What is molarity?
Molarity is the most common way chemists describe the concentration of a solution — how much solute is dissolved in a given volume of liquid. The unit is moles per liter, written M. A 1 M (one molar) solution contains one mole of solute in every liter of solution. A 0.1 M solution is ten times more dilute. A 12 M concentrated hydrochloric acid bottle has twelve moles of HCl per liter — enough to make a chemistry teacher tell you to put on goggles before you touch it.
The trick that catches first-year chemistry students: molarity is moles per liter of solution, not moles per liter of solvent. The volume is whatever you measure after mixing, not the water you started with. For dilute solutions the difference is tiny. For concentrated ones — like sulfuric acid, which contracts in volume when it dissolves in water — the difference is large enough to matter. Standard lab procedure is to dissolve the solute in less water than the target volume, then add water to reach the final mark on a volumetric flask. That gives you the right molarity by definition.
For example: dissolve 5 g of table salt (NaCl) in enough water to make 250 mL of solution. Sodium chloride's molar mass is 58.44 g/mol, so 5 g is 5 ÷ 58.44 = 0.0856 mol. The molarity is 0.0856 mol ÷ 0.250 L = 0.342 M. That's roughly twice the salinity of medical saline solution, in case you were wondering.
How to use the Molarity Calculator
Three solve modes — pick the one that matches whatever variable you don't yet know.
- Find molarity. You mixed a solution and want to know its concentration. Enter moles of solute and total volume. Or use the shortcut: enter the solute's mass in grams plus its molar mass in g/mol, and the calculator computes moles for you.
- Find moles. You have a known concentration and volume and want to know how much solute is in there. Enter molarity and volume. Useful for figuring out dose, reaction stoichiometry, or how much active ingredient is in a fixed sample.
- Find volume. You have a fixed amount of solute and want to know how much solution you can make at a target concentration. Enter moles (or mass + molar mass) and the target molarity.
Volume can be entered in liters or milliliters; the calculator normalizes to liters internally (1 mL = 0.001 L). Mass mode lets you skip the moles-to-mass conversion if you have a balance and a molar mass but no calculator for that step.
The formula behind molarity
The core equation is genuinely as simple as it looks:
M = n / V
M is molarity in mol/L. n is moles of solute. V is total solution volume in liters. The same formula rearranged solves the other two cases: n = M × V, V = n / M. Every molarity problem you'll ever solve is a rearrangement of this equation, possibly preceded by a mass-to-moles conversion: n = mass (g) / molar mass (g/mol).
Worked example: making 250 mL of 0.342 M NaCl solution. You don't have the salt already weighed — you need to figure out how much to scoop.
- Target: M = 0.342 mol/L, V = 0.250 L
- Moles needed: n = M × V = 0.342 × 0.250 = 0.0856 mol
- NaCl molar mass: Na (22.99) + Cl (35.45) = 58.44 g/mol
- Mass needed: 0.0856 × 58.44 = 5.00 g
Weigh out 5.00 g of NaCl, dissolve it in some water in a 250 mL volumetric flask, then top up with water to the 250 mL mark. That's exactly 0.342 M, which happens to be roughly twice the concentration of physiological saline (0.154 M, more on which in a moment).
Common solutions and their molarities
Real-world solutions span a huge concentration range. The everyday salty things sit around 0.1 to 1 M. Lab-bench acids and bases sit at 1 to 12 M when bought, then get diluted for use. Here are some reference points worth knowing.
| Solution | Approximate molarity | What it is |
|---|---|---|
| Physiological saline (0.9% NaCl) | 0.154 M | IV drip fluid; matches blood plasma osmolarity |
| Blood plasma (sodium) | 0.135 – 0.145 M | Normal human reference range; tightly regulated |
| Seawater (total dissolved ions) | ~0.6 M | Roughly 0.47 M NaCl + 0.05 M MgCl₂ + assorted others |
| Vinegar (5% acetic acid) | 0.83 M | Household white vinegar; weak acid |
| Bench-grade hydrochloric acid | 1.0 – 6.0 M | Typical dilution for lab use |
| Concentrated HCl (as sold) | ~12 M (37%) | Comes from the supplier this strong; always diluted before use |
| Concentrated NaOH (saturated) | ~19 M | Aggressive base; close to the solubility limit |
| Concentrated H₂SO₄ | ~18 M (98%) | Battery acid is a more dilute version of the same |
Bench dilutions used in coursework usually live between 0.01 M and 1 M. Anything beyond saturation precipitates out — at room temperature you can't make a 6 M NaCl solution because the salt won't dissolve past about 6.1 M. The Molarity Calculator doesn't enforce solubility limits; it'll happily compute the math for a saltwater solution thicker than physically possible. Use a solubility table to sanity-check.
