13.2 Molar Solutions, Normality & Buffer Preparation

13.2 Molar Solutions, Normality & Buffer Preparation

ASCP HT Exam Focus: Molar solutions is a named sub-topic under Laboratory Mathematics. Molarity questions on the ASCP HT examination almost always involve either a hydrated salt or a concentrated acid, because those are the two places where a plausible-looking wrong answer is easy to construct.

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Molarity

A mole is the formula weight of a substance expressed in grams. Molarity (M) is moles of solute per litre of finished solution.

$\text{Grams} = M \times \text{formula weight} \times \text{volume in litres}$

Worked example. Prepare 500 mL of 0.1 M citric acid (formula weight 192.12 g/mol) for a retrieval buffer:

$\text{Grams} = 0.1 \times 192.12 \times 0.500 = \mathbf{9.61\text{ g}}$

Worked example. Prepare 2 L of 0.5 M sodium chloride (formula weight 58.44):

$\text{Grams} = 0.5 \times 58.44 \times 2.0 = \mathbf{58.44\text{ g}}$

Millimolar (mM). Retrieval buffers are usually written in millimolar: $10\text{ mM} = 0.010\text{ M}$. A 10 mM citrate buffer is therefore one hundredth the mass of a 1 M solution.

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Waters of Hydration

Many laboratory salts are supplied as hydrates, and the water is part of the mass you weigh.

Worked example. Prepare 1 L of 10 mM sodium citrate buffer using the dihydrate:

$\text{Grams} = 0.010 \times 294.10 \times 1.0 = \mathbf{2.94\text{ g}}$

Using the anhydrous formula weight by mistake would give 2.58 g - a buffer roughly 12 percent weak, which in a heat-induced epitope retrieval protocol shows up as weak, patchy immunostaining.

Rule: read the label, not the name. If the bottle says "dihydrate", use the dihydrate formula weight printed on that label.

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Normality and Equivalents

Normality (N) is equivalents of solute per litre. An equivalent is the amount of substance that supplies one mole of reactive units - one mole of $\text{H}^{+}$ for an acid, one mole of $\text{OH}^{-}$ for a base, or one mole of charge for a salt.

$N = M \times \text{number of equivalents} \qquad \text{Equivalent weight} = \frac{\text{formula weight}}{\text{number of equivalents}}$

Worked example. Prepare 500 mL of 1 N sulfuric acid from the solid-equivalent calculation: the equivalent weight is $98.08 / 2 = 49.04$, so $1 \times 49.04 \times 0.500 = \mathbf{24.52\text{ g}}$ of equivalent mass, delivered in practice by diluting the concentrated acid.

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Converting a Concentrated Acid to Molarity

Concentrated reagents are labelled as percent weight/weight with a density, not as molarity. The conversion is:

$M = \frac{10 \times \%\ (\text{w/w}) \times \text{density in g/mL}}{\text{formula weight}}$

Worked example. Prepare 1 L of 1 M hydrochloric acid from the concentrated reagent: $V_1 = (1 \times 1000)/12.1 = \mathbf{82.6\text{ mL}}$ of concentrated HCl added slowly to roughly 900 mL of water, then brought to 1 L. Acid is always added to water, because the heat of dilution released at the interface can flash-boil water added to acid.

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Buffers That Histology Actually Prepares

A buffer resists pH change because it contains a weak acid and its conjugate base in equilibrium, described by the Henderson-Hasselbalch relationship:

$\text{pH} = \text{p}K_a + \log\frac{[\text{conjugate base}]}{[\text{weak acid}]}$

Buffering capacity is greatest when the two species are roughly equal, which is one pH unit either side of the $\text{p}K_a$. A buffer used far from its $\text{p}K_a$ drifts, which is why citrate is used near pH 6 and Tris near pH 8 to 9 rather than interchangeably.

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pH Meter Calibration

• Calibrate with at least two standard buffers that bracket the expected sample pH - typically pH 7.00 with pH 4.01 for acidic work, or pH 7.00 with pH 10.01 for alkaline retrieval buffers.
• Verify the electrode slope falls within the manufacturer's acceptance range; a drifting or out-of-slope electrode is a replacement item, not a recalibration item.
• Use temperature compensation, because electrode response and buffer pH both change with temperature. Measure standards and samples at the same temperature.
• Store the electrode in the manufacturer-specified storage solution (commonly potassium chloride), never in distilled water, which leaches ions out of the junction.
• Rinse with deionized water between measurements and blot rather than wipe, to avoid static charge on the bulb.
• Document calibration in the instrument log with the standards used, lot numbers, and the technologist's initials.