Problem 2 - A Complete Resource Book in Chemistry for JEE Main

Question

Which of the following mixture of gases does not obey Dalton's law of partial pressure? (a) \(\mathrm{O}_{2}\) and \(\mathrm{CO}_{2}\) (b) \(\mathrm{N}_{2}\) and \(\mathrm{O}_{2}\) (c) \(\mathrm{Cl}_{2}\) and \(\mathrm{SO}_{2}\) (d) \(\mathrm{NH}_{3}\) and \(\mathrm{HCl}\)

Step-by-Step Solution

Answer

(d) \(\mathrm{NH}_{3}\) and \(\mathrm{HCl}\) do not obey Dalton's Law due to their reaction forming ammonium chloride.

Step 1: Understanding Dalton's Law of Partial Pressure

Dalton's Law of Partial Pressure states that in a mixture of non-reacting gases, the total pressure exerted is equal to the sum of the partial pressures of the individual gases. This is mathematically represented as \( P_{\text{total}} = P_{1} + P_{2} + ... + P_{n} \), where each \( P_{i} \) is the partial pressure of a gas.

Step 2: Evaluating the Gas Mixtures

We are given four mixtures of gases. To find which one does not obey Dalton's Law, determine if any gases react with each other. If they react, they won't simply mix to contribute their individual partial pressures without changing the nature of the gases involved.

Step 3: Analyzing Each Option

(a) \(\mathrm{O}_{2}\) and \(\mathrm{CO}_{2}\) do not react together. (b) \(\mathrm{N}_{2}\) and \(\mathrm{O}_{2}\) are inert under normal conditions and thus do not react. (c) \(\mathrm{Cl}_{2}\) and \(\mathrm{SO}_{2}\) might form some reaction products under specific conditions, but under standard conditions they are not highly reactive with each other. (d) \(\mathrm{NH}_{3}\) and \(\mathrm{HCl}\) readily react to form ammonium chloride \(\mathrm{NH}_{4}\mathrm{Cl}\) which is a solid.

Step 4: Identifying the Reactive Pair

Among the given combinations, the gases \(\mathrm{NH}_{3}\) and \(\mathrm{HCl}\) react with each other to form a new compound. This reaction prevents them from following Dalton's Law, as they don't exist as separate gases in the mixture once they react.

Step 5: Final Answer

The gas mixture \(\mathrm{NH}_{3}\) and \(\mathrm{HCl}\) does not obey Dalton's Law of Partial Pressure because their reaction precludes them from acting as independent non-reacting gases.

Key Concepts

Reactive and Non-Reactive Gas Mixtures

In the world of gases, it's important to differentiate between reactive and non-reactive gas mixtures. Non-reactive gases simply coexist without interacting with each other. Examples include oxygen (\(\mathrm{O}_{2}\) and carbon dioxide (\(\mathrm{CO}_{2}\)) or nitrogen (\(\mathrm{N}_{2}\)) and oxygen (\(\mathrm{O}_{2}\)). These gases don't undergo chemical reactions when mixed, which allows them to obey Dalton's Law of Partial Pressure by summing their individual pressures.

On the other hand, reactive gases interact and form new products. The mixture of ammonia (\(\mathrm{NH}_{3}\)) and hydrogen chloride (\(\mathrm{HCl}\)) is a classic example. These gases combine to form ammonium chloride (\(\mathrm{NH}_{4}\mathrm{Cl}\)), a solid, altering the original gases. This reaction prevents them from following Dalton's Law, as they don't remain as separate gases.

When evaluating gas mixtures, always consider the reactivity between the components. Reactivity affects whether the mixture will adhere to Dalton's Law or not.

Partial Pressures of Gases

Dalton's Law of Partial Pressure shines a light on how gases behave when mixed. If you mix non-reacting gases, each gas contributes to the total pressure of the mixture just like a piece of a puzzle. The formula used is \( P_{\text{total}} = P_{1} + P_{2} + ... + P_{n} \), where each \( P_{i} \) represents the pressure of an individual gas.

Think of it as a room full of balloons, each balloon filled with a different gas. The pressure in the room is the sum of all the pressures exerted by each balloon. If they don’t physically change by reacting, this rule holds true.

• Non-reacting gas examples: Oxygen (\(\mathrm{O}_{2}\)) and nitrogen (\(\mathrm{N}_{2}\)) under room conditions.
• Partial pressures add up to form the total pressure.

Keeping these basic principles in mind helps in predicting and understanding how different gases will behave when combined in different scenarios.

Gas Reactions

When gases react, the story changes dramatically. Take, for example, ammonia (\(\mathrm{NH}_{3}\)) and hydrogen chloride (\(\mathrm{HCl}\)). These two gases react powerfully to yield ammonium chloride (\(\mathrm{NH}_{4}\mathrm{Cl}\)), which changes the game from a gas to a solid. When they react, they form a new substance, so they no longer exist as original gases to abide by Dalton's Law.

This reaction is significant because it alters how we calculate pressures in the mixture. Instead of summing traditional partial pressures, the reaction shifts the overall pressure scenario.

Reactions like these highlight the exception in Dalton's Law: reactive mixtures don't simply add pressures because the very identity of the gases changes. Understanding these reactions aids in recognizing which gas mixtures will not conform to the predictability of Dalton's Law, such as \(\mathrm{NH}_{3}\) and \(\mathrm{HCl}\), which defies the law due to their chemical transformation.