How to Convert 25 Oleum into 90 Sulfuric Acid: A Detailed Calculation Guide

Introduction

In chemical manufacturing, understanding the conversion of oleum (also known as fuming sulfuric acid) to pure sulfuric acid (90%) is crucial for ensuring process efficiency and safety. This article delves into the precise steps and formulas required for this conversion, providing a practical guide for chemists and industrial engineers.

The Concept of Oleum and Sulfuric Acid

Oleum is a solution of sulfur trioxide (SO3) in sulfuric acid (H2SO4). A 25 oleum indicates that 25% of its mass is sulfur trioxide, with the remaining 75% being sulfuric acid. Meanwhile, 90 sulfuric acid refers to a solution where, in 100 grams, 90 grams is pure sulfuric acid.

Step-by-Step Calculation for Conversion

To determine how much water is needed to convert 25 oleum to 90 sulfuric acid, we will use the concept of a mass balance. Here's a detailed step-by-step calculation:

Define Variables

Calculate the Amount of Sulfuric Acid and Sulfur Trioxide in Oleum

From 25 oleum, the amount of so? in x grams is 0.25x grams. The remaining mass of the oleum is sulfuric acid, which is 0.75x grams.

Total Mass of the Mixture

The total mass of the mixture after adding water is x y grams.

Desired Composition of the Final Solution

The final solution needs to contain 90% sulfuric acid. This means that in 100 grams of the final solution, 90 grams is pure sulfuric acid.

Setting Up the Equation

Let the mass of sulfuric acid in the final solution be 0.9y. The mass of sulfuric acid from 25 oleum in x grams is 0.75x grams. Therefore, we set up the equation:

0.75x 0.9y

Rearranging the Equation

Expanding and rearranging gives:

0.75x 0.9y

0.75x - 0.9y 0

0.90y 0.75x

y frac{0.75}{0.90}x

y frac{1}{6}x

This means for every 6 grams of oleum, you would need to add 1 gram of water. Therefore, the ratio of oleum to water is 6:1.

Example Calculation

Let's say you choose to use 600 grams of 25 oleum. In this case:

y frac{600}{6} 100 grams

Thus, 100 grams of water is required for 600 grams of 25 oleum.

Volume Conversion and Final Calculation

Volume plays a significant role in practical applications. Assuming you want to create 90% sulfuric acid from 100 ml of 25 oleum:

Formula to Convert x Oleum into y Sulfuric Acid

The formula to convert x oleum into y sulfuric acid is given by:

y 1000.225x

Substituting x 100 ml:

y 1000.225 * 100 105.6225 ml

This means that 105.6225 ml of 90% sulfuric acid can be made from 100 ml of 25 oleum. To find the additional volume of water required:

105.6225 ml - 100 ml 5.6225 ml

Therefore, 5.6225 ml of water is needed for every 100 ml of 25 oleum to achieve 90% sulfuric acid.

Conclusion

To convert 25 oleum into 90% sulfuric acid, maintain the 6:1 ratio of oleum to water. For practical applications, the precise volume calculations are crucial for efficient and safe production.