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Work out concentration, moles, volume or exactly how many grams to weigh out — type the formula and the molar mass fills itself in. Includes dilution using C₁V₁ = C₂V₂.
Dilution: C₁V₁ = C₂V₂
| Property | Value |
|---|
Molarity is a count of particles per unit volume, dressed up in units you can measure.
In practice the question is almost always the last one: how many grams do I put on the balance? The calculator above defaults to answering that, and will fill in the molar mass if you type the formula.
| Target | Volume | Working | Weigh out |
|---|---|---|---|
| 0.1 M NaCl | 500 mL | 0.05 mol × 58.44 | 2.92 g |
| 1.0 M HCl | 250 mL | 0.25 mol × 36.46 | 9.11 g |
| 0.5 M NaOH | 1 L | 0.5 mol × 40.00 | 20.00 g |
| 0.25 M glucose | 1 L | 0.25 mol × 180.16 | 45.04 g |
| 0.02 M KMnO₄ | 500 mL | 0.01 mol × 158.03 | 1.58 g |
This is the technique point that separates a correct calculation from a correct solution, and it is left out of most molarity guides.
This is why molarity is defined per litre of solution rather than per litre of solvent. The denominator is the finished volume, which you can only reach by topping up.
| Step | Why |
|---|---|
| Weigh the solute accurately | The mass sets the moles; everything follows from it |
| Dissolve in part of the final volume | Leaves room for the volume the solute itself occupies |
| Transfer to a volumetric flask | Flasks are calibrated to a single accurate volume |
| Make up to the mark | The graduation is the defined final volume |
| Invert to mix thoroughly | Concentration gradients settle out otherwise |
Diluting changes the volume, not the number of moles — which is the whole reason the formula works.
Note what the answer is: a final volume, not an amount to add. Take the 50 mL of stock and make it up to 200 mL. Working out the difference and measuring that separately is less accurate, because the solute's own volume is unaccounted for.
Three concentration measures that sound alike and are not.
| Molarity (M) | Molality (m) | Normality (N) | |
|---|---|---|---|
| Per | Litre of solution | Kilogram of solvent | Litre of solution |
| Counts | Moles of solute | Moles of solute | Reactive equivalents |
| Units | mol/L | mol/kg | eq/L |
| Temperature | Changes with it | Independent of it | Changes with it |
| Used for | Most laboratory work | Freezing and boiling point work | Titrations, acid–base |
Normality accounts for how many reactive units each molecule supplies. Sulfuric acid donates two protons, so 1 M H₂SO₄ is 2 N for acid–base purposes. It is still common in titration work, though IUPAC discourages it in favour of molarity with an explicit stoichiometric ratio.
| Unit | Equivalent | Where you meet it |
|---|---|---|
| 1 M | 1 mol/L = 1000 mM | Stock solutions, titrants |
| 1 mM | 0.001 M = 1000 µM | Buffers, biological media |
| 1 µM | 0.000001 M | Trace analysis, enzyme work |
| 1 nM | 0.000000001 M | Receptor binding, ultra-trace |
| 1 L | 1000 mL = 1000 cm³ | Volumetric flasks |
| 1 mL | 0.001 L = 1 cm³ | Pipettes, syringes |
| 1 µL | 0.001 mL | Micropipettes |
| 1 mol/L | 1 mmol/mL | The same number, smaller scale |
If your reagent bottle names a hydrate, the water is part of what you weigh — and using the anhydrous molar mass gives a solution well under strength.
| Reagent | Molar mass to use | For 250 mL of 0.5 M |
|---|---|---|
| CuSO₄ (anhydrous) | 159.61 | 19.95 g |
| CuSO₄·5H₂O | 249.68 | 31.21 g |
| Na₂CO₃ (anhydrous) | 105.99 | 13.25 g |
| Na₂CO₃·10H₂O | 286.14 | 35.77 g |
Weighing 19.95 g of the pentahydrate when you needed 31.21 g gives roughly 64% of the intended concentration. The formula field above accepts hydrate notation directly — type CuSO4·5H2O and the correct molar mass appears. Our molecular weight calculator covers the parsing in more detail.
