How Dilution Calculation Works
Dilution is the process of reducing the concentration of a substance in a solution. In biology and chemistry, dilution is often used when you want to prepare a lower concentration of a stock solution. Here’s how to calculate the dilution:
- Determine the desired final concentration and the volume of the solution you want to prepare.
- Identify the concentration of the stock solution that you will dilute.
- Use the dilution formula to calculate the volume of stock solution needed for the desired dilution. The dilution formula is:
- C₁V₁ = C₂V₂
- C₁: Concentration of the stock solution (before dilution).
- V₁: Volume of the stock solution needed for the dilution.
- C₂: Desired concentration of the final solution (after dilution).
- V₂: Final volume of the solution you want to prepare (after dilution).
- Rearrange the formula to solve for the unknown. For example, to find \( V_1 \) (the volume of stock solution to use), you would rearrange the formula as:
- V₁ = \(\frac{C₂V₂}{C₁}\)
- Calculate the volume of stock solution needed and add the appropriate amount of solvent to reach the final volume.
Example Calculation
Suppose you have a stock solution with a concentration of 10 M, and you want to prepare 500 mL of a 1 M solution. Using the dilution formula:
- C₁ = 10 M
- C₂ = 1 M
- V₂ = 500 mL (final volume)
Now, solve for V₁ (the volume of stock solution needed):
- V₁ = \(\frac{C₂V₂}{C₁}\) = \(\frac{1 \, \text{M} \times 500 \, \text{mL}}{10 \, \text{M}}\) = 50 mL
This means you need 50 mL of the 10 M stock solution. To prepare the 1 M solution, you would add enough solvent (e.g., water) to make the final volume 500 mL. Subtracting the 50 mL of stock solution from the final volume, you would add 450 mL of solvent to achieve the final dilution.
Extra Tip
When preparing dilutions, it's important to add the stock solution first, then the solvent, to ensure thorough mixing. You can perform serial dilutions if you need to create very specific concentrations.
Example
Calculating Dilution
Dilution is the process of reducing the concentration of a solute in a solution, typically by adding more solvent. It is a critical concept in chemistry for preparing solutions of specific concentrations. The dilution equation helps to determine the resulting concentration or volume after dilution.
The general approach to calculating dilution includes:
- Identifying the initial concentration (C₁) and initial volume (V₁).
- Using the dilution equation to solve for the desired concentration (C₂) or volume (V₂).
- Ensuring that the units of concentration and volume are consistent (e.g., molarity for concentration and liters for volume).
Dilution Equation
The general formula for dilution calculation is:
\[ C_1 \times V_1 = C_2 \times V_2 \]Where:
- C₁ is the initial concentration of the solution.
- V₁ is the initial volume of the solution.
- C₂ is the final concentration after dilution.
- V₂ is the final volume after dilution.
Example:
If you have a 10 M (molar) solution of hydrochloric acid (HCl) and want to dilute it to a 2 M solution, and you need to prepare 500 mL of the final solution, you can calculate the volume of the original solution required using the dilution equation:
- Step 1: Use the equation \( C_1 \times V_1 = C_2 \times V_2 \). Plug in the known values: \( 10 \, \text{M} \times V_1 = 2 \, \text{M} \times 500 \, \text{mL} \).
- Step 2: Solve for \( V_1 \): \( V_1 = \frac{2 \, \text{M} \times 500 \, \text{mL}}{10 \, \text{M}} = 100 \, \text{mL} \).
- Step 3: You need 100 mL of the 10 M solution to prepare 500 mL of a 2 M solution.
Real-life Applications of Dilution
Understanding and calculating dilution has several practical applications, such as:
- Preparing solutions of precise concentrations in laboratory experiments.
- Adjusting concentrations of industrial chemicals to meet specific requirements.
- Performing titrations in analytical chemistry to determine unknown concentrations.
Common Units in Dilution
SI Unit: The standard unit of concentration is molarity (M), which is moles per liter (mol/L). Volume is typically measured in liters (L) or milliliters (mL).
Dilution can also be expressed using different units of concentration, such as percentage solutions or weight/volume ratios, but molarity (M) is the most commonly used in chemical calculations.
Common Operations with Dilution
Serial Dilution: When preparing multiple solutions with progressively lower concentrations by repeating dilution steps.
Concentration of Stock Solutions: When a concentrated stock solution is diluted to make less concentrated solutions for use in experiments.
Volume Adjustments: When adjusting volumes of solutions to achieve desired concentrations, using the dilution equation.
| Problem Type | Description | Steps to Solve | Example |
|---|---|---|---|
| Calculating Final Concentration after Dilution | Finding the final concentration of a solution after diluting it with a solvent. |
|
If you dilute a 10 M stock solution by adding 90 mL of solvent to 10 mL of the solution, the final concentration will be 1 M. |
| Determining Dilution Factor | Calculating the dilution factor needed to achieve a target concentration. |
|
If you start with a 10 M solution and need a 1 M solution, the dilution factor is 10. |
| Volume of Stock Solution Needed for Desired Concentration | Calculating how much stock solution is needed to achieve a target concentration in a final volume. |
|
If you need 50 mL of a 1 M solution from a 10 M stock, the volume of stock needed is 5 mL. |
| Real-life Applications of Dilution Calculations | Using dilution calculations for laboratory preparations, including reagents, buffers, and solutions. |
|
If you're preparing a dilution series for a bioassay, calculate the volume of concentrated stock required to achieve different concentrations. |
