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Daily Dose of Utilities

Molarity & Dilution Calculator

Molarity is moles of solute per liter of solution. 5.844 g of NaCl is 0.1 mol, so dissolved to make 500 mL (0.5 L) of solution it gives 0.1 ÷ 0.5 = 0.2 M.

g
mL

Molarity

0.2 M

Moles of solute

0.1 mol

Molar mass

58.44 g/mol

Show the math

  1. 1

    Molar mass of NaCl

    22.99 + 35.45 = 58.44 g/mol

    = 58.44 g/mol

Read the steps as text
  1. Molar mass of NaCl. 22.99 + 35.45 = 58.44 g/mol
  2. Convert the volume to liters. 500 mL ÷ 1000 = 0.5 L Molarity is moles per liter, so the volume must be in liters.
  3. Grams to moles. 5.844 g ÷ 58.44 g/mol = 0.1 mol
  4. Molarity = moles ÷ liters. 0.1 mol ÷ 0.5 L = 0.2 M 1 M (one molar) means one mole of solute per liter of solution.

Molarity from mass and volume

To find molarity, first convert the mass of solute to moles by dividing by its molar mass, which the calculator works out from the formula. Then divide the moles by the volume of the solution in liters. Volumes in milliliters are divided by 1000 first.

Working backwards tells you what to weigh out. For 250 mL of 1 M sodium chloride you need 1 mol/L × 0.25 L = 0.25 mol, and 0.25 mol × 58.44 g/mol = 14.61 g. Dissolve it in less water than you need, then top up to exactly 250 mL: the volume in the formula is the final solution, not the water you started with.

Dilutions with C₁V₁ = C₂V₂

Diluting a solution adds solvent but not solute, so the moles of solute (concentration × volume) are the same before and after. That gives C₁V₁ = C₂V₂, where 1 is the stock solution and 2 is the diluted one. Know any three and you can find the fourth.

To make 500 mL of 1 M acid from a 12 M stock, V₁ = 1 × 500 ÷ 12 = 41.67 mL. Measure 41.67 mL of stock and make it up to 500 mL. With acids, always add the acid to the water, never water to acid.

Frequently asked questions

What is the formula for molarity?
Molarity (M) = moles of solute ÷ liters of solution. Moles come from mass ÷ molar mass.
What's the difference between molarity and molality?
Molarity is moles per liter of solution; molality is moles per kilogram of solvent. Molality doesn't change with temperature, because mass doesn't expand when heated the way volume does.
Do the units in C1V1 = C2V2 have to be liters and molar?
No. Any units work as long as both concentrations use the same unit and both volumes use the same unit, because the units cancel.
How much water do I add to dilute a solution?
The final volume minus the stock volume. Diluting 50 mL of 2 M solution to 1 M needs a final volume of 100 mL, so you add 50 mL of water.

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