Medication Unit Conversions (mg/mmol/mEq)

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Accurate medication dosing is critical to patient safety and therapeutic efficacy. One common challenge is converting between different units of measurement, such as milligrams (mg), milliequivalents (mEq), and millimoles (mmol). This article provides a comprehensive guide to understanding these conversions, complete with equations, reference tables, and practical examples.

Why Unit Conversions Matter

Medications, particularly electrolytes and IV preparations, are often prescribed in units like mEq or mmol, while their formulations are labeled in mg. Understanding these conversions ensures:

1. Accurate dosing: Prevents underdosing or overdosing.
2. Patient safety: Reduces the risk of medication errors.
3. Therapeutic efficacy: Ensures the prescribed dose achieves the desired therapeutic effect.

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Key Concepts and Equations

1. Milligrams (mg)

• Definition: A unit of mass (weight).
• Use: Commonly used to express the weight of a medication or its active ingredient.

2. Millimoles (mmol)

• Definition: A unit of amount of substance, based on the molecular weight of the compound.
• Equation:
  $$\text{mmol} = \frac{\text{mg}}{\text{Molecular Weight (MW)}}$$
  Where:
• mg: Milligrams of the compound.
• MW: Molecular weight of the compound (g/mol).

3. Milliequivalents (mEq)

• Definition: A unit of chemical activity, based on the valence (charge) of the ion.
• Equation:
  $$\text{mEq} = \frac{\text{mg} \times \text{Valence}}{\text{Molecular Weight (MW)}}$$
  Where:
• Valence: Charge of the ion (e.g., Na⁺ = 1, Ca²⁺ = 2).

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Conversion Formulas

Conversion	Formula
mg to mmol	$$\text{mmol} = \frac{\text{mg}}{\text{Molecular Weight (MW)}}$$
mmol to mg	$$\text{mg} = \text{mmol} \times \text{Molecular Weight (MW)}$$
mg to mEq	$$\text{mEq} = \frac{\text{mg} \times \text{Valence}}{\text{MW}}$$
mEq to mg	$$\text{mg} = \frac{\text{mEq} \times \text{MW}}{\text{Valence}}$$
mmol to mEq	$$\text{mEq} = \text{mmol} \times \text{Valence}$$
mEq to mmol	$$\text{mmol} = \frac{\text{mEq}}{\text{Valence}}$$

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Reference Table: Common Medications and Their Properties

Medication	Compound	Molecular Weight (MW)	Element	Atomic Weight (AW)	Valence
Sodium Chloride	NaCl	58.44 g/mol	Sodium (Na)	23 g/mol	1
Potassium Chloride	KCl	74.55 g/mol	Potassium (K)	39.1 g/mol	1
Magnesium Chloride	MgCl2	95.21 g/mol	Magnesium (Mg)	24.3 g/mol	2
Magnesium Sulphate	MgSO4·7H₂O	246.47 g/mol	Magnesium (Mg)	24.3 g/mol	2
Calcium Chloride	CaCl2·2H₂O	147.02 g/mol	Calcium (Ca)	40.08 g/mol	2
Calcium Gluconate	C12H22CaO14	430.4 g/mol	Calcium (Ca)	40.08 g/mol	2
Calcium Glubionate	C18H32CaO19.2H₂O	628.5 g/mol	Calcium (Ca)	40.08 g/mol	2

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Practical Examples

Example 1: Converting mg to mEq for “Potassium Chloride“

• Given: 100 mg of Potassium Chloride (KCl).
• MW: 74.55 g/mol.
• Valence: 1.
• Calculation:
  $$\text{mEq} = \frac{100 \, \text{mg} \times 1}{74.55 \, \text{g/mol}} = 1.34 \, \text{mEq}$$

Example 2: Converting mEq to mg for “Calcium Gluconate“

• Given: 4.65 mEq of Calcium Gluconate.
• MW: 430.4 g/mol.
• Valence: 2.
• Calculation:
  $$\text{mg} = \frac{4.65 \, \text{mEq} \times 430.4 \, \text{g/mol}}{2} = 1000 \, \text{mg}$$

Example 3: Converting mmol to mg for “Magnesium Sulphate“

• Given: 2 mmol of Magnesium Sulphate (MgSO₄·7H₂O).
• MW: 246.47 g/mol.
• Calculation:
  $$\text{mg} = 2 \, \text{mmol} \times 246.47 \, \text{g/mol} = 492.94 \, \text{mg}$$

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* Notes on Hydrated Salts

Hydrated Salts and Molecular Weight

• Hydrated salts (e.g., MgSO₄·7H₂O, CaCl₂·2H₂O) contain water molecules as part of their crystal structure.
• The molecular weight of a hydrated salt includes the weight of the water molecules.
• For example:
  • Magnesium Sulphate Heptahydrate (MgSO₄·7H₂O):
    • Molecular Weight = 246.47 g/mol (includes 7 water molecules).
  • Calcium Chloride Dihydrate (CaCl₂·2H₂O):
    • Molecular Weight = 147.02 g/mol (includes 2 water molecules).
• When calculating conversions, always use the correct molecular weight for the hydrated form of the compound.

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** Clarification of Atomic Weight in the Formula

Formula:

$$\text{mgElement} = \frac{\text{mgProduct} \times (\text{Number of atoms} \times \text{Element Atomic Weight (AW)})}{\text{Compound Molecular Weight (MW)}}$$

Explanation:

• Element Atomic Weight (AW):
  • This refers to the atomic weight of the element (e.g., Na = 23 g/mol, Ca = 40.08 g/mol).
  • It represents the mass of one mole of the element.
• Compound Molecular Weight (MW):
  • This refers to the molecular weight of the entire compound (e.g., NaCl = 58.44 g/mol, CaCl₂ = 110.98 g/mol).
  • It represents the mass of one mole of the compound.
• The formula calculates the proportion of the element’s mass relative to the total mass of the compound.
• Don’t assumes one atom of the element is present in the compound. If there are multiple atoms, adjust the formula accordingly

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Tips for Accurate Conversions

1. Verify Molecular Weights: Always use the correct molecular weight for the compound (including hydrates if applicable).
2. Check Valence: Ensure the valence corresponds to the ion (e.g., Ca²⁺ = 2, Na⁺ = 1).
3. Use Reference Tables: Keep a reference table of common medications and their properties for quick access.
4. Double-Check Calculations: Use a calculator or conversion tool to verify results.