A correct calculation still gives a wrong solution if the measurement is loose. Which piece of glassware you reach for decides how good the answer can be.
| Equipment | Use it for | Typical accuracy |
|---|---|---|
| Volumetric flask | Preparing a solution to an exact final volume | ±0.1% or better |
| Volumetric pipette | Transferring one accurate fixed volume | ±0.1–0.2% |
| Burette | Delivering a variable measured volume in titration | ±0.05 mL |
| Graduated pipette | Moderately accurate variable transfers | ±1% |
| Measuring cylinder | Approximate volumes | ±1–5% |
| Beaker or conical flask | Dissolving and mixing — not measuring | ±5–10% |
| Practice | Why it matters |
|---|---|
| Weigh on a balance suited to the amount | An analytical balance reads to 0.0001 g; weighing 1.58 g of KMnO₄ on a 0.1 g balance loses two significant figures |
| Read the meniscus at eye level | Looking down or up shifts the apparent level — parallax can move a reading by more than the flask's tolerance |
| Dissolve fully before making up | Undissolved solute is not in solution, so the concentration is below target until it is |
| Work at room temperature | Glassware is calibrated at about 20 °C, and warm solutions occupy more volume |
| Invert a stoppered flask several times | The last of the solvent sits on top otherwise, leaving a concentration gradient |
| Standardise anything hygroscopic | Sodium hydroxide absorbs water and carbon dioxide from the air, so its weighed mass is not reliable |
| Field | Typical use |
|---|---|
| Teaching labs | Preparing standard solutions for titration and analysis |
| Analytical chemistry | Calibration standards, where concentration accuracy sets the result |
| Pharmacy and compounding | Dose calculations, often expressed in mg/mL rather than molarity |
| Environmental testing | Contaminant levels, usually in µM or mg/L for trace amounts |
| Biology and molecular work | Buffers, media and reagents — commonly mM and µM |
| Industrial process control | Feed concentrations and reaction stoichiometry |
What is molarity?
The number of moles of solute per litre of solution, written mol/L or M. A 1 M solution contains one mole of solute in every litre of finished solution — note that this is per litre of solution, not per litre of solvent added.
How do you calculate molarity?
Divide the moles of solute by the volume of solution in litres. If you have 0.05 mol in 500 mL, that is 0.05 ÷ 0.5 = 0.1 M. Starting from a mass instead, divide the mass by the molar mass first to get moles.
How do I calculate molarity from grams?
Divide the mass by the molar mass to get moles, then divide by the volume in litres. For 2.92 g of sodium chloride in 500 mL: 2.92 ÷ 58.44 = 0.05 mol, and 0.05 ÷ 0.5 = 0.1 M. Enter the formula above and the molar mass is filled in for you.
How many grams do I need for a 0.1 M solution?
Multiply the volume in litres by the molarity to get moles, then multiply by the molar mass. For 500 mL of 0.1 M sodium chloride: 0.5 × 0.1 × 58.44 = 2.92 g. Check whether your reagent is a hydrate before weighing.
What is the unit of molarity?
Moles per litre, written mol/L and commonly abbreviated to M. Lower concentrations use millimolar (mM, one thousandth) and micromolar (µM, one millionth), which are standard in biological and environmental work.
What is M₁V₁ = M₂V₂?
The dilution equation. Diluting does not change how many moles of solute you have, only the volume they occupy, so concentration times volume stays constant. Rearranged, V₂ = C₁V₁ ÷ C₂ gives the final volume you need to reach.
How do you calculate a dilution?
Multiply the stock concentration by the volume you are using, then divide by the target concentration. Taking 50 mL of 2 M stock to 0.5 M: (2 × 50) ÷ 0.5 = 200 mL final volume, so make the 50 mL up to 200 mL rather than adding 200 mL.
