Alligation Calculator
To calculate the amounts of two solutions needed to reach a desired concentration, use the alligation formula: C1 * V1 + C2 * V2 = C * V. This formula helps you find how much of each solution to mix.
The alligation calculator is used to calculate how much of two solutions with different concentrations you need to mix to achieve a final solution with a specific concentration. For example, if you have two solutions and want a third one in between, this method helps find the right amounts. It’s commonly used in pharmacy and chemistry.
Formula:
C1 * V1 + C2 * V2 = C * V
- C1: Concentration of the first solution
- V1: Volume of the first solution
- C2: Concentration of the second solution
- V2: Volume of the second solution
- C: Desired concentration of the final mixture
- V: Total volume of the final mixture
How to Calculate ?
- Identify the concentrations (C1 and C2) of the two solutions.
- Decide the final concentration (C) and total volume (V) of the mixture you want.
- Use the formula to calculate how much of each solution (V1 and V2) to mix.
Solved Calculations:
Example 1:
Mixing two solutions:
- Solution A: 10% concentration (C1)
- Solution B: 30% concentration (C2)
Desired: 500 mL of a 20% solution (C)
| Step | Calculation | Explanation |
|---|---|---|
| 1 | Formula: C1 * V1 + C2 * V2 = C * V | Start with the formula. |
| 2 | 10 * V1 + 30 * (500 – V1) = 20 * 500 | Plug in values for C1, C2, C, and V. |
| 3 | 10 * V1 + 15,000 – 30 * V1 = 10,000 | Multiply out the terms. |
| 4 | -20 * V1 + 15,000 = 10,000 | Combine like terms. |
| 5 | -20 * V1 = -5,000 | Subtract 15,000 from both sides. |
| 6 | V1 = 250 mL | Divide by -20 to solve for V1. |
| 7 | V2 = 500 – 250 = 250 mL | Subtract V1 from total volume to find V2. |
Answer: You need 250 mL of Solution A (10%) and 250 mL of Solution B (30%).
Example 2:
Mixing two glucose solutions:
- Solution A: 5% concentration (C1)
- Solution B: 15% concentration (C2)
Desired: 1,000 mL of a 10% solution (C)
| Step | Calculation | Explanation |
|---|---|---|
| 1 | Formula: C1 * V1 + C2 * V2 = C * V | Start with the formula. |
| 2 | 5 * V1 + 15 * (1,000 – V1) = 10 * 1,000 | Plug in values for C1, C2, C, and V. |
| 3 | 5 * V1 + 15,000 – 15 * V1 = 10,000 | Multiply out the terms. |
| 4 | -10 * V1 + 15,000 = 10,000 | Combine like terms. |
| 5 | -10 * V1 = -5,000 | Subtract 15,000 from both sides. |
| 6 | V1 = 500 mL | Divide by -10 to solve for V1. |
| 7 | V2 = 1,000 – 500 = 500 mL | Subtract V1 from total volume to find V2. |
Answer: You need 500 mL of Solution A (5%) and 500 mL of Solution B (15%).
What is Alligation Calculator ?
The Alligation Calculator is a helpful tool used primarily in pharmacy and mathematics to determine the proportions of different ingredients in a mixture. It simplifies the process of calculating how to mix solutions or compounds with different concentrations to achieve a desired final concentration.
Using the alligation method involves two main steps: identifying the values of the components and applying the alligation formula. For example, if you’re mixing two solutions with different strengths, the calculator helps you figure out how much of each solution is needed to reach a specific concentration.
Final Words:
This method is widely used in pharmaceutical calculations, where precise measurements are critical. Additionally, the alligation rule helps in visualizing how the components relate to each other in terms of concentration. It can be applied to practice problems, enhancing understanding and efficiency in making dilutions or mixtures.
Overall, the Alligation Calculator is an essential resource for students and professionals dealing with mixture calculations
