Molarity and Dilutions

Molarity (M) and Dilutions

In clinical settings, we rarely work with pure solids. Instead, we use solutions—homogeneous mixtures where a solute (like a drug) is dissolved in a solvent (usually water).

Defining Concentration

Molarity (M): The most common chemical unit for concentration, defined as the moles of solute per liter of solution.
Formula: M = moles of solute / Liters of solution.

Clinical Calculation Examples

✏️ Practice Problem 1: Calculating Concentration
A solution contains 30.5 g of NaCl dissolved in 500 mL of water. What is the Molarity? (Molar Mass of NaCl = 58.44 g/mol). Click for Solution

1. Convert grams to moles: 30.5 g * (1 mol / 58.44 g) = 0.522 mol NaCl.
2. Convert mL to L: 500 mL = 0.500 L.
3. Calculate Molarity: 0.522 mol / 0.500 L = 1.04 M NaCl.

✏️ Practice Problem 2: IV Fluid Delivery
A patient needs 25.0 g of glucose (C₆H₁₂O₆). Your IV bag is labeled 0.500 M glucose. How many Liters must be administered? (Molar Mass of glucose = 180.18 g/mol). Click for Solution

1. Moles needed: 25.0 g * (1 mol / 180.18 g) = 0.139 mol glucose.
2. Use Molarity to find Volume: 0.139 mol * (1 L / 0.500 mol) = 0.278 L (or 278 mL).

The Dilution Equation (C₁V₁ = C₂V₂)

In the lab or pharmacy, we often start with a concentrated stock solution and add solvent to create a more dilute working solution. Because the total moles of solute do not change during dilution, we use the equation:

C₁V₁ = C₂V₂

✏️ Practice Problem 3: Diluting Stock Solutions
How many mL of a 6.00 M NaOH stock solution are needed to prepare 500.0 mL of a 0.300 M NaOH solution?. Click for Solution

C₁ = 6.00 M | V₁ = ? | C₂ = 0.300 M | V₂ = 500.0 mL.
V₁ = (C₂ * V₂) / C₁
V₁ = (0.300 M * 500.0 mL) / 6.00 M = 25.0 mL.

Summary for Lab Practice

If given Mass/Moles and Volume ➞ Calculate Molarity.
If given Molarity and Volume ➞ Calculate Mass/Moles.
If given Molarity and Mass ➞ Calculate Volume.

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