Question

What is the \(\%\) of free \(\mathrm{SO}_{3}\) is an oleum that is labelled as ' \(109 \% \mathrm{H}_{2} \mathrm{SO}_{4} ?\) a. 10 b. 40 c. 20 d. 9

Short answer

The percentage of free \(\mathrm{SO}_3\) in the oleum is 9%.

Step-by-step solution

Understanding Oleum and its Labeling System

Oleum is essentially a solution of sulfur trioxide (\(\mathrm{SO}_3\)) in sulfuric acid (\(\mathrm{H}_2\mathrm{SO}_4\)). When it is labeled as '109% \(\mathrm{H}_{2}\mathrm{SO}_{4}\),' it doesn't actually mean the solution has 109 grams of \(\mathrm{H}_{2}\mathrm{SO}_{4}\) per 100 grams of solution. Instead, it means the sulfur trioxide content is such that if all \(\mathrm{SO}_3\) were to convert to \(\mathrm{H}_2\mathrm{SO}_4\), it would correspond to 109% of \(\mathrm{H}_{2}\mathrm{SO}_{4}\).

Defining the Problem in Percent Terms

The percentage labeled in oleum refers to the mass of \(\mathrm{H}_{2}\mathrm{SO}_4\) that could theoretically be formed per 100 grams of oleum. Therefore, when labeled as '109% \(\mathrm{H}_2\mathrm{SO}_4\),' 9 percent represents the excess \(\mathrm{SO}_3\) that hasn't been converted to \(\mathrm{H}_2\mathrm{SO}_4\).

Calculating Free \(\mathbf{SO_3}\) in Oleum

To calculate the percentage of free \(\mathrm{SO}_{3}\), we need to calculate what part of the oleum corresponds to the 'extra' above 100%. '100%' would be the actual \(\mathrm{H}_{2}\mathrm{SO}_4\), and anything above represents free \(\mathrm{SO}_3\). Thus, '109%' means 9% is the free \(\mathrm{SO}_3\).

Conclusion

The problem asks for the percentage of free \(\mathrm{SO}_3\) in the oleum labeled as '109% \(\mathrm{H}_{2}\mathrm{SO}_4\)'. From the determination, the free \(\mathrm{SO}_3\) corresponds to the excess percentage above 100. Therefore, the correct percentage of free \(\mathrm{SO}_3\) is 9%.

Key concepts

Oleum

Oleum is a fascinating and somewhat mysterious chemical substance that plays a significant role in industrial chemistry. It is essentially a solution containing sulfur trioxide ( SO_3 ) dissolved in sulfuric acid ( H_2SO_4 ). This solution is also known as fuming sulfuric acid due to its ability to release smoke or fumes when exposed to air. These fumes are a result of SO_3 escaping from the liquid solution.
Oleum is not measured in the typical way like other chemical solutions. Instead of specifying the exact concentration of SO_3 in the solution, it is labeled with a percentage that indicates the theoretical amount of H_2SO_4 that could be formed if all free SO_3 were converted. This unique measurement system helps chemists predict the solution's behavior and potential chemical reactions.

Sulfur Trioxide

Sulfur trioxide ( SO_3 ) is a key component of oleum and plays a critical role in the production of sulfuric acid. It is a reactive compound known for its powerful acid-producing capabilities. When dissolved in water, SO_3 forms H_2SO_4 , a highly exothermic reaction that releases a lot of energy.
This reactivity means that SO_3 is seldom found in pure form. Instead, it is often managed within solutions like oleum, where it is stabilized by the sulfuric acid. In industrial applications, this setup is beneficial, allowing for safer and more controlled processes. In oleum labeling, the amount of SO_3 present directly affects the labeled percentage, as it represents the potential additional H_2SO_4 that could be formed.

Percentage Composition

The concept of percentage composition is central to understanding labeling systems like that of oleum. It involves calculating what fraction of a chemical species exists within a compound or mixture compared to the whole. In the case of oleum, the label given (e.g., '109% H_2SO_4 ') is not a straightforward measurement of mass. Instead, it converts the SO_3 present into an equivalent amount of H_2SO_4 , should all SO_3 be converted.
The percentage exceeding 100% indicates the amount of SO_3 that is not yet converted into H_2SO_4 . Therefore, in a 109% H_2SO_4 labeled oleum, 9% of that composition denotes free, unreacted SO_3 . This labeling allows chemists to accurately gauge potential reactions and the concentration of usable acid in such sulfur trioxide enriched solutions.

Conversion Calculations

Conversion calculations are essential for deciphering oleum percentages and understanding their implications in practical applications. These calculations revolve around transforming one chemical compound into another, governed by the stoichiometry of the reaction.
For oleum, the key conversion is from sulfur trioxide ( SO_3 ) to sulfuric acid ( H_2SO_4 ). This conversion involves a reaction that is fundamental in the labeling of oleum. The percentage value exceeding 100% denotes the extent of these potential conversions.
In practical terms, if you have a labeled oleum solution, determining unconverted SO_3 involves straightforward arithmetic: subtracting 100% from the total percentage. Hence, for oleum labeled as 109%, a simple calculation illustrates that 9% is attributed to unreacted SO_3 . This arithmetic is crucial for industries relying on precise acid concentrations to maintain efficiency and safety in chemical processes.