Dilution: the C₁V₁ = C₂V₂ rule
Most lab-bench solutions arrive at higher concentration than you need and get diluted before use. The math for dilution is even simpler than the math for the original solution:
C₁V₁ = C₂V₂
C₁ and V₁ are the concentration and volume of your stock solution. C₂ and V₂ are the concentration and volume of the diluted product you want. The logic: moles of solute are conserved during dilution. You're not adding more solute, just more solvent, so n stays constant — and since n = C × V, the product C × V on both sides must be equal.
Worked example: making 100 mL of 0.1 M HCl from a 6 M stock bottle. You know C₁ = 6 M, C₂ = 0.1 M, V₂ = 100 mL. Solve for V₁:
- V₁ = (C₂ × V₂) / C₁ = (0.1 × 100) / 6 = 1.67 mL
Pipette 1.67 mL of 6 M HCl into a 100 mL volumetric flask, then add water to the 100 mL mark. You now have 100 mL of 0.1 M HCl. The same math handles any single-step dilution. For a series (1 M → 0.1 M → 0.01 M → 0.001 M), just repeat C₁V₁ = C₂V₂ at each step.
One safety note that's been beaten into every chemistry student since the dawn of safety glasses: when diluting concentrated acid, add acid to water, never water to acid. The reaction releases heat; with acid on the bottom and water on top, the surface can boil and splatter. The mnemonic "AAA" — Always Add Acid — works.
Molarity vs. molality and other concentration units
Molarity is the dominant unit, but it's not the only way to describe a solution. Knowing when to switch saves trouble.
- Molarity (M) — moles of solute per liter of solution. Volume-based. Changes slightly with temperature because liquids expand and contract. Used for nearly all lab procedures.
- Molality (m) — moles of solute per kilogram of solvent. Mass-based. Doesn't change with temperature, which makes it the right choice for thermodynamics calculations involving boiling-point elevation or freezing-point depression.
- Mass percent (% w/w) — grams of solute per 100 g of solution. Used on consumer product labels and for very concentrated reagents (concentrated H₂SO₄ is sold as 98% w/w, which works out to about 18 M).
- Parts per million (ppm) — milligrams of solute per liter of solution, for dilute aqueous solutions. Used for trace contaminants in drinking water, environmental monitoring. 1 ppm ≈ 0.001 g/L; for low molar masses around 50–100 g/mol, 1 ppm ≈ 10⁻⁵ M.
- Normality (N) — older unit, equal to moles of reactive species per liter. For monoprotic acid like HCl, N = M. For diprotic like H₂SO₄, N = 2M. Mostly retired from modern coursework in favor of molarity plus explicit stoichiometry.
For everyday lab work, stick with molarity. Reach for molality when temperature varies. Use ppm or % w/w when you're reading a consumer label and need to translate to lab units before computing anything.
Edge cases and traps
A few things that trip people up when they sit down with the Molarity Calculator for the first time.
- Volume changes on dissolving. Adding 100 g of NaCl to 1 L of water doesn't give you 1 L of solution — the salt occupies some of its own volume once dissolved. For accurate work, use a volumetric flask: add solute, add solvent until you reach the line, mix. Don't measure out the solvent first.
- Hydrated salts. Many reagents come as hydrates — copper sulfate pentahydrate (CuSO₄·5H₂O) is the classic example, molar mass 249.69 g/mol instead of 159.61 for the anhydrous form. Mistaking one for the other gives you a solution off by 36%. Always check the bottle label.
- The strong-acid stoichiometry catch. A 1 M solution of sulfuric acid has 1 mol H₂SO₄ per liter — but H₂SO₄ donates two protons in solution. The proton concentration [H⁺] is approximately 2 M, not 1 M. Worth keeping straight for any titration or pH calculation.
