Calculating Dilution Rate: A Step-by-Step Guide

The dilution rate measures the extent to which a solution has been diluted by another substance, typically a solvent or another solution. The formula to calculate dilution rate depends on the initial and final volumes and concentrations of the substances involved. Here's a step-by-step guide:

1. Understand the Components:

• Initial Solution: The concentration and volume of the initial (stock) solution.
• Diluted Solution: The concentration and volume of the final diluted solution after dilution.

2. Use the Dilution Formula:

• The dilution formula is: $C_1V_1 = C_2V_2$
• Where:
  • $C_1$ = Initial concentration of the solution.
  • $V_1$ = Initial volume of the solution.
  • $C_2$ = Final concentration of the solution after dilution.
  • $V_2$ = Final volume of the solution after dilution.

3. Calculate Dilution Rate:

• Rearrange the dilution formula to solve for the dilution rate or final concentration ($C_2$).
• The formula for dilution rate after rearranging the equation is: $C_2 = \frac{{C_1V_1}}{{V_2}}$

4. Plug in the Values:

• Input the known values into the formula.
• If you know the initial concentration ($C_1$) and volume ($V_1$) of the stock solution and the final volume ($V_2$) of the diluted solution, use the formula to calculate the final concentration ($C_2$).

5. Solve for the Dilution Rate:

• Perform the calculations using the given values to find the final concentration ($C_2$), which represents the dilution rate after the solution has been diluted.

Example:Suppose you have a 100 mL stock solution with a concentration of 0.2 M. You dilute this solution by adding water to reach a final volume of 500 mL. To find the final concentration after dilution ($C_2$):

$C_2 = \frac{{C_1V_1}}{{V_2}}$$C_2 = \frac{{0.2 \, \text{M} \times 100 \, \text{mL}}}{{500 \, \text{mL}}}$$C_2 = \frac{{20 \, \text{mol}}}{{500 \, \text{mL}}}$$C_2 = 0.04 \, \text{M}$

In this example, after dilution, the final concentration of the solution ($C_2$) is 0.04 M.

This calculation method helps determine the dilution rate or final concentration of a solution after diluting it with another substance or solvent. Adjust the formula based on the known values to solve for the unknown variable.

DF = V₁ / V₀

DF = 1000 mL / 100 mL = 10

Dilution rate = 1:10 (1 part solute to 10 parts solvent)

M₁V₁ = M₂V₂

DF = V₂ / V₀