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Hematology

Molarity & Normality

While routine hematology testing often relies on pre-packaged commercial reagents, a fundamental understanding of Molarity and Normality is essential for the laboratory scientist. These concepts are critical for reagent preparation, verification of stain components, understanding buffer capacities, and troubleshooting discrepancies in manual methods. Unlike simple percent solutions, these measurements take into account the chemical reactivity and molecular weight of the solute, providing a precise standard for chemical concentration

Molarity (\(M\))

Molarity is the most standard unit of concentration used in the clinical laboratory. It describes the concentration of a solution in terms of the number of “moles” of solute per liter of solution. A mole is a specific quantity of particles (\(6.022 \times 10^{23}\), Avogadro’s number), but in practical laboratory mathematics, it represents the gram-molecular weight (GMW) of a substance

The Fundamental Concepts

  • Gram-Molecular Weight (GMW): This is the sum of the atomic weights of all the atoms in a molecule. To calculate GMW, one must reference the periodic table
    • Example (NaCl): Sodium (Na) = 22.99, Chlorine (Cl) = 35.45. The GMW of NaCl is approximately 58.44 grams
  • The Molarity Formula \[ M = \frac{\text{Moles of Solute}}{\text{Liters of Solution}} \]
  • The Working Formula: Since laboratories measure in grams rather than moles, the formula is expanded for daily use: \[ \text{Grams required} = \text{Molarity desired} \times \text{GMW} \times \text{Volume in Liters} \]

Calculating Molarity: Step-by-Step

To prepare a molar solution, the laboratory scientist must determine how many grams of dry chemical are needed to reach the desired concentration in a specific volume

  • Scenario: Prepare 500 mL of a 0.5 M solution of Sodium Chloride (NaCl)
  • Step 1: Determine GMW. NaCl = 58.44 g/mol
  • Step 2: Convert Volume. 500 mL = 0.5 Liters
  • Step 3: Apply the Formula.
    • \(\text{Grams} = M \times \text{GMW} \times L\)
    • \(\text{Grams} = 0.5 \times 58.44 \times 0.5\)
    • \(\text{Grams} = 14.61\)
  • Action: Weigh 14.61 grams of NaCl and dissolve it in enough deionized water to make a total volume: of 500 mL

Normality (\(N\))

Normality is a specialized concentration unit that focuses on the chemical reactivity of a substance rather than just its molecular weight. It is defined as the number of “gram equivalent weights” per liter of solution. Normality is frequently used in acid-base chemistry and titrations, which may be relevant in Hematology for neutralizing waste or preparing specific acidic lysing agents

The Concept of Valence & Equivalents

The key difference between Molarity and Normality is the Valence (or reactive capacity). An “Equivalent” is the amount of substance that will react with or supply one mole of hydrogen ions (\(H^+\)) or electrons

  • Determining Valence
    • Acids: The number of displaceable Hydrogen ions (\(H^+\))
      • \(\text{HCl} \rightarrow 1\ H^+\) (Valence = 1)
      • \(\text{H}_2\text{SO}_4 \rightarrow 2\ H^+\) (Valence = 2)
    • Bases: The number of Hydroxide ions (\(OH^-\))
      • \(\text{NaOH} \rightarrow 1\ OH^-\) (Valence = 1)
    • Salts: The total positive charge of the cation
      • \(\text{NaCl} \rightarrow \text{Na}^+\) (Valence = 1)
      • \(\text{CaCl}_2 \rightarrow \text{Ca}^{2+}\) (Valence = 2)
  • Equivalent Weight (EqWt): This is the weight of the substance that contains one equivalent of reactive particles \[ \text{Equivalent Weight} = \frac{\text{Gram Molecular Weight (GMW)}}{\text{Valence}} \]

Calculating Normality

The formula for Normality mirrors Molarity but substitutes Equivalent Weight for GMW

  • The Formula \[ N = \frac{\text{Grams of Solute}}{\text{Equivalent Weight} \times \text{Liters of Solution}} \]
  • The Working Formula \[ \text{Grams required} = \text{Normality desired} \times \text{EqWt} \times \text{Volume in Liters} \]

Relationship Between Molarity & Normality

Because Normality accounts for the multiplication of reactive units, Normality is always equal to or greater than Molarity. They are related by the valence (\(n\))

  • Conversion Formula \[ N = M \times n \quad \text{or} \quad M = \frac{N}{n} \]
  • Case Study 1: Hydrochloric Acid (\(\text{HCl}\))
    • GMW = 36.5
    • Valence = 1 (\(1\ H^+\))
    • Since the valence is 1, 1 M \(\text{HCl}\) = 1 N \(\text{HCl}\). The Molarity and Normality are identical
  • Case Study 2: Sulfuric Acid (\(\text{H}_2\text{SO}_4\))
    • GMW = 98.0
    • Valence = 2 (\(2\ H^+\))
    • Since the valence is 2, a 1 M solution is equal to a 2 N solution. The solution is twice as legally “strong” in terms of available protons (\(H^+\)) compared to its Molarity because every single molecule breaks apart to release two protons. Consequently, to make a 1 N solution, you only need half the weight of the acid required for a 1 M solution

Practical Application in Dilutions

Just as the \(C_1V_1 = C_2V_2\) equation is used for percent solutions, it is perfectly applicable to Molarity and Normality. This is often used when a laboratory purchases a concentrated “Stock Acid” and must dilute it for a working reagent

  • Formula: \(M_1V_1 = M_2V_2\) (or \(N_1V_1 = N_2V_2\))
  • Example: You have a stock bottle of 12 M Hydrochloric Acid. You need to prepare 200 mL of 1 M HCl for a specific cytochemical stain
    • \(12 \times V_1 = 1 \times 200\)
    • \(12 V_1 = 200\)
    • \(V_1 = 16.7 \text{ mL}\)
    • Procedure: Measure 16.7 mL of the concentrated 12 M acid and add it to a volumetric flask containing water (remembering the safety rule: Always Add Acid: to water, never the reverse) to reach a total volume of 200 mL