Preparing solutions and buffers

Awareness level only. This lesson explains the ideas so you recognise them. It does not qualify you to do this work. Before you use lab equipment or handle chemicals, biological materials or patient samples for real, you need the training your employer or institution requires, and you must work under supervision until they sign you off.

Why it matters

Buffers and reagent solutions are the background of nearly every assay. An enzyme assay at the wrong pH, a cell wash at the wrong salt concentration or a standard made at the wrong molarity can make a whole run invalid. The good news is that the maths is short and the same few formulas cover most lab work.

Molarity and the core formula

Molarity (M) is moles of solute per litre of solution. To find the mass you need:

mass (g) = molarity (mol/L) x volume (L) x molar mass (g/mol)

Worked example: 500 mL of 0.150 M NaCl

NaCl has a molar mass of 58.44 g/mol.

mass = 0.150 x 0.500 x 58.44 = 4.383 g

Weigh 4.383 g, dissolve it in less than 500 mL of water in a beaker, transfer quantitatively to a 500 mL volumetric flask (rinsing the beaker into the flask), and make up to the line.

Check the label for the exact form. Many salts come as hydrates. Magnesium chloride hexahydrate (MgCl2·6H2O, 203.30 g/mol) needs more than twice the mass of anhydrous MgCl2 (95.21 g/mol) for the same molarity. Using the wrong molar mass is one of the most common prep errors.

Dilutions

When you dilute a stock, the amount of solute stays the same:

C1 x V1 = C2 x V2

To make 250 mL of 0.10 M from a 2.0 M stock: V1 = 0.10 x 250 / 2.0 = 12.5 mL of stock, made up to 250 mL. A serial dilution repeats a fixed step (for example 1:10 each time) to reach very low concentrations accurately.

Other units you will meet: percent w/v (grams per 100 mL, so 0.9 percent NaCl is 0.9 g per 100 mL) and mg/mL or µg/mL for standards.

Buffers

A buffer resists changes in pH. It is a mixture of a weak acid (HA) and its conjugate base (A-). The Henderson-Hasselbalch equation links pH to their ratio:

pH = pKa + log10( [A-] / [HA] )

Rearranged, the base-to-acid ratio you need is:

[A-] / [HA] = 10 ** (pH - pKa)

A buffer works best within about one pH unit of its pKa. Outside that range it has little capacity to absorb added acid or base.

Worked example: 1 L of 0.10 M phosphate buffer, pH 7.40

1. Ratio: 10 ** (7.40 - 7.21) = 10 ** 0.19 = 1.549.
2. Fraction that is base: 1.549 / (1 + 1.549) = 0.608. Base = 0.0608 M, acid = 0.0392 M.
3. Masses for 1 L, using anhydrous salts:
   • Na2HPO4 (base, 141.96 g/mol): 0.0608 x 1 x 141.96 = 8.63 g
   • NaH2PO4 (acid, 119.98 g/mol): 0.0392 x 1 x 119.98 = about 4.71 g (4.707 g before rounding the molarity)

The calculation gets you close. Real solutions differ from the ideal equation because of ionic strength and temperature, so the standard practice is:

• Dissolve the components in about 80 percent of the final volume.
• Measure with a calibrated pH meter at the temperature you will use the buffer, and adjust with small additions of acid or base as your SOP specifies.
• Make up to the final volume after adjusting the pH.
• Label it: name, concentration, pH, date, your initials, expiry and lot numbers of the components.

Tris is a classic trap: its pKa falls by about 0.03 units per °C, so a Tris buffer set to pH 8.0 at room temperature is noticeably more alkaline in a cold room.

Common mistakes

• Using the molar mass of the anhydrous salt when the bottle is a hydrate (or the reverse).
• Making up to volume before adjusting the pH.
• Choosing a buffer whose pKa is more than one unit away from the target pH.
• Setting the pH at room temperature for a buffer used at 4 °C or 37 °C.
• Leaving bottles unlabelled "just for today".

Quick recap

• mass = M x V x molar mass; dilute with C1V1 = C2V2.
• Henderson-Hasselbalch gives the base-to-acid ratio: 10 ** (pH - pKa).
• Pick a buffer with a pKa within one unit of your target, then confirm with a calibrated pH meter.
• Label every solution completely.

Try it

Open the Do tab and finish a small Python buffer calculator. The code already runs: you write one line, the Henderson-Hasselbalch ratio.