Which is the correct formula for osmolality when concentrations are given in mg/dL?

Which is the correct formula for osmolality when concentrations are given in mg/dL?

• A. Osm = 2Na + Glucose/18 + BUN/2.8
• B. Osm = Na + Glucose + BUN
• C. Osm = 2Na + Glucose/18 + BUN/2.8 divided by 2
• D. Osm = Na^2 + Glucose^2 + BUN^2

Answer: (A)

Osmolality is calculated by summing the osmoles contributed by the major dissolved solutes in serum. Sodium contributes two osmoles per mole because each Na+ is accompanied by an anion, so its contribution is 2 × Na. Glucose and urea (BUN as a surrogate) contribute based on their molar concentrations, which require converting from mg/dL to mmol/L: glucose is divided by 18 (since 180 g/mol), and BUN is divided by 2.8 (approximate conversion from mg/dL to mmol/L for urea). Put together, the practical formula is Osm ≈ 2 × Na + Glucose/18 + BUN/2.8, yielding osmolality in mOsm/kg. This is the best choice because it uses the correct sodium factor and the proper unit conversions for glucose and BUN. Options that sum the raw mg/dL values, or that include an extra division or square the terms, do not reflect how osmoles add up in solution.

Osmolality is calculated by summing the osmoles contributed by the major dissolved solutes in serum. Sodium contributes two osmoles per mole because each Na+ is accompanied by an anion, so its contribution is 2 × Na. Glucose and urea (BUN as a surrogate) contribute based on their molar concentrations, which require converting from mg/dL to mmol/L: glucose is divided by 18 (since 180 g/mol), and BUN is divided by 2.8 (approximate conversion from mg/dL to mmol/L for urea). Put together, the practical formula is Osm ≈ 2 × Na + Glucose/18 + BUN/2.8, yielding osmolality in mOsm/kg.

This is the best choice because it uses the correct sodium factor and the proper unit conversions for glucose and BUN. Options that sum the raw mg/dL values, or that include an extra division or square the terms, do not reflect how osmoles add up in solution.