Understanding the Calculation of Aligation: A Comprehensive Technical Guide

Calculation of aligation is a fundamental technique used to determine proportions in mixtures. It simplifies complex blending problems in various industries.

This article explores detailed formulas, common values, and real-world applications of aligation calculation. Master this essential skill with expert insights.

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Calculate the ratio for mixing 30% and 70% concentration solutions to get 50% concentration.
Determine the quantity of 10% and 25% sugar solutions to prepare 100 liters of 18% solution.
Find the proportion of 5% and 15% salt solutions to obtain 12% concentration.
Calculate the amount of 40% and 60% alcohol solutions needed to make 200 ml of 50% solution.

Extensive Tables of Common Values in Calculation of Aligation

Aligation calculations often involve standard concentration values or percentages used in pharmaceuticals, chemistry, and food industries. The following tables provide a comprehensive reference of common values for quick and accurate aligation computations.

Concentration (%)	Common Use	Density (g/mL)	Typical Volume (mL)	Remarks
5	Salt solution	1.02	100	Low concentration saline
10	Sugar solution	1.04	100	Standard sweetener mix
15	Salt solution	1.05	100	Moderate saline
20	Alcohol solution	0.98	100	Low strength ethanol
25	Sugar solution	1.07	100	High sweetener concentration
30	Alcohol solution	0.95	100	Medium strength ethanol
40	Alcohol solution	0.92	100	High strength ethanol
50	Alcohol solution	0.89	100	Very high strength ethanol
60	Alcohol solution	0.85	100	Concentrated ethanol
70	Alcohol solution	0.83	100	Near pure ethanol
80	Alcohol solution	0.79	100	Highly concentrated ethanol
90	Alcohol solution	0.78	100	Almost pure ethanol
100	Pure substance	Varies	Varies	Absolute concentration

These values serve as a baseline for aligation calculations, enabling professionals to quickly estimate mixture ratios without extensive trial and error.

Fundamental Formulas for Calculation of Aligation

Aligation is a mathematical method used to find the ratio in which two or more ingredients at different concentrations must be mixed to obtain a mixture of desired concentration. The core principle is based on the difference between the concentrations of the components and the target concentration.

Basic Aligation Formula

The primary formula for aligation is:

Ratio of quantities = (C2 – Cx) : (Cx – C1)

C1 = Concentration of the first component (lower concentration)
C2 = Concentration of the second component (higher concentration)
Cx = Desired concentration of the mixture

This formula calculates the ratio of the quantities of two solutions or substances to be mixed.

Explanation of Variables and Their Common Values

C1: Usually the lower concentration component, e.g., 5%, 10%, or 20%.
C2: The higher concentration component, e.g., 40%, 50%, or 70%.
Cx: The target concentration, which must lie between C1 and C2.

It is critical that C1 < Cx < C2 for the formula to be valid. If the desired concentration is outside this range, aligation cannot be applied directly.

Calculating Quantities from Ratios

Once the ratio is determined, the actual quantities can be calculated if the total volume or mass is known:

Quantity of C1 = (Total quantity) × (C2 – Cx) / (C2 – C1)

Quantity of C2 = (Total quantity) × (Cx – C1) / (C2 – C1)

These formulas ensure the total quantity is split correctly to achieve the desired concentration.

Aligation Medial and Allegation Alternate

Aligation has two classical methods:

Aligation Medial: Used to find the mean concentration when mixing known quantities of different concentrations.
Aligation Alternate: Used to find the ratio of quantities to mix to get a desired concentration.

Aligation Medial formula:

Cx = (C1 × Q1 + C2 × Q2) / (Q1 + Q2)

Q1 and Q2 are quantities of components with concentrations C1 and C2 respectively.

This formula calculates the resulting concentration after mixing known quantities.

Real-World Applications of Calculation of Aligation

Aligation is widely used in pharmaceutical compounding, chemical manufacturing, food processing, and even metallurgy. Below are two detailed examples demonstrating its practical application.

Example 1: Pharmaceutical Solution Preparation

A pharmacist needs to prepare 500 mL of a 25% w/v (weight/volume) glucose solution. The available stock solutions are 10% and 40% glucose. Determine the volumes of each stock solution required.

Step 1: Identify variables

C1 = 10%
C2 = 40%
Cx = 25%
Total volume (Q) = 500 mL

Step 2: Calculate ratio using aligation formula

Ratio = (C2 – Cx) : (Cx – C1) = (40 – 25) : (25 – 10) = 15 : 15 = 1 : 1

Step 3: Calculate volumes

Volume of 10% solution = 500 × (40 – 25) / (40 – 10) = 500 × 15 / 30 = 250 mL

Volume of 40% solution = 500 × (25 – 10) / (40 – 10) = 500 × 15 / 30 = 250 mL

Result: Mix 250 mL of 10% glucose solution with 250 mL of 40% glucose solution to obtain 500 mL of 25% glucose solution.

Example 2: Industrial Chemical Mixing

An industrial process requires 1000 liters of a 60% acid solution. The plant has 40% and 80% acid solutions available. Calculate the volumes of each solution needed.

Step 1: Define variables

C1 = 40%
C2 = 80%
Cx = 60%
Total volume (Q) = 1000 L

Step 2: Calculate ratio

Ratio = (C2 – Cx) : (Cx – C1) = (80 – 60) : (60 – 40) = 20 : 20 = 1 : 1

Step 3: Calculate volumes

Volume of 40% solution = 1000 × (80 – 60) / (80 – 40) = 1000 × 20 / 40 = 500 L

Volume of 80% solution = 1000 × (60 – 40) / (80 – 40) = 1000 × 20 / 40 = 500 L

Result: Mix 500 liters of 40% acid solution with 500 liters of 80% acid solution to produce 1000 liters of 60% acid solution.

Advanced Considerations and Extended Applications

While the basic aligation method is straightforward, real-world scenarios often require adjustments for factors such as density differences, temperature effects, and non-ideal mixing behavior.

Density Corrections: When mixing liquids of different densities, volume-based calculations may not be accurate. Mass-based calculations using density values ensure precision.
Temperature Effects: Concentrations can vary with temperature due to expansion or contraction. Adjustments may be necessary for temperature-sensitive processes.
Multiple Component Mixtures: Aligation can be extended to mixtures involving more than two components by iterative application or matrix methods.

For example, in pharmaceutical compounding, precise mass measurements and density corrections are critical to ensure dosage accuracy and regulatory compliance.

Additional Resources and Authoritative References

FDA Pharmaceutical Quality Resources – Guidelines on pharmaceutical compounding and mixture calculations.
Chemistry Explained: Concentration – Detailed explanations of concentration concepts and calculations.
ScienceDirect: Allegation Method – Technical articles on aligation and mixture calculations.
PharmaGuideline: Allegation Method in Pharmacy – Practical examples and formulas for pharmaceutical applications.

Summary of Key Points for Expert Application

Aligation is a ratio-based method to mix two solutions of different concentrations to achieve a desired concentration.
The fundamental formula involves the difference between concentrations and the target concentration.
Common concentrations and densities are tabulated for quick reference in various industries.
Real-world examples demonstrate practical application in pharmaceuticals and industrial chemistry.
Advanced considerations include density corrections, temperature effects, and multi-component mixtures.
Authoritative resources provide further guidance and regulatory context.

Mastering the calculation of aligation empowers professionals to optimize mixture formulations efficiently and accurately, ensuring quality and compliance across diverse technical fields.