How the Molarity Calculator Works
Chemists describe how strong a solution is by its concentration. The most common measure is molarity, which is the number of moles of a substance dissolved in each liter of solution. A solution of 1 mol/L is called a 1 molar solution, written 1 M. The Molarity Calculator finds the molarity of a solution, works out how much solute to weigh to make one, and shows how to dilute a stock solution.
The formula
molarity (M) = moles of solute / liters of solution
The volume is the volume of the whole solution, with the solute dissolved in it. It is not the volume of the solvent that you started with. This is why you dissolve the solute first, and then add solvent until the solution reaches the mark.
The three things this calculator does
- Find the molarity of a solution, from the amount of solute and the volume.
- Find how much solute to weigh, to make a solution of a wanted molarity and volume.
- Dilute a stock solution, to make a weaker solution from a stronger one.
1. Finding the molarity
Enter the amount of solute in moles, millimoles, grams or milligrams, and the volume in liters or milliliters. If you use grams, you also need the molar mass of the solute, which is the mass of one mole in g/mol. There is a list of common solutes that fills it in for you.
moles = grams / molar mass
| Example | Calculation | Molarity |
|---|---|---|
| 0.5 mol in 1 L | 0.5 / 1 | 0.5 M |
| 5.844 g of NaCl in 100 mL | (5.844 / 58.44) / 0.1 = 0.1 / 0.1 | 1 M |
| 58.44 mg of NaCl in 10 mL | (0.05844 / 58.44) / 0.01 = 0.001 / 0.01 | 0.1 M (100 mM) |
| 0.02 mmol in 1 L | 0.00002 / 1 | 0.00002 M (20 µM) |
- Example: 0.5 mol in 1 L
Calculation: 0.5 / 1
Molarity: 0.5 M - Example: 5.844 g of NaCl in 100 mL
Calculation: (5.844 / 58.44) / 0.1 = 0.1 / 0.1
Molarity: 1 M - Example: 58.44 mg of NaCl in 10 mL
Calculation: (0.05844 / 58.44) / 0.01 = 0.001 / 0.01
Molarity: 0.1 M (100 mM) - Example: 0.02 mmol in 1 L
Calculation: 0.00002 / 1
Molarity: 0.00002 M (20 µM)
The calculator also gives the concentration by mass in grams per liter. For the second example, it is 58.44 g/L.
2. How much solute to weigh
To make a solution, you need the mass of solute. Work it out from the molarity, the volume and the molar mass:
moles = molarity x liters grams = moles x molar mass
| You want | Calculation | Weigh |
|---|---|---|
| 500 mL of 0.1 M NaOH | 0.1 x 0.5 = 0.05 mol, x 39.997 | 2.0 g |
| 1 L of 5 mM glucose | 0.005 x 1 = 0.005 mol, x 180.156 | 0.9008 g |
| 1 L of 1 M NaCl | 1 mol x 58.44 | 58.44 g |
- You want: 500 mL of 0.1 M NaOH
Calculation: 0.1 x 0.5 = 0.05 mol, x 39.997
Weigh: 2.0 g - You want: 1 L of 5 mM glucose
Calculation: 0.005 x 1 = 0.005 mol, x 180.156
Weigh: 0.9008 g - You want: 1 L of 1 M NaCl
Calculation: 1 mol x 58.44
Weigh: 58.44 g
Then dissolve the solute in a little solvent, pour it into a volumetric flask, and add solvent up to the mark, so that the total volume is exactly what you want.
Chart: how much to weigh for 1 liter of a 0.1 M solution
Each block is about 0.86 g.
NaOH █████ 4.0 g NaCl ███████ 5.8 g KCl █████████ 7.5 g CuSO4 ███████████████████ 16.0 g Glucose █████████████████████ 18.0 g Sucrose ████████████████████████████████████████ 34.2 g
The same molarity needs very different masses, because the molar masses are different.
3. Diluting a stock solution
Many laboratories keep strong stock solutions and dilute them when needed. When you add solvent, the amount of solute does not change, only its concentration. This gives the dilution formula:
M1 x V1 = M2 x V2 V1 = M2 x V2 / M1
M1 and V1 are the concentration and the volume of the stock. M2 and V2 are the concentration and the final volume that you want. The calculator finds V1, the volume of stock to take, and the volume of solvent to add.
Example: you have a 12 M stock of hydrochloric acid, and you want 250 mL of a 1 M solution.
| Step | Result |
|---|---|
| Volume of stock (1 x 250 / 12) | 20.83 mL |
| Solvent to add (250 - 20.83) | about 229.17 mL |
| Dilution factor (12 / 1) | 12 times |
████████████████████████████████████████ ■ Stock 20.8 mL ■ Solvent 229.2 mL
Other solutions made from the same 12 M stock, with a final volume of 250 mL:
| Wanted molarity | Stock to take | Solvent to add |
|---|---|---|
| 1 M | 20.83 mL | 229.17 mL |
| 0.5 M | 10.42 mL | 239.58 mL |
| 0.1 M | 2.08 mL | 247.92 mL |
When you dilute a strong acid, add the acid slowly to the water, and not the other way round. The mixing can give off a lot of heat.
The scale of concentrations
Concentrations cover a huge range, so they are best compared on a scale of tens. Each block is a factor of 1.5. Some examples:
1 µM (a very weak solution) █ 5 mM (blood glucose, about) █████████████████████ 154 mM (physiological saline) ██████████████████████████████ 1 M ██████████████████████████████████ 12 M (concentrated HCl) ████████████████████████████████████████
The calculator draws a scale from 1 µM to 10 M, with a line that shows where your solution is.
Units of concentration
| Unit | Meaning | In mol/L |
|---|---|---|
| M | mol per liter | 1 |
| mM | millimol per liter | 0.001 |
| µM | micromol per liter | 0.000001 |
Tips
- Use the total volume of the solution. The volume of the solvent alone is not the volume of the solution.
- Use the right molar mass. For a hydrate, such as CuSO4·5H2O, include the water. Use a molecular weight calculator if you are not sure.
- Check the purity of the stock. A stock that is 98% pure is a little weaker than its label says.
- Keep the units the same. The calculator changes milliliters and millimoles for you.
- Work safely. Wear eye protection, and follow the rules of your laboratory.
What this calculator does not include
- Concentrations by mass percent, molality and normality.
- The change of the volume when a solute and a solvent are mixed. In a real mixture the volumes are not exactly additive.
- The purity or the density of the stock solution.
- Solutions that are made of several solutes.
This tool gives a calculation for study and general use. In a laboratory, follow your written method and the safety rules of your institution.