Problem 99 - A Complete Resource Book in Chemistry for JEE Main

Question

Two grams of sulphur is completely burnt in oxygen to form \(\mathrm{SO}_{2}\), In this reaction, what is the volume (in litres) of oxygen consumed at STP? (At. wt of sulphur and oxygen are 32 and 16 respectively) (a) \(\frac{22.414}{16}\) (b) \(\frac{16}{22.441}\) (c) \(\frac{32.414}{18}\) (d) \(\frac{42.414}{16}\)

Step-by-Step Solution

Answer

Option (a) \(\frac{22.414}{16}\) is the volume of oxygen consumed at STP.

Step 1: Understand the Reaction

The chemical reaction for the combustion of sulphur in oxygen is \( \mathrm{S} + \mathrm{O}_2 \rightarrow \mathrm{SO}_2 \). This equation shows that one mole of sulphur reacts with one mole of oxygen to produce one mole of sulphur dioxide \(\mathrm{SO}_2\).

Step 2: Calculate Moles of Sulphur

The number of moles of a substance is given by the mass divided by the molar mass. The molar mass of sulphur is 32 g/mol. Therefore, the moles of sulphur is \( \frac{2}{32} = 0.0625 \text{ moles} \).

Step 3: Find Moles of Oxygen Consumed

According to the stoichiometry of the reaction, 1 mole of sulphur reacts with 1 mole of oxygen. Therefore, the moles of oxygen consumed is also 0.0625 moles.

Step 4: Calculate Volume of Oxygen Consumed at STP

At standard temperature and pressure (STP), 1 mole of a gas occupies 22.414 L. Thus, the volume of oxygen consumed is \( 0.0625 \text{ moles} \times 22.414 \text{ L/mole} = 1.400875 \text{ L} \).

Step 5: Simplify the Expression

We are given options involving fractional forms, so check which option matches the volume of 1.400875 L. Simplifying \( \frac{22.414}{16} \approx 1.400875 \), which matches the calculated volume.

Key Concepts

Chemical Reaction

When it comes to understanding chemical reactions, we must first grasp what is happening on a molecular level. In the exercise, the reaction involves sulphur (S) burning in oxygen (O₂) to form sulphur dioxide (\( \mathrm{SO}_{2} \)). This is a classic combustion reaction where a substance combines with oxygen to release energy in the form of light or heat. The given reaction can be written as \( \mathrm{S} + \mathrm{O}_{2} \rightarrow \mathrm{SO}_{2} \).
In this context:

• The reactants are sulphur and oxygen.
• The product is sulphur dioxide.
• Each reactant and product is represented in moles, a fundamental unit in chemistry.

In a balanced chemical equation like the one given, the coefficients (numbers before the chemical formulas) represent the relative amounts of moles of each substance involved in the reaction. Here, 1 mole of sulphur reacts with 1 mole of oxygen to form 1 mole of sulphur dioxide. This stoichiometric relationship is crucial for understanding how much of each substance is used or produced.

Molecular Weight

Molecular weight, often synonymous with molar mass, is an important concept when dealing with chemical reactions. It allows us to convert between the mass of a substance and the number of moles, forming a bridge between the microscopic (molecules) and macroscopic (grams) worlds.
In this exercise, the atomic weights are given:

• Sulphur (S) = 32 g/mol
• Oxygen (O) = 16 g/mol

The molecular weight is simply the sum of the atomic weights of all atoms in a molecule. For instance, a molecule like sulphur dioxide (\( \mathrm{SO}_{2} \)) consists of one sulphur atom and two oxygen atoms. Thus, its molecular weight equals \( 32 + 2 \times 16 = 64 \) grams/mole.
In practical terms, finding out how many grams a mole of a certain substance weighs helps in calculating the moles if you have its mass, like with the 2 grams of sulphur in our exercise. By using the formula \( \text{Number of moles} = \frac{\text{Mass in grams}}{\text{Molar mass}} \), you can solve many stoichiometric problems.

Mole Concept

The mole concept is a fundamental principle in chemistry. It defines the quantity of a substance. One mole contains Avogadro's number of entities (approximately \(6.022 \times 10^{23}\)), whether atoms, molecules, ions, or electrons.
In chemistry, the mole bridges the gap between the atomic world (individual atoms and molecules) and the amounts of substances we use and measure in the lab. In our exercise, sulphur is measured in grams, but its reaction with oxygen is understood in moles. Therefore, by calculating the moles of sulphur, we can predict the amount of oxygen needed and sulphur dioxide produced.

• 2 grams of sulphur \( \rightarrow \) \( \frac{2}{32} = 0.0625 \) moles of sulphur
• Since one mole of sulphur reacts with one mole of oxygen, \(0.0625\) moles of sulphur means \(0.0625\) moles of oxygen is consumed.

This conversion is essential in calculating the volume of gas used or produced in reactions under the mole concept.

Standard Temperature and Pressure (STP)

Standard temperature and pressure (STP) provide a reference point for us to measure gases. It's defined as 0°C (273.15 K) and 1 atm pressure, where gases exhibit consistent and predictable behaviors.
Under these conditions, one mole of any ideal gas occupies 22.414 liters. This uniformity makes calculations simpler because we can directly relate the number of moles to the volume of gas. For instance, in the exercise, since the oxygen gas is at STP, we calculated that \(0.0625\) moles of oxygen equates to \(0.0625 \times 22.414\) liters of oxygen.

• Knowing that one mole of any gas at STP occupies 22.414 L helps us convert moles to volume easily.
• This simplifies real-world predictions of how much space a gas will require or the amount of gas present in a particular volume.

Hence, understanding STP is crucial to solving gas-related problems, making it an indispensable concept in chemistry.