Molarity Calculator

Formula

Molarity (M) = moles (n) ÷ volume (L)

Molarity equals moles of solute divided by liters of solution. Rearrange to find moles (M×V) or volume (n÷M).

Worked Examples

Example 1: Prepare NaCl Solution

Problem:How much NaCl is needed to prepare 500 mL of 0.9% saline (approximately 0.154 M)?

Solution:Moles needed = M × V moles = 0.154 M × 0.5 L = 0.077 mol Mass = moles × MW mass = 0.077 × 58.44 = 4.5 g Dissolve 4.5g NaCl in water to make 500mL

Result:4.5 g NaCl in 500 mL water

Example 2: Calculate Concentration

Problem:25 grams of glucose dissolved in 500 mL solution. What is the molarity?

Solution:Moles = mass ÷ MW moles = 25 g ÷ 180.16 g/mol = 0.139 mol Molarity = moles ÷ volume M = 0.139 ÷ 0.5 L = 0.278 M

Result:0.278 M (278 mM)

Example 3: Dilution Calculation

Problem:Dilute 2M HCl to make 250 mL of 0.5M solution. How much stock needed?

Solution:C₁V₁ = C₂V₂ 2M × V₁ = 0.5M × 250mL V₁ = (0.5 × 250) ÷ 2 = 62.5 mL Add 62.5 mL of 2M HCl to ~187.5 mL water

Result:62.5 mL of 2M stock

Frequently Asked Questions

What is molarity?

Molarity (M) is the concentration of a solution expressed as moles of solute per liter of solution. A 1M solution contains 1 mole of solute in 1 liter. Formula: M = moles ÷ volume (L).

How do I calculate molarity from mass?

First calculate moles: moles = mass (g) ÷ molar mass (g/mol). Then: Molarity = moles ÷ volume (L). For example, 5.84g NaCl (MW=58.44) in 1L = 0.1M.

What's the difference between molarity and molality?

Molarity (M) = moles/liter of solution. Molality (m) = moles/kg of solvent. Molality doesn't change with temperature since mass doesn't expand like volume.

How do I dilute a solution?

Use C₁V₁ = C₂V₂. If you have 1M solution and need 0.1M: 1M × V₁ = 0.1M × 100mL, so V₁ = 10mL. Add 10mL of 1M stock to 90mL water.

What is a mole?

A mole is 6.022 × 10²³ particles (Avogadro's number). One mole of any substance contains the same number of particles. It bridges the atomic and macroscopic scales.

How do I find molar mass?

Add atomic masses of all atoms in the formula. For H₂O: 2(1.008) + 16.00 = 18.015 g/mol. Use a periodic table for atomic masses.

What is millimolar (mM)?

Millimolar is 1/1000 of molar. 1 mM = 0.001 M. Common in biology where concentrations are often small. 1 M = 1000 mM = 1,000,000 μM.

How do I prepare a specific molarity solution?

Calculate mass needed: mass = Molarity × Volume (L) × Molar mass. For 100mL of 0.5M NaCl: 0.5 × 0.1 × 58.44 = 2.92g. Dissolve in water to final volume.

Why use molarity instead of percent?

Molarity relates directly to the number of molecules, essential for stoichiometry. Percent concentration doesn't account for molecular weight differences between substances.

What is the difference between molarity and molality?

Molarity (M) is moles of solute per liter of solution. Molality (m) is moles of solute per kilogram of solvent. Molarity changes with temperature (because volume changes), while molality does not. Molality is preferred for colligative property calculations like boiling point elevation.

Background & Theory

Molarity is the most common way to express solution concentration in chemistry and biology. It directly relates to the number of molecules, making it ideal for stoichiometric calculations.

Key Formula:
M = n / V

Where:

M = Molarity (mol/L)
n = moles of solute
V = volume of solution (L)

Related Formulas:

n = M × V (find moles)
V = n / M (find volume)
n = mass / MW (find moles from mass)
mass = n × MW (find mass from moles)

Concentration Units:

Unit	Abbreviation	Value
Molar	M	mol/L
Millimolar	mM	0.001 M
Micromolar	μM	0.000001 M
Nanomolar	nM	10⁻⁹ M

Dilution Formula:
C₁V₁ = C₂V₂

Preparing Solutions:

Calculate moles needed: n = M × V
Calculate mass: mass = n × MW
Weigh the solute
Dissolve in less than final volume
Add solvent to reach final volume

Common Concentrations:

Physiological saline: 0.154 M NaCl
Blood glucose (normal): ~5 mM
Stomach acid: ~0.1 M HCl

History

The concept of concentration developed alongside modern chemistry in the 18th-19th centuries. Before standardized measures, chemists used vague terms like "strong" or "weak" solutions. The mole concept, fundamental to molarity, was developed by Wilhelm Ostwald in 1893, though the word "mole" (from German "Molekül") wasn't widely used until later. Avogadro's number was named after Amedeo Avogadro, whose 1811 hypothesis about equal volumes of gases containing equal numbers of molecules laid the groundwork. Molarity became the standard concentration unit in the 20th century as chemistry became more quantitative. It allowed chemists to predict exactly how much product reactions would yield and to reproduce experiments precisely. The International System of Units (SI) technically prefers "amount concentration" in mol/m³, but molarity (mol/L) remains ubiquitous in laboratories worldwide due to its practical convenience.