Determine dilution factor based on volume of original sample and volume of diluent
The correct answer and explanation is:
Correct answer:
The dilution factor (DF) is calculated as the ratio of the total volume after dilution to the volume of the original sample.
Mathematically: Dilution Factor=Volume of original sample+Volume of diluentVolume of original sample\text{Dilution Factor} = \frac{\text{Volume of original sample} + \text{Volume of diluent}}{\text{Volume of original sample}}
Explanation (about 300 words):
When you dilute a sample, you add a certain amount of diluent (like water or buffer) to the original sample to decrease its concentration. The dilution factor tells you by how much the original sample has been diluted.
- Understanding the volumes:
- Volume of original sample (V₁): This is the volume of the undiluted sample before adding any diluent.
- Volume of diluent (V₂): This is the volume of liquid added to dilute the original sample.
- Total volume after dilution (V_total): This is the sum of the original sample volume and the diluent volume.
- Dilution factor calculation: The dilution factor is how much the sample is “spread out” or diluted. Since dilution is the increase in volume while keeping the amount of solute constant, the factor is: DF=VtotalV1=V1+V2V1DF = \frac{V_{\text{total}}}{V_1} = \frac{V_1 + V_2}{V_1} For example, if you have 1 mL of sample (V₁ = 1 mL) and add 9 mL of diluent (V₂ = 9 mL), the total volume is 10 mL, and DF=101=10DF = \frac{10}{1} = 10 This means the sample is diluted 10-fold.
- Importance in calculations: The dilution factor is important when calculating the concentration of substances in the original sample after measuring in the diluted sample. For instance, if you measure the concentration in the diluted sample, multiply it by the dilution factor to find the concentration in the original sample.
- Related concepts:
- Dilution ratio: Sometimes used interchangeably, but dilution factor is more precise for calculations.
- Serial dilutions: When multiple dilutions are performed sequentially, multiply the dilution factors of each step to get the overall dilution factor.
Summary:
The dilution factor is the ratio of the total volume after dilution to the original sample volume. It quantifies how much the original sample concentration has been reduced by the addition of diluent, and it’s critical for accurately interpreting measurements from diluted samples.