Understanding the Dilution Equation

The dilution equation is a fundamental formula in pharmaceutical calculations, chemistry, and biology. It is used to prepare solutions of a desired concentration by diluting a more concentrated solution. The equation is:

Where:

• C₁: Initial concentration of the solution (before dilution)
• V₁: Volume of the initial solution used
• C₂: Final concentration of the solution (after dilution)
• V₂: Final total volume of the solution

This equation is based on the principle that the total amount of solute remains constant before and after dilution. By rearranging the formula, you can solve for any of the variables:

Examples and Solutions

Below are practical examples, including unit conversions and detailed explanations:

Example 1:

You have 10 mL of a 20% solution. How much total volume in liters is needed to dilute it to a 5% solution?

1. Use the formula:
   
2. Convert mL to liters:
   

Answer: 0.04 L (40 mL).

Example 2:

You need 500 mL of a 0.2% solution. How much 10% stock solution is required in liters?

1. Use the formula:
   
2. Convert mL to liters:
   

Answer: 0.01 L (10 mL).

Example 3:

You have 2 L of a 15% solution. How much distilled water must you add to make a 3% solution?

1. Calculate the final volume:
   
2. Calculate the water to add:
   

Answer: Add 8 L of water.

Example 4:

A pharmacist has 250 mL of a 25% solution. They dilute it to 2 L. What is the final concentration?

1. Convert 2 L to mL:
   
2. Use the formula:
   

Answer: 3.125%.

Example 5:

You need to prepare 0.5 L of a 0.1% solution from a 50% stock solution. How much stock is needed in mL?

1. Convert 0.5 L to mL:
   
2. Use the formula:
   

Answer: 1 mL.

Example 6:

A laboratory technician mixes 5 mL of a 30% solution with 95 mL of water. What is the final concentration?

1. Calculate the total volume:
   
2. Use the formula:
   

Answer: 1.5%.

Example 7:

Dilute 50 mL of a 2 mg/mL solution to a concentration of 0.1 mg/mL. What is the final volume?

1. Use the formula:
   
2. Convert mL to L:
   

Answer: 1 L (1000 mL).

Example 8:

You have 1 L of a 5% glucose solution. You need to dilute it to 2.5%. What volume in mL of distilled water should you add?

1. Calculate the final volume:
   
2. Calculate the water to add:
   
3. Convert to mL:
   

Answer: Add 1000 mL of water.

Conclusion

The dilution equation:

is an essential tool for solution preparation in the lab or clinic. Incorporating unit conversions and understanding the calculations in detail ensures accuracy in practical applications. Practice these examples to build confidence in your calculations!