Problem 148 - A Complete Resource Book in Chemistry for JEE Main

Question

If 1000 cc of air is passed again and again over heated \(\mathrm{Cu}\) and \(\mathrm{Mg}\) till the reduction in volume stops, the volume finally obtained would be approx. (a) \(800 \mathrm{cc}\) (b) \(200 \mathrm{cc}\) (c) \(10 \mathrm{cc}\) (d) zero \(\mathrm{cc}\)

Step-by-Step Solution

Answer

(a) 800 cc

Step 1: Examine the Components of Air

Air consists mainly of nitrogen (approximately 78%) and oxygen (approximately 21%), with a small amount of other gases such as carbon dioxide and argon. Only the oxygen component reacts in this setup.

Step 2: Reaction of Cu and Mg with Oxygen

When air is passed over heated copper (Cu) and magnesium (Mg), these elements react with oxygen to form oxides. Copper reacts with oxygen to form copper(II) oxide (CuO), and magnesium reacts with oxygen to form magnesium oxide (MgO). Both metals effectively remove oxygen from the air.

Step 3: Calculate the Volume of Oxygen in the Air

Given that 21% of air is oxygen, the volume of oxygen in 1000 cc of air is calculated as follows:\[ \text{Volume of Oxygen} = 0.21 \times 1000 = 210 \text{ cc} \]

Step 4: Determine the Remaining Volume After Reaction

Since copper and magnesium will completely react with all the oxygen, only nitrogen and the trace gases will be left. The remaining volume would be the volume of nitrogen and other minor components:\[ 1000 \text{ cc} - 210 \text{ cc} = 790 \text{ cc} \]Approximately, the answer would be 800 cc as nitrogen constitutes almost all of the remaining volume.

Key Concepts

Air Composition

Air is a mixture of various gases. The main components are nitrogen and oxygen. Nitrogen makes up about 78% of air, while oxygen comprises roughly 21%. There are also trace amounts of other gases such as argon and carbon dioxide, but these are present in much smaller amounts. When analyzing chemical reactions involving air, it's important to focus on its reactive constituents. In many experiments, nitrogen is considered inert and does not participate in the chemical reactions. However, oxygen is quite reactive, especially with metals, and plays a crucial role in various reactivity studies. Understanding air composition is essential for calculating how much of each component is available for reactions.

Copper and Magnesium Reactions

When heated, both copper (Cu) and magnesium (Mg) react readily with oxygen, forming their respective oxides. Copper reacts with oxygen to form copper(II) oxide

• Reaction: \( 2 ext{Cu} + ext{O}_2 ightarrow 2 ext{CuO} \)

Magnesium, on the other hand, reacts with oxygen to produce magnesium oxide

• Reaction: \( 2 ext{Mg} + ext{O}_2 ightarrow 2 ext{MgO} \)

Both reactions are exothermic, meaning they release energy in the form of heat. These metals effectively capture and remove oxygen when passed over them in a heated state. This reactive behavior is utilized in experiments to determine the volume of non-oxygen gases remaining in a sample of air.

Oxygen Removal

In the exercise involving air passed over copper and magnesium, oxygen is selectively removed from the air. The metals react with the oxygen, forming oxides, and thus reduce the overall volume of air. The key aspect of this process is the complete removal of oxygen. Once oxygen is removed, the remaining air is composed primarily of nitrogen and other trace gases. Since nitrogen does not react with these metals, it stays in the gaseous phase. This concept of oxygen removal is pivotal in experiments where the aim is to assess how much oxygen is present in a gaseous mixture or how much volume it occupies. By eliminating oxygen, it allows us to focus on the inert components.

Volume Calculation

The calculation of the final air volume after oxygen removal is straightforward if you know the composition percentages. Since oxygen accounts for 21% of air's volume, in a 1000 cc sample of air, the volume of oxygen is:

• Volume of Oxygen = \(0.21 \times 1000 = 210\) cc

Once all the oxygen is removed via reaction with heated copper and magnesium, the remaining volume consists mostly of nitrogen, which is inert. The remaining volume is therefore:

• Remaining Volume = \(1000 \text{ cc} - 210 \text{ cc} = 790\) cc

Generally, we round this up for simplicity, considering that the presence of other inert gases like argon is minimal, to an approximate final volume of 800 cc. This calculation shows how chemical reactions can be used not only to understand air composition but also to determine the reactive volume and the subsequent volume reduction.