Concentration to Molarity Converter | w/v % to mol/L

What Is a Concentration to Molarity Converter?

A concentration to molarity converter turns a percentage concentration (weight per volume, written w/v) into molarity, the number of moles of a substance dissolved in one liter of solution. It needs two numbers: the percentage concentration and the molecular weight of the dissolved substance, given in grams per mole.

What Is Molarity?

Molarity is a way to measure how much of a substance is dissolved in a liquid. It is defined as the number of moles of solute per liter of solution.

$\text{Molarity (M)} = \frac{\text{moles of solute}}{\text{volume of solution in liters}}$

The unit is mol/L, often written as M. A "0.5 M" solution of sodium chloride contains 0.5 moles of sodium chloride in every liter of solution.

Chemical reactions happen between particles, not between grams. Molarity tells a chemist how many particles are present in a given volume, which is why it is the standard unit for chemistry calculations. The International Union of Pure and Applied Chemistry (IUPAC) lists molarity as a standard way to express concentration.

Percentage to Molarity Formula

$\text{Molarity (M)} = \frac{\text{Percentage Concentration (w/v)} \times 10}{\text{Molecular Weight (g/mol)}}$

A w/v percentage means grams of solute per 100 mL of solution. Multiplying by 10 converts that to grams per liter, since one liter equals 1,000 mL. Dividing by the molecular weight converts grams to moles.

This formula only works for w/v percentages. A w/w (weight per weight) percentage, common on bottles of concentrated acids, needs the solution's density as well (see below).

How to Calculate Molarity from Percentage Concentration

1. Multiply the percentage concentration by 10. This gives the concentration in grams per liter.
2. Divide that number by the molecular weight of the substance, in grams per mole.
3. The result is the molarity, in mol/L.

Why the Formula Works

A 5% w/v solution has 5 grams of solute in 100 mL of solution.

1. Grams per liter: 5 g × 10 = 50 g/L.
2. Moles per liter: 50 g/L ÷ molecular weight (g/mol) = mol/L.

Worked example

A solution is 5% (w/v) sodium chloride (NaCl). The molecular weight of NaCl is 58.44 g/mol.

$\text{Molarity} = \frac{5 \times 10}{58.44} = 0.856 \text{ mol/L}$

A 5% NaCl solution is about 0.856 M.

More Examples

• Normal saline (0.9% NaCl): (0.9 × 10) ÷ 58.44 = 0.154 M
• 5% glucose solution (C₆H₁₂O₆, 180.16 g/mol): (5 × 10) ÷ 180.16 = 0.278 M
• 10% sodium hydroxide solution (NaOH, 40.00 g/mol): (10 × 10) ÷ 40.00 = 2.50 M

How to Use the Converter

1. Enter the percentage concentration (w/v), a number between 0 and 100.
2. Enter the molecular weight of the substance, in g/mol. It must be greater than 0.
3. The molarity appears automatically, in mol/L.
4. Use the copy button to copy the result.

Results below 10 mol/L are shown to three significant figures. Results of 10 mol/L and above are shown to one decimal place.

Common Molecular Weights

Other Ways to Express Concentration

Molality (m) counts moles of solute per kilogram of solvent, not solution. It does not change with temperature, so scientists use it for freezing point and boiling point calculations.

$\text{Molality (m)} = \frac{\text{moles of solute}}{\text{mass of solvent in kg}}$

Mass percentage (w/w) is grams of solute per 100 grams of solution. It is common on bottles of concentrated acids and bases. Converting it to molarity requires the solution's density:

$\text{Molarity} = \frac{\text{Mass Percentage} \times \text{density (g/mL)} \times 10}{\text{Molecular Weight}}$

Volume percentage (v/v) is used for liquid-in-liquid mixtures, such as ethanol in water. A 70% v/v ethanol solution has 70 mL of ethanol per 100 mL of total solution.

Normality (N) counts gram equivalents per liter. It appears in older titration literature but has mostly been replaced by molarity in modern chemistry.

Accuracy Limitations

The conversion itself is exact for a w/v percentage. A w/v percentage already counts grams of solute in a fixed volume of solution, so the density of the solution never enters the calculation. The errors come from the numbers put into it.

• Using a w/w percentage by mistake: Concentrated acids and bases are labeled by mass (w/w), not by volume. Concentrated hydrochloric acid is about 37% w/w with a density near 1.19 g/mL, which is about 44% w/v, or roughly 12.1 mol/L. Entering 37 instead of 44 understates the molarity by about a sixth. Convert with the density formula above first.
• Very dense solutions: A w/v percentage can pass 100 when a solution is much denser than water. Concentrated sulfuric acid, about 96% w/w at a density of 1.84 g/mL, is roughly 177% w/v, or about 18 mol/L. This converter accepts percentages from 0 to 100 only, so figures above 100 have to be worked out by hand.
• Temperature: Solution volume changes with temperature, so molarity shifts slightly as temperature changes. Molality does not, because it is based on mass rather than volume.
• Hydrated compounds: Some compounds absorb water into their crystal structure and this changes their molecular weight. Anhydrous copper sulfate (CuSO₄) has a molecular weight of 159.61 g/mol. Copper sulfate pentahydrate (CuSO₄·5H₂O) has a molecular weight of 249.68 g/mol, more than 50% higher. Using the wrong value gives a molarity that is far off.
• Reagent purity: Commercial chemicals are rarely 100% pure. A reagent labeled 98% pure contains 2% of other material by weight, which slightly lowers the true molarity of a solution made from it.

Frequently asked questions

What is the difference between molarity and molality?

Molarity is moles of solute per liter of solution. Molality is moles of solute per kilogram of solvent. Molarity changes slightly with temperature because liquid volume changes with temperature. Molality stays constant because mass does not change with temperature.

Why is molarity used more often than percentage concentration?

Chemical reactions occur between molecules, and molarity states directly how many moles of a substance are present in a given volume. Percentage concentration states mass, which must be converted to moles before it is useful for reaction calculations.

How do I convert molarity back to percentage concentration?

Reverse the formula:

$\text{Percentage Concentration (w/v)} = \frac{\text{Molarity} \times \text{Molecular Weight}}{10}$

A 0.5 M sodium chloride solution equals (0.5 × 58.44) ÷ 10 = 2.92% w/v.

Does this formula work for weight/weight (w/w) percentages?

No. The formula on this page is for w/v percentages only. Converting a w/w percentage to molarity requires the density of the solution, using the formula given in the "Other Ways to Express Concentration" section above.

Does solution density affect the result?

No. A w/v percentage already states grams of solute per 100 mL of solution, so the volume is fixed by the definition and density drops out. Density is needed only to turn a w/w percentage, which states grams per 100 grams of solution, into a w/v percentage or a molarity.

How do I prepare a solution of a specific molarity?

Calculate the mass needed with Mass (g) = Molarity (mol/L) × Volume (L) × Molecular Weight (g/mol). Weigh out that mass, dissolve it in less than the final volume of solvent, transfer it to a volumetric flask, then add solvent up to the mark. Adding solvent to the full volume before the solute is dissolved is a common mistake, since it can make the final volume too large.

References

1. IUPAC Gold Book – Amount Concentration
2. NIST Chemistry WebBook
3. Harris, D. C. (2015). Quantitative Chemical Analysis (9th ed.). W. H. Freeman and Company.
4. United States Pharmacopeia (USP)