Molarity and Dilution Calculator: Concentration, Mass of Solute, C1V1 = C2V2 and PPM

Make and dilute solutions: molarity, mass of solute needed, dilution volumes and ppm.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

Choose molarity, mass needed, dilution or ppm.

Enter the molar mass, the volume of the solution and the other values that apply to your choice.

For a dilution the calculator gives the volume of stock to take and the volume of water to add, and the dilution factor.

Formulas used

  • c = \frac{n}{V} = \frac{m}{MV}
  • C_1V_1 = C_2V_2
  • \mathrm{ppm} = \frac{m_{solute}}{m_{total}}\times10^6

Worked example

With the default numbers in the calculator above:

  1. Moles of solute: 0.10 mol
  2. Molarity (concentration): 0.20 mol/L
  3. Mass concentration: 11.69 g/L

Change the numbers in the calculator to see the full working, every step, for your own case.

A second worked example

A different case, with these numbers: What do you want? Dilution of a stock solution.

  1. Volume of the stock solution to take: 31.25 mL
  2. Volume of water to add: 218.75 mL (make up to 250.00 mL in total)
  3. Dilution factor: 8.00 times (a 8.00 fold dilution)

Common questions

What is molarity?

The number of moles of solute in one litre of solution, in mol/L (written M).

How do I dilute a stock solution?

Take V1 = C2 V2 / C1 of the stock, put it in a flask and add water up to the final volume V2.

Is the volume the water or the solution?

The volume of the finished solution. Dissolve the solute in some water, then make up to the mark.

What does ppm mean?

Parts per million: one gram of solute in a million grams of solution. In dilute water solutions 1 ppm is about 1 mg per litre.

Related calculators

Got a question about this? Ask an engineering question and get a plain-language answer with references.

Further reading: Any first-year chemistry text (solutions and dilutions).

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