The Tocris Molarity Calculator is based on the equation:

Mass of compound (g)= Molarity (M) x Volume of solution (l)
Molecular Weight (g/mol)

(Please see Molarity Calculations Explained for the derivation of this equation).

The calculator works on the principle that you know the MOLECULAR WEIGHT of a compound, and either 2 of the 3 variables, MASS, VOLUME and CONCENTRATION
(N.B. the terms molarity and concentration are interchangeable).

The Molarity Calculator will enable you to calculate:

• The MASS of a compound required to make a solution of known VOLUME and CONCENTRATION
• The VOLUME of solution required to dissolve a compound of known MASS to a desired CONCENTRATION
• The CONCENTRATION of a solution resulting from dissolving a known MASS of compound in a specific VOLUME

The Molarity Calculator automatically uses the structural Molecular Weight of the product that you are looking at for calculations and enters this value into the Molecular Weight box. The structural Molecular Weight can be used in mock calculations; however, if you are making a stock solution for your experiments, it is necessary to use the batch-specific Molecular Weight value of the product.

e.g. What is the MASS of D-AP5 (Cat. No. 0106) required to make a stock concentration of 10 mM in 10 ml of water?

1. Find the MOLECULAR WEIGHT for the batch of D-AP5 that you have (this information is batch-specific and is stated on the product datasheet and on the vial label).
   e.g. For batch 50 of D-AP5 the MOLECULAR WEIGHT is 197.13 g/mole.
2. Enter 197.13 into the MOLECULAR WEIGHT box.
3. Enter 10 into the CONCENTRATION box and select the correct unit (mM)
4. Enter 10 into the VOLUME box and select the correct unit (ml).
5. Press CALCULATE.
6. The answer of 19.72 mg appears in the MASS box.

Molarity Calculations Explained

To understand the basis of Molarity Calculations, you should be first familiar with the terms Mole and Molarity. These are defined below:

Mole (mol)
SI unit for the amount of a compound in grams which contains Avogadro‘s number (6.022 x 10²³) of atoms or molecules of it.

One mole of a compound has a mass equal to its Molecular Weight in grams.

i.e. 1 mol of compound ≡ 6.022 x 10²³ atoms/molecules of compound ≡ Molecular Weight of compound (g)

No. of moles (mol)= Mass of compound (g)(Equation 1)
Molecular Weight (g/mol)

Molarity (molar concentration; M)
The concentration of a solution measured as the number of moles of the compound per litre of solution. A 1 M solution contains one mole of substance per litre of solution (1 M = 1 mol/l).

e.g. A 10 mM (or 0.01 M) stock solution of the protein kinase JNK inhibitor SP 600125 (Cat. No. 1496) contains 0.01 moles of compound per litre of solution.

Molarity (M) = No. of moles (mol) (Equation 2)
Volume of solution (l)

Molecular Weight (g/mol)
The average mass of a compound calculated by summing the atomic weights of atoms in the molecular formula.

The Molecular Weight is the number of grams of a compound which contains a mole of it.

Equations 1 and 2 can be combined since ‘No. of moles (mol)’ is common to both equations. The resulting equation is:

Mass of compound (g)= Molarity (M) x Volume of solution (l)
Molecular Weight (g/mol)

Therefore if you know the Molecular Weight of a compound, and either 2 of the 3 variables, Mass, Molarity or Volume, the unknown variable can be calculated.

How to use the Dilution Calculator

The Tocris Dilution Calculator is based on the equation:

Concentration_[start] x Volume_[start] = Concentration_[final] x Volume_[final]

This equation is commonly abbreviated to C₁V₁ = C₂V₂

(Please see Dilution Calculations Explained for the derivation of this equation).

The calculator works on the principle that you know 3 of the 4 variables and will calculate the desired unknown.

The calculator can be used to work out:

• How to dilute a stock solution of known concentration
• How to perform serial dilutions

e.g. What volume of a 10 mM stock concentration of scopolamine (Cat. No. 1414) is required to make 20 ml of a 50 μM solution?

Using C₁V₁ = C₂V₂, C₁=10 mM, C₂=50 μM, V₂=10 ml and V₁ is the unknown.

1. Enter 10 into the Concentration[start] box and select the correct unit (mM).
2. Enter 50 into the Concentration[final] box and select the correct unit (μM).
3. Enter 20 into the Volume[final] box and select the correct unit (ml).
4. Press CALCULATE.
5. The answer of 0.1 ml appears in the Volume[start] box.

Dilution Calculations Explained

The dilution equation is fairly straightforward since in diluting a solution, you are simply increasing the amount of solvent in the solution whilst the number of moles of compound remains the same. Therefore, the number of moles in the concentrated (start) solution should equal the number of moles in the dilute (final) solution.

i.e. No. of moles_[start] = No. of moles_[final]

From Equation 2 (Molarity Calculations Explained):

No. of moles = Molarity x Volume of solution

Substituting Concentration for Molarity as these terms are interchangeable:

No. of moles_[start] = Concentration_[start] x Volume_[start] = C₁V₁
No. of moles _[final] = Concentration_[final] x Volume_[final] = C₂V₂