Determining Moles of Oxygen Required for the Reaction of Sulfur Dioxide with Sulfur Trioxide

The conversion of sulfur dioxide (SO2) to sulfur trioxide (SO3) is a crucial process in the production of sulfuric acid. This reaction is often performed in the presence of a catalyst at high temperatures. To understand the stoichiometry of this reaction, let's first look at the balanced chemical equation:

2SO2 O2 → 2SO3

This equation signifies that two moles of sulfur dioxide react with one mole of oxygen to produce two moles of sulfur trioxide. The mole ratio of SO2:O2:SO3 is 2:1:2, which is crucial for any quantitative analysis involving these compounds.

Evaluating the Requirement of Oxygen for 5 Moles of Sulfur Dioxide

Given 5 moles of sulfur dioxide, we need to determine how many moles of oxygen are required for the reaction to proceed completely. Using the mole ratio from the balanced equation, we can set up a proportion:

Moles of O2 required (5 moles SO2) / 2 2.5 moles O2

Therefore, 2.5 moles of oxygen are required to completely react with 5 moles of sulfur dioxide.

Chemical Reaction and Mole Ratios

The provided chemical equation clearly indicates that the reaction can be represented as:

2SO2 (g) O2 (g) → 2SO3 (g)

From this balanced equation, it is evident that the mole ratio of SO2 to O2 is 2:1. Therefore, for every 2 moles of SO2, 1 mole of O2 is required.

Practical Application: Determination for 5.09 Moles of Sulfur Dioxide

For 5.09 moles of sulfur dioxide, we can calculate the moles of oxygen needed as follows:

Moles of O2 required for 5.09 moles SO2 (5.09 moles) / 2 2.545 moles

Thus, 2.545 moles of oxygen are needed to completely react with 5.09 moles of sulfur dioxide.

The reaction typically proceeds under controlled conditions, with sulfur dioxide reacting with oxygen in the presence of a catalyst at temperatures between 450 to 500 degrees Celsius. However, in a closed system, the reaction is often not complete and can reach equilibrium, where the forward and reverse reactions coexist.

Equilibrium Considerations

The reaction can exist in an equilibrium state, where sulfur dioxide (SO2) and oxygen (O2) react to form sulfur trioxide (SO3). While in equilibrium, the concentrations of these gases can be represented as:

2SO2 (g) O2 (g) ? 2SO3 (g)

At any given point, the proportions may not be exactly 2:1:2 due to equilibrium considerations. However, for complete reaction, the stoichiometry remains the same, and 2.5 moles of O2 would be required for 5 moles of SO2.

Understanding these stoichiometric relationships is crucial for industrial processes and laboratory experiments involving sulfur dioxide and sulfur trioxide.

Conclusion

The conversion of sulfur dioxide to sulfur trioxide is a fundamental process in chemical engineering and environmental science. By knowing the balanced chemical equation and the mole ratios, scientists and engineers can precisely control and optimize these reactions for various applications, including the production of sulfuric acid and pollution control measures.

For those studying chemistry or industrial processes, understanding the stoichiometry of reactions such as the conversion of SO2 to SO3 is essential. This knowledge can be applied to various fields, from atmospheric chemistry to process engineering.