Problem 105 - A Complete Resource Book in Chemistry for JEE Main

Question

What is the volume (in litre) of oxygen required at STP to completely convert \(1.5\) moles of sulphur to sulphur dioxide? (a) \(33.6\) (b) \(43.6\) (c) \(11.2\) (d) \(23.6\)

Step-by-Step Solution

Answer

The volume of oxygen required is 33.6 liters.

Step 1: Write the chemical reaction

To find the volume of oxygen required, first note the chemical reaction involved. Sulfur ( \(S\)) reacts with oxygen ( \(O_2\)) to form sulfur dioxide ( \(SO_2\)). The balanced equation is: \[ S + O_2 \rightarrow SO_2 \]

Step 2: Relate moles of reactants to volume

According to the balanced equation, 1 mole of sulfur ( \(S\)) reacts with 1 mole of oxygen ( \(O_2\)) to produce 1 mole of sulfur dioxide ( \(SO_2\)). Thus, to convert 1.5 moles of sulfur, you need 1.5 moles of oxygen.

Step 3: Convert moles of gas to volume at STP

At standard temperature and pressure (STP), 1 mole of any gas occupies 22.4 liters. Therefore, to find the volume of 1.5 moles of oxygen, multiply the number of moles by 22.4 L/mol: \[ 1.5 \, \text{moles} \times 22.4 \, \text{L/mol} = 33.6 \, \text{liters} \]

Key Concepts

Stoichiometry

When it comes to chemistry problems, stoichiometry is a term you'll often encounter. It's the process of using a chemical equation to calculate the quantities of reactants and products involved in a reaction. The key here is understanding that chemical reactions follow a balanced equation. This means, for every mole of a substance that reacts, a specific number of moles of another substance will also react or be produced.

For instance, in our exercise, we have the equation:

• Reactants: Sulfur (\(S\)) combines with Oxygen (\(O_2\))
• Product: Forming Sulfur Dioxide (\(SO_2\))

The balanced equation is crucial since it shows that one mole of sulfur reacts with one mole of oxygen. So, if we want to convert 1.5 moles of sulfur, we will need exactly 1.5 moles of oxygen. Stoichiometry helps us predict the amounts of materials needed and produced, which is essential for both theoretical calculations and real-life applications in laboratories.

Chemical Reactions

Chemical reactions underpin everything in chemistry, and they're the reason why stoichiometry is even necessary. A chemical reaction occurs when substances, known as reactants, transform into different substances, called products. This transformation is represented by a chemical equation.

Several key elements make up a chemical reaction:

• Reactants: Substances that start the reaction (\(S\) and \(O_2\) in our example)
• Products: Substances formed as a result of the reaction (\(SO_2\))
• Coefficients: Numbers before compounds in a balanced equation indicating the number of moles

In our example, the reaction of sulfur with oxygen to form sulfur dioxide is a straightforward combination reaction. It is important to balance the equation to ensure the law of conservation of mass is followed. This law states that matter cannot be created or destroyed in a chemical reaction, hence every atom in the reactants must be accounted for in the products. Thus, balancing the equation ensures all atoms balance out, which gives us a one-to-one-to-one relationship in this particular scenario.

Gas Laws

Understanding gas laws is critical when dealing with problems involving gases, like finding the volume of oxygen needed in a reaction at standard temperature and pressure (STP). The significant law here is Avogadro's Law, which states that equal volumes of gases, at the same temperature and pressure, contain an equal number of molecules. At STP, one mole of any gas occupies 22.4 liters.

To apply this in our exercise, we use the relationship:

• 1 mole of any gas = 22.4 L at STP
• From stoichiometry, we know 1.5 moles of\(O_2\) is required
• Using Avogadro's concept, 1.5 moles of \(O_2\) = 1.5 × 22.4 liters

This results in 33.6 liters of oxygen needed, illustrating how gas laws simplify calculations involving gases. Knowing and applying these concepts provides us the tools to effectively solve chemistry problems involving gases.