How do you prepare a molar solution?
Weigh the calculated mass, dissolve it in roughly two-thirds of the final volume, transfer to a volumetric flask, make up to the mark and invert to mix. Dissolving in the full volume first gives a solution that is too dilute, because the solute adds volume of its own.
Why not just add the solute to a litre of water?
Because the solute occupies volume too, so a litre of water plus the solute comes to more than a litre and the concentration falls below target. Molarity is defined per litre of solution, which you reach by topping up to a calibrated mark.
What is the difference between molarity and molality?
Molarity is moles per litre of solution; molality is moles per kilogram of solvent. Because liquids expand when warmed, molarity changes with temperature while molality does not — which is why molality is used for freezing and boiling point calculations.
What is normality?
Concentration expressed in reactive equivalents per litre rather than moles per litre. Sulfuric acid donates two protons, so 1 M H₂SO₄ is 2 N for acid–base purposes. It remains common in titration work, though molarity with an explicit stoichiometric ratio is now preferred.
Does molarity change with temperature?
Yes, slightly. The solution expands as it warms, so the same moles occupy more volume and the molarity falls. The effect is small for most laboratory work but matters for precise measurement, and it is the reason molality exists as an alternative.
What is a standard solution?
A solution whose concentration is known accurately, used to determine unknown concentrations by titration. Primary standards are prepared by weighing a stable, pure, non-hygroscopic solid directly. Solutions that absorb water or degrade, such as sodium hydroxide, must be standardised against a primary standard instead.
Should I use the hydrate molar mass?
Yes, if the reagent you are weighing is a hydrate. Copper sulfate pentahydrate is 249.68 g/mol against 159.61 for the anhydrous salt, so using the wrong figure gives about 64% of the intended concentration. Check the bottle label.
What is the difference between molarity and concentration?
Concentration is the general idea of how much solute sits in a given amount of solution; molarity is one specific way of expressing it, in moles per litre. Other measures include g/L, percentage by mass, parts per million and molality, all describing the same underlying property differently.
How do I convert mg/mL to molarity?
Multiply mg/mL by 1000 to get mg/L, divide by the molar mass to get millimoles per litre, then divide by 1000 for mol/L. More simply, molarity equals grams per litre divided by molar mass — so 5.844 g/L of sodium chloride is 5.844 ÷ 58.44 = 0.1 M.
What glassware should I use to prepare a solution?
A volumetric flask, which is calibrated to one accurate volume, typically within 0.1%. Dissolve the solute in a beaker or directly in the flask with part of the solvent, then make up to the mark. Beaker graduations are indicative only at roughly 5–10% and should never be used to set a final volume.
Why can't sodium hydroxide be weighed accurately?
Because it is hygroscopic — it absorbs water and carbon dioxide from the air, so a weighed pellet is partly water and partly sodium carbonate. Prepare it approximately, then standardise by titration against a stable primary standard such as potassium hydrogen phthalate.
Does 1 mol/L equal 1 mmol/mL?
Yes, exactly. A millimole is one thousandth of a mole and a millilitre one thousandth of a litre, so the ratio is unchanged. This makes 0.1 M the same as 0.1 mmol/mL, which is convenient when a protocol specifies millimoles and millilitres.
Why is molarity important?
Because chemical reactions proceed in ratios of particles, not masses, and molarity converts a volume you can measure into a number of particles you can reason about. Titration, dosing, buffer preparation and reaction planning all depend on it.
The arithmetic here is short — moles divided by litres, and a multiplication by molar mass to get something you can weigh. The errors are elsewhere: millilitres read as litres, an anhydrous molar mass used for a hydrate, or solute added to a full flask instead of dissolved and topped up.
Two habits prevent nearly all of it. Type the formula rather than looking up the molar mass, and check the reagent bottle for the word "hydrate" before you weigh anything.
For molar masses in detail, use the molecular weight calculator. For solution densities, the density calculator.