Calculate molarity, moles, volume, mass, solution dilution, mixing, and gas solubility with step-by-step solutions and detailed explanations.
Number of moles of solute
Volume of solution
The amount of substance, measured in moles (mol), represents the number of particles (atoms, molecules, ions) in a sample. One mole contains particles (Avogadro's constant).
Molarity is defined as the number of moles of solute per liter of solution: . It's the most common concentration unit in chemistry laboratories.
At standard temperature and pressure (STP: 273.15 K, 101.325 kPa), one mole of any ideal gas occupies . This is useful for converting between gas volumes and moles.
Select a calculation mode, enter the required values, and click "Calculate" to get step-by-step solutions with detailed explanations.
My chemistry professor said "make a 0.5 M NaCl solution" like it was obvious. I stared at the lab bench for ten minutes before asking my partner what M meant. She said "molar" like that explained anything.
Molarity is just a recipe. Seriously. It tells you how much stuff (solute) is dissolved in how much liquid (solvent). A 0.5 M NaCl solution means 0.5 moles of sodium chloride per liter of solution. The hard part isn't the concept — it's remembering what a "mole" is and how to convert grams to moles.
A mole is 6.022 × 10²³ of anything. That's Avogadro's number. It's absurdly large because molecules are absurdly small. One mole of water molecules weighs about 18 grams — roughly a tablespoon.
The molar mass of a substance tells you how many grams equal one mole. For NaCl: sodium is 22.99 g/mol, chlorine is 35.45 g/mol. Add them: 58.44 g/mol. So one mole of table salt weighs 58.44 grams — about 4 tablespoons.
That's the bridge between the scale in your lab and the formula on the board. Weigh grams, convert to moles, divide by volume. Done.
Your professor wants 500 mL of 0.5 M NaCl. How many grams of salt do you weigh out?
Work backwards from the molarity formula:
Rearrange to find mass:
Weigh 14.61 grams of NaCl, dissolve it in water, and bring the total volume to 500 mL in a volumetric flask. That's your 0.5 M solution. The whole process is three multiplications.
Common mistake: adding 500 mL of water to the salt. That gives you more than 500 mL of solution (the salt takes up volume). You dissolve the salt in less than 500 mL of water, then top off to the 500 mL mark. The final volume of the solution is what matters, not the volume of water you added.
You need 250 mL of 1.0 M glucose (C₆H₁₂O₆) solution. Walk through it:
| Step | What You Do | Result |
|---|---|---|
| 1. Find molar mass | 6(12.01) + 12(1.008) + 6(16.00) | 180.16 g/mol |
| 2. Convert volume to L | 250 mL ÷ 1000 | 0.250 L |
| 3. Find moles needed | M × V = 1.0 × 0.250 | 0.250 mol |
| 4. Convert to grams | 0.250 × 180.16 | 45.04 g |
Weigh 45.04 g of glucose, dissolve, bring to 250 mL. Done. Every molarity problem follows these same four steps. The numbers change; the process doesn't.
You have a 6.0 M HCl stock solution and need 100 mL of 0.5 M HCl. How much stock do you use?
Take 8.33 mL of the concentrated acid, add it to water (never the reverse — always acid to water), and bring the total to 100 mL. The dilution formula works because the total moles of solute stay the same — you're just spreading them across more volume.
The connection to density is direct: concentrated solutions are denser because there's more solute packed into the same volume. Diluting reduces the concentration and the density simultaneously.
Molarity (M) = moles of solute per liter of solution. Molality (m) = moles of solute per kilogram of solvent. The difference: molarity uses total solution volume; molality uses solvent mass.
For dilute aqueous solutions, they're nearly identical (because 1 L of water ≈ 1 kg). For concentrated solutions or non-water solvents, they diverge. Molality doesn't change with temperature (mass doesn't expand); molarity does (volume expands when heated). That's why physical chemistry problems about boiling point elevation and freezing point depression use molality.
For general chemistry lab work? Molarity is what you'll use 95% of the time. Just remember which one your professor asked for.
Molarity (M) is the number of moles of solute dissolved in one liter of solution. A 1.0 M NaCl solution contains 1 mole (58.44 grams) of sodium chloride per liter. It's the most common way to express concentration in chemistry.
Molarity (M) = moles per liter of solution. Molality (m) = moles per kilogram of solvent. Molarity depends on temperature (because volume changes with temperature); molality doesn't. For dilute water-based solutions, the values are nearly identical. Use molarity for lab prep; use molality for colligative property calculations.
Use the dilution formula: M₁V₁ = M₂V₂. Multiply the desired molarity by the desired volume, then divide by the stock concentration to find how much stock solution you need. Add the stock to water (not water to acid) and bring to the final volume. Always add acid to water for safety.
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