# How to Calculate Plasma Osmolarity

by Allan Robinson, Demand Media

Osmolarity is a measure of the concentration of the solutes in a solution, and is measured in moles of solute particles in a given volume of solution. Plasma osmolarity refers specifically to the osmolarity of blood plasma and typically measures only specific solutes. It is a common diagnostic tool for identifying electrolyte imbalances, especially low blood sodium (hyponatremia). Plasma osmolarity may be calculated from the concentrations of the individual solutes.

### Items you will need

• Calculator With Statistical Functions
Step 1

Obtain the concentrations for the solutes you wish to calculate the plasma osmolarity for. The most common solutes of interest include sodium (Na+), glucose and blood urea nitrogen (BUN).

Step 2

Convert mg/dl to the standard units of millimoles per liter (mmol/L). To convert deciliters to liters, multiply by 10. To convert milligrams to millimoles, divide by the molecular weight. Therefore, to convert mg/dl to mmol/L, multiply by 10/Ds, where Ds is the molecular weight of the solute s.

Step 3

Calculate 10/Ds where Ds is the molecular weight for glucose and BUN. The molecular weight for glucose is 180, so 10/Ds for glucose is 1/18. BUN is diatomic nitrogen (N2), so its molecular weight is 28. Therefore, 10/Ds for BUN is 10/28 = 1/2.8. We now have a plasma molarity of [Na+] + [Glucose]/18 + [BUN]/2.8, where [Na+], [Glucose] and [BUN] indicate the respective concentrations of these solutes in standard units of mmol/L.

Step 4

Calculate the plasma osmolarity from the plasma molarity obtained in Step 3, [Na+] + [Glucose]/18 + [BUN]/2.8. To convert to osmolarity, multiply the molarity values by the number of particles each of these solutes dissociates into. Na+ dissociates into two particles, while glucose and BUN each dissociate into one particle. Thus, the osmolarity is 2[Na+] + [Glucose]/18 + [BUN]/2.8.

Step 5

Use standard reference values for the calculation of plasma osmolarity. The standard Na+ concentration is 140 millimoles/liter (mmol/L), the standard glucose concentration is 150 milligrams/deciliter (mg/dl) and the standard BUN concentration is 20 mg/dl. From the equation 2[Na+] + [Glucose]/18 + [BUN]/2.8 in Step 4, we have 2(140) + (150/18) + (20/2.8) = 280 + 8.3 + 7.1 = 295. A typical plasma osmolarity is therefore about 295 mmol/L.

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