Problem 94 - A Complete Resource Book in Chemistry for JEE Main

Question

4 moles each of \(\mathrm{SO}_{2}\) and \(\mathrm{O}_{2}\) gases are allowed to react to form \(\mathrm{SO}_{3}\) in a closed vessel. At equilibrium \(25 \%\) of \(\mathrm{O}_{2}\) is used up. The total number of moles of all the gases at equilibrium is (a) \(6.5\) (b) \(7.0\) (c) \(8.0\) (d) \(2.0\)

Step-by-Step Solution

Answer

The total number of moles at equilibrium is 7.

Step 1: Write the Balanced Equation

The reaction between sulfur dioxide and oxygen forms sulfur trioxide: \[ 2\, \mathrm{SO}_{2} (g) + \mathrm{O}_{2} (g) \rightarrow 2\, \mathrm{SO}_{3} (g) \]

Step 2: Analyze Initial Moles

Initially, 4 moles each of \(\mathrm{SO}_{2}\) and \(\mathrm{O}_{2}\) are present.

Step 3: Calculate Moles of \(\mathrm{O}_{2}\) Used

At equilibrium, 25% of \(\mathrm{O}_{2}\) is used. So, the moles of \(\mathrm{O}_{2}\) used is: \[ 0.25 \times 4 = 1 \, \text{mole} \]

Step 4: Determine Moles of Reacted \(\mathrm{SO}_{2}\)

Since the balanced equation shows 2 moles of \(\mathrm{SO}_{2}\) react with 1 mole of \(\mathrm{O}_{2}\), the moles of \(\mathrm{SO}_{2}\) reacted are: \[ 2 \times 1 = 2 \, \text{moles} \]

Step 5: Calculate Moles of \(\mathrm{SO}_{3}\) Formed

According to the balanced equation, 2 moles of \(\mathrm{SO}_{2}\) produce 2 moles of \(\mathrm{SO}_{3}\), so 2 moles of \(\mathrm{SO}_{3}\) are formed.

Step 6: Calculate Remaining Moles

Remaining moles at equilibrium are: - \(\mathrm{SO}_{2}\): \(4 - 2 = 2\) moles- \(\mathrm{O}_{2}\): \(4 - 1 = 3\) moles- \(\mathrm{SO}_{3}\): 2 moles

Step 7: Total Moles at Equilibrium

Add all the moles to find the total moles at equilibrium: \[ 2 + 3 + 2 = 7 \, \text{moles} \]

Key Concepts

Stoichiometry

Stoichiometry plays a crucial role in understanding chemical reactions, especially when determining the amounts of reactants and products involved in chemical equilibrium. It involves the use of a balanced chemical equation to ascertain the proportions in which substances react. In a balanced reaction, the number of atoms of each element is conserved, which aligns with the law of conservation of mass.
For example, in the reaction between \( \mathrm{SO}_{2} \) and \( \mathrm{O}_{2} \) to form \( \mathrm{SO}_{3} \):\[ 2\, \mathrm{SO}_{2} (g) + \mathrm{O}_{2} (g) \rightarrow 2\, \mathrm{SO}_{3} (g) \]for every 2 moles of \( \mathrm{SO}_{2} \), 1 mole of \( \mathrm{O}_{2} \) is needed to produce 2 moles of \( \mathrm{SO}_{3} \). This reaction clearly shows stoichiometric coefficients, which tell us the ratio of the reactants to products.
Using stoichiometry, you can easily calculate the amount of each substance consumed or formed at equilibrium.

Mole Concept

The mole concept is foundational in chemistry as it provides a way to translate between the mass of a substance and the number of individual molecules or atoms it contains. One mole of any substance contains Avogadro's number of entities, which is approximately \( 6.022 \times 10^{23} \).
In our example, initially, we have 4 moles each of \( \mathrm{SO}_{2} \) and \( \mathrm{O}_{2} \). At equilibrium, knowing that 25% of \( \mathrm{O}_{2} \) is used up, we can find that 1 mole of \( \mathrm{O}_{2} \) has reacted. This decrease further affects the quantity of \( \mathrm{SO}_{2} \) and \( \mathrm{SO}_{3} \) through stoichiometric relationships.
The mole concept allows us to determine exactly how much of each product forms (2 moles of \( \mathrm{SO}_{3} \)) and how much of each reactant is left unreacted at equilibrium.

Chemical Reactions

Chemical reactions involve the transformation of reactants to products, which can often reach a state of equilibrium where no net change occurs. In this scenario, the interaction of sulfur dioxide (\( \mathrm{SO}_{2} \)) with oxygen (\( \mathrm{O}_{2} \)) forms sulfur trioxide (\( \mathrm{SO}_{3} \)).
At equilibrium, reactions don't stop; rather, the rates of the forward and reverse reactions are equal, allowing the concentrations of reactants and products to remain constant over time. By understanding this, we can grasp why only 25% of \( \mathrm{O}_{2} \) is used, influencing the amounts of \( \mathrm{SO}_{2} \) and \( \mathrm{SO}_{3} \) present at equilibrium.
Through the careful analysis of chemical reactions using stoichiometry and the mole concept, predicting the equilibrium state becomes attainable, as seen with the conclusion that the total moles of gases at equilibrium is 7.