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) \(\frac{42.414}{16}\)

Short answer

Option (a) \(\frac{22.414}{16}\) is correct.

Step-by-step solution

Write the balanced chemical equation

The chemical reaction for the combustion of sulphur in oxygen is given by: \[ S + O_2 \rightarrow SO_2 \] This equation is balanced as one sulphur atom reacts with one molecule of oxygen to form one molecule of sulfur dioxide.

Calculate moles of sulphur

To find the moles of sulphur, we use its atomic weight: \(32 \text{ g/mol}\). Given that the mass of sulphur is 2 grams, the moles of sulphur are calculated as: \[ \text{Moles of S} = \frac{2 \text{ g}}{32 \text{ g/mol}} = 0.0625 \text{ mol} \]

Relate moles of sulphur to moles of oxygen

The balanced equation shows that one mole of sulphur reacts with one mole of oxygen. Therefore, 0.0625 moles of sulphur will react with 0.0625 moles of oxygen.

Convert moles of oxygen to volume at STP

At standard temperature and pressure (STP), 1 mole of any gas occupies 22.414 litres. Hence, the volume of 0.0625 moles of oxygen is: \[ V = 0.0625 \times 22.414 \text{ L/mol} \approx 1.40087 \text{ L} \]

Check answer against options

The calculated volume of oxygen is closest to the option: \(\frac{22.414}{16} = 1.400875 \text{ litres}\). Thus, option (a) is the correct answer.

Key concepts

Chemical Reactions

Chemical reactions are processes where substances, known as reactants, transform into different substances called products. During a chemical reaction, bonds between atoms in the reactants are broken and new bonds are formed to create the products. In the case of sulfur burning in oxygen, sulfur reacts with oxygen to form sulfur dioxide, a chemical reaction that can be represented by the equation \( S + O_2 \rightarrow SO_2 \).
- Here, \( \text{S} \) (sulfur) and \( \text{O}_2 \) (oxygen) are the reactants.- \( \text{SO}_2 \) (sulfur dioxide) is the product.
Chemical reactions are central to the study of chemistry as they explain how and why substances interact the way they do. They can involve changes in energy, states of matter, and mass. Understanding chemical reactions allows us to predict product formation and understand real-life processes, such as combustion.

Molar Volume

Molar volume refers to the volume occupied by one mole of a gas at a given temperature and pressure. At standard temperature and pressure (STP), which is 0°C (273.15 K) and 1 atmosphere (atm) of pressure, one mole of any ideal gas occupies 22.414 litres. This principle helps chemists relate the amount of gas involved in reactions to their volume.
- For our problem, knowing the molar volume is key to finding out how much oxygen gas (volume-wise) reacts with sulfur. - Calculating the molar volume at STP is straightforward because it assumes ideal gas behavior, making this a handy concept for solving gas-related problems in stoichiometry.
Molar volume is particularly useful in understanding fuel combustion and respiration processes, where gases are often involved. Recognizing and using the molar volume allows you to convert between moles of gas and volume, an important skill in many chemical calculations.

Balanced Equations

Balanced equations are crucial for accurately representing chemical reactions. They ensure that the number of atoms for each element is the same on both sides of the equation, respecting the Law of Conservation of Mass. In our example, the equation \( S + O_2 \rightarrow SO_2 \) is balanced, as it shows an equal number of sulfur and oxygen atoms among reactants and products.
- Each side of the equation has one sulfur atom and two oxygen atoms. - Balancing equations is necessary because it shows the exact ratio in which reactants combine to form products.
This balance allows us to use stoichiometry, which is the method of calculating the amounts (in moles or grams) of reactants and products in a chemical reaction. A properly balanced equation is the foundation of any stoichiometric calculation. It helps chemists and students alike understand the quantitative aspects of chemical reactions.

Mole Concept

The mole concept is a fundamental principle in chemistry, allowing chemists to count particles by weighing them. One mole represents \(6.022 \times 10^{23}\) entities (Avogadro's number), which can be atoms, molecules, ions, or electrons. This unit bridges the atomic scale to the observable scale.
In our problem, converting grams of sulfur to moles was essential:- Given the atomic weight of sulfur is 32 g/mol, two grams of sulfur corresponds to \( \frac{2 \text{ g}}{32 \text{ g/mol}} = 0.0625 \text{ moles} \).- The balanced equation then tells us that 0.0625 moles of sulfur require 0.0625 moles of oxygen to react entirely.
The mole concept simplifies chemical calculations, enabling easy conversion between mass and the number of particles. It's essential for determining proportions in reactions, calculating yields, and understanding chemical processes at a molecular level.