Mastering the calculation of solution preparation from concentrated stocks is essential in chemistry. This process ensures precise dilutions for accurate experimental results.
Understanding dilution calculations involves applying key formulas and interpreting concentration values. This article covers formulas, tables, and real-world examples for expert comprehension.
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- Calculate the volume of stock solution needed to prepare 500 mL of 0.1 M NaCl from a 1 M stock.
- Determine the final concentration after diluting 250 mL of 2 M HCl to 1 L.
- Find the volume of 5 M glucose stock required to make 200 mL of 0.5 M glucose solution.
- Calculate the dilution factor when 100 mL of 3 M sulfuric acid is diluted to 1 L.
Comprehensive Tables of Common Concentrations and Volumes for Dilution Calculations
| Stock Concentration (M) | Desired Concentration (M) | Volume of Final Solution (mL) | Volume of Stock Solution Required (mL) | Volume of Diluent Required (mL) | Dilution Factor (DF) |
|---|---|---|---|---|---|
| 1.0 | 0.1 | 1000 | 100 | 900 | 10 |
| 2.0 | 0.5 | 500 | 125 | 375 | 4 |
| 5.0 | 1.0 | 250 | 50 | 200 | 5 |
| 10.0 | 2.0 | 1000 | 200 | 800 | 5 |
| 0.5 | 0.05 | 200 | 20 | 180 | 10 |
| 3.0 | 0.3 | 100 | 10 | 90 | 10 |
| 4.0 | 1.0 | 500 | 125 | 375 | 4 |
| 6.0 | 0.6 | 1000 | 100 | 900 | 10 |
| 8.0 | 2.0 | 250 | 62.5 | 187.5 | 4 |
| 1.5 | 0.15 | 300 | 30 | 270 | 10 |
| 7.0 | 1.4 | 700 | 140 | 560 | 5 |
| 9.0 | 3.0 | 600 | 200 | 400 | 3 |
| 0.2 | 0.02 | 1000 | 100 | 900 | 10 |
| 12.0 | 1.2 | 500 | 50 | 450 | 10 |
| 15.0 | 3.0 | 1000 | 200 | 800 | 5 |
Fundamental Formulas for Dilution Calculations
Calculating the preparation of solutions from a concentrated stock primarily involves the dilution equation, which relates concentrations and volumes before and after dilution.
Dilution Equation:
- C1: Initial concentration of the stock solution (mol/L or Molarity)
- V1: Volume of the stock solution required (mL or L)
- C2: Desired concentration of the diluted solution (mol/L or Molarity)
- V2: Final volume of the diluted solution (mL or L)
This formula assumes volumes are additive and the solute amount remains constant during dilution.
Explanation of Variables and Common Values:
- C1: Typically ranges from 0.1 M to 15 M in laboratory stock solutions.
- V1: Calculated volume of stock solution needed, usually in milliliters or liters.
- C2: Desired working concentration, often much lower than C1.
- V2: Final volume of the diluted solution, commonly prepared in volumes from milliliters to liters.
Another useful concept is the Dilution Factor (DF), which quantifies how many times the stock solution is diluted:
This factor helps in quickly determining the volume of stock solution needed or the extent of dilution.
For cases where mass or molarity is not directly used, the formula can be adapted to molality or percent concentration, but molarity-based dilution is most common in aqueous solutions.
Extended Formulas for Specific Scenarios
In some cases, the preparation involves multiple dilution steps or requires accounting for density and temperature effects. Here are additional formulas:
- Multiple Dilution Steps: When diluting in stages, the overall dilution factor is the product of individual dilution factors:
- Volume Correction for Temperature: Since volume can change with temperature, the corrected volume Vcorr is:
- Where Ī² is the volumetric thermal expansion coefficient (1/Ā°C), T is the temperature of measurement, and Tref is the reference temperature.
This correction is critical in high-precision analytical chemistry.
Real-World Application Examples
Example 1: Preparing a 0.1 M Sodium Chloride Solution from a 1 M Stock
A laboratory technician needs to prepare 500 mL of 0.1 M NaCl solution from a 1 M stock solution. Using the dilution formula:
1 M Ć V1 = 0.1 M Ć 500 mL
Solving for V1:
The technician must measure 50 mL of the 1 M stock solution and dilute it with distilled water to a final volume of 500 mL.
Volume of diluent required:
This ensures the final solution has the desired concentration.
Example 2: Diluting 250 mL of 2 M Hydrochloric Acid to 1 L
A chemist has 250 mL of 2 M HCl and wants to dilute it to 1 L. The final concentration is calculated as:
The chemist will add 750 mL of water to the 250 mL of 2 M HCl to obtain 1 L of 0.5 M HCl.
Additional Considerations for Accurate Dilution
- Volume Additivity: In many aqueous solutions, volumes are approximately additive, but for highly concentrated or non-ideal solutions, volume contraction or expansion may occur.
- Temperature Effects: Temperature changes can affect volume and concentration; always prepare solutions at or correct to a standard temperature (usually 20Ā°C or 25Ā°C).
- Precision in Measurement: Use calibrated volumetric flasks and pipettes to ensure accuracy.
- Concentration Units: While molarity is common, sometimes mass/volume percent or molality is used; conversion between units may be necessary.