- Temperature dependence. Molarities drift by about 0.05% per °C for water-based solutions because the water expands. Tiny for everyday work, meaningful for precision analytical chemistry. Most lab molarities are reported at 25°C; if you store at 4°C and use at room temperature, the molarity has changed slightly.
- Ionic strength. A 0.1 M NaCl solution contains 0.1 M Na⁺ and 0.1 M Cl⁻ — total ion concentration 0.2 M. For thermodynamics calculations (activity coefficients, conductivity), the relevant quantity is ionic strength, not molarity. Molarity is the bookkeeping unit; ionic strength is the effective interaction strength.
If a calculation gives you a number that feels wildly off — a result a hundred times what you expected — the most common cause is a unit slip (milliliters vs. liters; grams vs. milligrams) followed by a molar-mass mistake. Double-check both before redoing the chemistry.
Related calculations
Molarity often shows up alongside other quantitative-chemistry calculations. A few useful neighbors:
- Density Calculator — converts between mass and volume for a substance of known density. Handy when a recipe gives you mL but your balance reads grams.
- Scientific Notation Converter — keeps big and small numbers readable. A 1 µM solution is 10⁻⁶ M; a typical bench reagent is 10⁰ to 10¹ M. Sliding between them in plain decimal form is a recipe for misplaced zeros.
- Half-Life Calculator — for first-order chemical kinetics. The same exponential math that handles radioactive decay handles first-order reaction kinetics where concentration falls by a constant fraction per unit time.
- Exponent Calculator — useful for pH (pH = −log[H⁺]), Beer-Lambert absorbance, and other places where concentration shows up as an exponent.
Frequently asked questions
What's molarity in one sentence?
Moles of solute per liter of solution — written M, with 1 M meaning one mole per liter. The volume is the total after mixing, not the volume of pure solvent you started with.
What's the difference between molarity and molality?
Molarity is moles per liter of solution (volume-based). Molality is moles per kilogram of solvent (mass-based). Molarity changes a little with temperature because volumes expand; molality doesn't because masses don't. Lab procedures usually specify molarity. Thermodynamics calculations usually want molality.
How do I compute molar mass?
Add up the atomic masses of all atoms in the molecular formula. NaCl: 22.99 + 35.45 = 58.44 g/mol. Water (H₂O): 2 × 1.008 + 16.00 = 18.02 g/mol. Sucrose (C₁₂H₂₂O₁₁): 12 × 12.01 + 22 × 1.008 + 11 × 16.00 = 342.30 g/mol. Atomic masses are on the periodic table; the Molarity Calculator's mass mode asks you to enter the molar mass directly so you don't have to redo this every time.
How do I dilute a solution to a target molarity?
Use C₁V₁ = C₂V₂. C₁ and V₁ are the stock concentration and volume you'll use; C₂ and V₂ are the target concentration and final volume. Solve for whichever is unknown — usually V₁. Pipette V₁ of stock into the volumetric flask, then add solvent to V₂. Always add concentrated acid to water, never the other way around.
Does temperature affect molarity?
Yes, slightly. The volume of liquids expands with temperature, so the same moles in a now-larger volume gives a lower molarity. The effect is about 0.05% per °C for water-based solutions — negligible for most work, real for high-precision analytical chemistry. Molality (which uses mass instead of volume) avoids the problem.
Why must the volume be the total solution volume, not the solvent volume?
Because solute occupies space when dissolved. Add 50 g of NaCl to 1 L of water and you get slightly more than 1 L of solution. For concentrated solutions, the difference is significant. Standard procedure: dissolve the solute in less water than the target volume, then top up to the mark on a volumetric flask. That guarantees the final volume — and thus the molarity — is right.
What's a saturated solution?
A solution in which no more solute will dissolve at the given temperature. Solubility is the maximum molarity you can reach. For NaCl in water at 25°C that's about 6.1 M; for sucrose it's about 5.8 M; for hard-to-dissolve salts it can be 10⁻⁵ M or less. Heating usually raises solubility for solids in water; for gases, it lowers solubility.
Can the Molarity Calculator handle non-aqueous solutions?
Yes — the equation M = n/V doesn't care what the solvent is. As long as you have moles of solute and total solution volume, the math works for ethanol-based, oil-based, or any other solvent. Solubility tables and density values change, but the molarity formula doesn't.