Molarity calculator

Molarity, stock solutions and aliquots

A stock solution is the concentrated solution made by dissolving a weighed or labelled mass of peptide in a measured volume of solvent. Its mass concentration is the mass divided by the volume, in mg/mL. Its molar concentration, or molarity, counts molecules instead of milligrams: moles of peptide per litre of solution, written M, mM, µM or nM.

Molarity is what lets you compare peptides of different sizes on equal terms. A 1 mg/mL solution of a small peptide holds more molecules than a 1 mg/mL solution of a large one, so work that depends on molecule count is planned in molar units. The bridge between the two is the molecular weight in g/mol, which you enter from the certificate of analysis.

An aliquot is a measured portion of the stock. Its transfer volume, the figure set on the pipette, is the aliquot mass divided by the mass concentration, or the target amount in moles divided by the molarity.

How the calculator works

Molarity is moles of solute per litre of solution. The calculator links four quantities through mass = concentration × volume × molecular weight. Enter the molecular weight in g/mol, choose the quantity to solve for, and enter the other two.

The mass-to-moles panel divides a mass by the molecular weight and shows the amount of substance in the most readable unit, from mol down to nmol.

Units and conversions

• 1 M = 1000 mM, 1 mM = 1000 µM and 1 µM = 1000 nM.
• 1 g = 1000 mg and 1 mg = 1000 µg.
• 1 L = 1000 mL and 1 mL = 1000 µL.
• 1 mM equals 1 µmol per mL, a quick hand check.

Worked examples

Each example uses a generic peptide with a molecular weight of 1419.5 g/mol.

1. Mass for a target concentration: 1 mL of a 1 mM solution needs 0.001 mol/L × 0.001 L × 1419.5 g/mol = 1.4195 mg.
2. Volume for a target concentration: 5 mg made up to 1 mM needs 0.005 g ÷ (1419.5 g/mol × 0.001 mol/L) = 3.522 mL.
3. Concentration of a known solution: 5 mg in 2 mL is 0.005 g ÷ (1419.5 g/mol × 0.002 L) = 1.761 mM.
4. Moles in a 5 mg vial: 0.005 g ÷ 1419.5 g/mol = 3.522 µmol.
5. Working dilution: 1 mL at 10 µM from a 1 mM stock takes 10 µM × 1 mL ÷ 1000 µM = 0.01 mL (10 µL) of stock, the pipetting threshold the peptide calculator flags.

From vial to molarity, step by step

Three linked examples: a stock concentration, an aliquot transfer volume and the molarity of a solution, using the molecular weight you enter.

1. Stock concentration: 10 mg of peptide dissolved in 2.0 mL of solvent gives 10 ÷ 2.0 = 5 mg/mL. In other units that is 5,000 µg/mL, or 5 µg in every microlitre.
2. Transfer volume: a 250 µg aliquot is 0.25 mg. Divided by the 5 mg/mL stock, 0.25 ÷ 5 = 0.05 mL, which is 50 µL. The vial holds 10,000 µg, so it gives 40 aliquots of that size.
3. Molarity: enter the molecular weight from the certificate of analysis. For a peptide of 1419.5 g/mol, a 1 mg/mL solution is 1 g/L ÷ 1419.5 g/mol = 0.7045 mM, or 704.5 µM. The 5 mg/mL stock above is 3.522 mM.

Significant figures and pipette resolution

The mass, volume and concentration panel reports six significant figures, so you can carry full precision into the next calculation. Round only at the end, to the precision your balance and pipette support: a balance that reads to 0.01 mg and a 0.1 µL pipette step set the useful limit, not the number of digits on screen.

Molar units help here. A 3.522 mM stock is easier to read and to dilute than 0.003522 M. For transfer volumes, use the smallest pipette whose range covers the volume, because accuracy is best toward the top of each pipette's range, and plan an intermediate dilution when a single step would call for less than 10 µL.

Which molecular weight to enter

Use the molecular weight stated for the material you hold. A salt form, such as an acetate salt, weighs more per mole than the free peptide, so the two give different molarities for the same mass.

Concentration from UV absorbance

Weighing gives a nominal concentration: counter-ions, residual water and purity all change how much peptide a solution actually holds. Absorbance measures it. The absorbance panel estimates the molar absorption coefficient (ε) from the one-letter sequence, then applies the Beer–Lambert law, c = A ÷ (ε × l), with l the path length in cm.

• ε280 (Pace et al., 1995): 5,500 per Trp, 1,490 per Tyr and 125 per disulfide bond, in M⁻¹ cm⁻¹. Free cysteines add nothing at 280 nm, so enter only the bonded pairs.
• ε205 (Anthis & Clore, 2013): 2,780 per peptide bond, plus Trp 20,400, Phe 8,600, Tyr 6,080, His 5,200, Met 1,830, Arg 1,350, Cys 690, Gln 400 and Asn 400.
• A peptide without Trp or Tyr absorbs too weakly at 280 nm. Read it at 205 nm.
• With both readings, the two concentrations sit side by side, and a difference above 10% is flagged as a cue to check the buffer, purity or counter-ion.

Measuring absorbance

• A quartz cuvette. Standard plastic and glass absorb strongly in the far UV, where 205 nm sits.
• A buffer with low absorbance at the wavelength you read. Many common buffer components absorb at 205 nm.
• A blank of the same buffer, in a matched cuvette.
• Readings below about 2.0. Above that, most spectrophotometers leave the linear range, so dilute and measure again.

Worked example: antioxidin

Antioxidin, TWYFITPYIPDK-NH2 (1542.77 g/mol), has 1 Trp, 2 Tyr, 1 Phe and 11 peptide bonds.

1. ε280 = 1 × 5,500 + 2 × 1,490 = 8,480 M⁻¹ cm⁻¹.
2. ε205 = 20,400 + 2 × 6,080 + 8,600 + 11 × 2,780 = 71,740 M⁻¹ cm⁻¹.
3. A reading of 0.100 at 280 nm in a 1 cm cuvette gives 0.100 ÷ 8,480 = 11.79 µM, and 11.79 µM × 1542.77 g/mol = 0.01819 mg/mL.
4. A reading of 0.850 at 205 nm gives 0.850 ÷ 71,740 = 11.85 µM, 0.47% from the 280 nm figure and well inside the 10% flag.

Antioxidin worked example courtesy of Daniel C. Moreira, mdcscience.com (opens in a new tab).

Frequently asked questions