molecules pack better. That is why you fill to the mark of the flask instead of adding volumes.

What is wrong with diluting 1 mL into 9 mL and calling it 1:9?

It depends on the protocol. 1 mL plus 9 mL is factor 10. Calling it 1:9 is valid if the ratio is between parts (1 part solution to 9 of diluent), but the factor is 10. The tool shows both.

Next steps

The same solution in every unit
Unit	Value
Molarity (mol/L)	0.100 mol/L
Millimolarity (mmol/L)	100 mmol/L
Normality (eq/L)	0.100 eq/L
Molality (mol/kg)	0.101 mol/kg
Mole fraction (x)	0.00181
Mass concentration (g/L)	5.84 g/L
Milligrams per liter (mg/L)	5840 mg/L
% mass/volume (g/100 mL)	0.584 % m/v
% volume/volume	needs solute density
% mass/mass	0.584 % m/m
Mass fraction (titer)	0.00584
Parts per million (ppm, mg/kg)	5840 ppm
Parts per billion (ppb, µg/kg)	5.84 × 10⁶ ppb

The same solution in every unit

Unit

Value

Molarity (mol/L)

0.100 mol/L

Millimolarity (mmol/L)

100 mmol/L

Normality (eq/L)

0.100 eq/L

Molality (mol/kg)

0.101 mol/kg

Mole fraction (x)

0.00181

Mass concentration (g/L)

5.84 g/L

Milligrams per liter (mg/L)

5840 mg/L

% mass/volume (g/100 mL)

0.584 % m/v

% volume/volume

needs solute density

% mass/mass

0.584 % m/m

Mass fraction (titer)

0.00584

Parts per million (ppm, mg/kg)

5840 ppm

Parts per billion (ppb, µg/kg)

5.84 × 10⁶ ppb

Solute conservation, final volume and serial dilution

Before and after diluting there is the same number of moles, n = C1 × V1 = C2 × V2. Concentration units cancel as long as C1 and C2 share one (mol/L, g/L, % or ppm), and the same goes for V1 and V2. To make 500 mL of 1 mol/L HCl from 12.08 mol/L: V1 = 1 × 500 ÷ 12.08 = 41.4 mL. For 250 mL of 0.5 mol/L NaOH from 2 mol/L: V1 = 0.5 × 250 ÷ 2 = 62.5 mL. For 1 L of 1 mol/L H2SO4 from 18.39 mol/L: V1 = 54.4 mL.

V2 is the final volume of the solution, not the solvent volume. Taking 41.4 mL of acid and adding 500 mL of water would give 541 mL at 0.92 mol/L. The right way is to put the concentrate in the 500 mL flask and fill to the mark. The solvent to add, V2 − V1 = 458.6 mL, only holds as an estimate when volumes add, which is not true of strong sulfuric acid, which contracts on mixing. The tool also warns when the result would require concentrating (C2 above C1 or V2 below V1).

In serial dilution the same step repeats. With a factor of 10 per tube, moving 1 mL into 9 mL of diluent (10 mL total), a 1 mol/L solution becomes 0.1, 0.01, 0.001 and so on, and tube 6 reaches 1 × 10⁻⁶ mol/L, a total dilution of 1,000,000. The 1:10 notation usually means 1 part plus 9 of diluent (factor 10), but some protocols mean 1 plus 10 (factor 11); read the protocol. Enter a target concentration and the table marks the tube that reaches it.

Dilutions solved

Concentrated HCl to 1 mol/L

Input: C1 = 12.08; C2 = 1; V2 = 500 mL
Expected output: V1 = 41.4 mL

Top up with water to 500 mL.

NaOH 2 to 0.5 mol/L

Input: C1 = 2; C2 = 0.5; V2 = 250 mL
Expected output: V1 = 62.5 mL

Dilution factor 4.

98 % H2SO4 to 1 mol/L

Input: C1 = 18.39; C2 = 1; V2 = 1000 mL
Expected output: V1 = 54.4 mL

Add the acid to the water.

100 mg/L stock to 5 mg/L

Input: C1 = 100; C2 = 5; V2 = 250 mL
Expected output: V1 = 12.5 mL

Factor 20.

Concentration after diluting

Input: C1 = 2; V1 = 25 mL; V2 = 250 mL
Expected output: C2 = 0.2

25 mL at 2 mol/L topped up to 250 mL.

1:10 serial, 6 tubes, from 1 mol/L

Input: C0 = 1; fator 10; 6 etapas
Expected output: 1e-6 mol/L

Each tube: 1 mL + 9 mL of diluent.

Full tool FAQ

How do I calculate the molarity of a solution?

What is the difference between molarity and molality?

How do I convert % w/w to mol/L?

How much should I weigh to prepare a solution, with hydrate and purity?

How do I use C1V1 = C2V2 and what does a 1:10 dilution mean?

How do I calculate the pH of a weak acid and when does the 5 % approximation hold?

Why is the pH of 1e-8 mol/L HCl not 8?

How does a buffer work and when does Henderson-Hasselbalch fail?

How do I read a titration curve and choose the indicator?

What are the limits of the calculations and what should the tool not be used for?

Frequently asked questions

Can I use C1V1 = C2V2 with percent and ppm?

Yes, as long as C1 and C2 use the same unit and so do V1 and V2. The relation only requires the amount of solute to be conserved.

Why do volumes not always add up to the final volume?

Mixtures like ethanol and water or sulfuric acid and water contract because the molecules pack better. That is why you fill to the mark of the flask instead of adding volumes.

What is wrong with diluting 1 mL into 9 mL and calling it 1:9?

It depends on the protocol. 1 mL plus 9 mL is factor 10. Calling it 1:9 is valid if the ratio is between parts (1 part solution to 9 of diluent), but the factor is 10. The tool shows both.

The same solution in every unit
Unit	Value
Molarity (mol/L)	0.100 mol/L
Millimolarity (mmol/L)	100 mmol/L
Normality (eq/L)	0.100 eq/L
Molality (mol/kg)	0.101 mol/kg
Mole fraction (x)	0.00181
Mass concentration (g/L)	5.84 g/L
Milligrams per liter (mg/L)	5840 mg/L
% mass/volume (g/100 mL)	0.584 % m/v
% volume/volume	needs solute density
% mass/mass	0.584 % m/m
Mass fraction (titer)	0.00584
Parts per million (ppm, mg/kg)	5840 ppm
Parts per billion (ppb, µg/kg)	5.84 × 10⁶ ppb

The same solution in every unit

Unit

Value

Molarity (mol/L)

0.100 mol/L

Millimolarity (mmol/L)

100 mmol/L

Normality (eq/L)

0.100 eq/L

Molality (mol/kg)

0.101 mol/kg

Mole fraction (x)

0.00181

Mass concentration (g/L)

5.84 g/L

Milligrams per liter (mg/L)

5840 mg/L

% mass/volume (g/100 mL)

0.584 % m/v

% volume/volume

needs solute density

% mass/mass

0.584 % m/m

Mass fraction (titer)

0.00584

Parts per million (ppm, mg/kg)

5840 ppm

Parts per billion (ppb, µg/kg)

5.84 × 10⁶ ppb