One method by which the components of air can be separated is which of the following?

Introduction / Context:
Air is a mixture of gases, mainly nitrogen and oxygen, with smaller amounts of argon, carbon dioxide, and other gases. Separating these components is important for industrial uses such as supplying pure oxygen for medical purposes or nitrogen for chemical industries. This question tests your understanding of the modern industrial method used to separate the components of air.

Given Data / Assumptions:

• We are dealing with separation of air into its different gaseous components.
• Options describe various physical or chemical treatments of air.
• We assume large scale industrial separation methods, not just laboratory tests.
• The key concept is how mixtures of gases can be separated based on physical properties.

Concept / Approach:
The industrial separation of air relies on differences in boiling points of its components. Air is first cooled and compressed until it liquefies, forming liquid air. Then, using fractional distillation at very low temperatures, nitrogen, oxygen, and argon are separated as they boil off at different temperatures. Chemical methods, such as reacting oxygen with substances, are not used for complete industrial separation of all components, and simply shaking with water or caustic soda does not separate the main gases effectively.

Step-by-Step Solution:
Step 1: Recognise that air is a mixture mainly of nitrogen (about 78 percent) and oxygen (about 21 percent), with minor gases. Step 2: To separate gases in a mixture, one effective method is fractional distillation based on differences in boiling points. Step 3: In industry, air is compressed and cooled until it becomes liquid. This liquid air is then gradually warmed in a fractionating column. Step 4: Nitrogen, having the lowest boiling point among the major components, boils off first, followed by argon and then oxygen at higher temperatures. Step 5: Shaking air with caustic soda or water does not yield separate liquid nitrogen and oxygen; it may absorb some gases like carbon dioxide, but does not separate the main components. Step 6: Passing air over heated magnesium would chemically remove oxygen, not cleanly separate all gases, and compressing air alone does not separate components.

Verification / Alternative check:
You can verify from industrial chemistry references that large air separation units are based on the Linde process, which uses cooling, compression, liquefaction, and fractional distillation. Diagrams of these plants show tall fractionating columns where liquid air is separated into nitrogen and oxygen streams. No major industrial process relies simply on shaking or single chemical reactions to separate all components of air on a large scale, which confirms fractional distillation of liquid air as the correct method.

Why Other Options Are Wrong:
Shaking with caustic soda solution: This can absorb acidic gases like carbon dioxide, but it does not separate nitrogen and oxygen fully.
Shaking with water: Water may dissolve small amounts of gases but cannot separate major components of air efficiently.
Passing air over heated magnesium: Magnesium can react with oxygen to form magnesium oxide, but this destroys oxygen rather than separating all gases in a controlled way.
Only compressing air at high pressure: Compression alone just increases density; without cooling and distillation it does not separate components.

Common Pitfalls:
Students sometimes think any reaction that removes oxygen counts as a method for separation of air, but proper separation should produce usable volumes of each gas. Another mistake is to confuse laboratory tests for gas absorption with industrial gas separation plants. Always think of separation in terms of physical methods like distillation when dealing with mixtures of volatile components such as gases or liquids.

Final Answer:
The components of air can be separated by fractional distillation of liquefied air.