Question

If a vessel containing hydrogen chloride at a pressure \(p\) is connected with another vessel of the same volume containing ammonia at a pressure \(P\) so that they mix with each other to form solid ammonium chloride. Then, the gas pressure (1) is equal to the pressure (2) will be \(\frac{p}{P}=1\) (3) will be doubled, i.e., \(2 \mathrm{P}\) (4) drops to zero

Short answer

The gas pressure drops to zero.

Step-by-step solution

- Understand the chemical reaction

Hydrogen chloride (\text{HCl}) reacts with ammonia (\text{NH}_3) to form solid ammonium chloride (\text{NH}_4\text{Cl}). The chemical equation for this reaction is: \[ \text{HCl (g)} + \text{NH}_3 (\text{g}) \rightarrow \text{NH}_4\text{Cl (s)} \]

- Analyze the volume and pressure setup

Both vessels have the same volume, and initially, one contains hydrogen chloride at pressure \(p\), and the other contains ammonia at pressure \(P\). When they are mixed, all the gas phase react.

- Determine the resulting gas pressure

Since the gases react completely to form a solid, there would be no gas molecules left in the vessel. Thus, the pressure drops to zero after the reaction.

Key concepts

chemical reaction

A chemical reaction occurs when substances interact and transform into new substances. In this case, hydrogen chloride (HCl) and ammonia (NH₃) combine to form a new substance, solid ammonium chloride (NH₄Cl).

The chemical equation for the reaction is:
\[ \text{HCl (g)} + \text{NH}_3 (\text{g}) \rightarrow \text{NH}_4\text{Cl (s)} \]

This equation shows the reactants (on the left side) and the product (on the right side). Notice that both reactants are gases, but the product is a solid. This transformation significantly influences the pressure and volume aspects of the reaction.

ammonium chloride formation

Ammonium chloride forms when hydrogen chloride and ammonia gases are combined.

Here’s how it happens:

• Hydrogen chloride, a strong acid, releases H⁺ ions.
• Ammonia, a weak base, contains NH₃ molecules that accept H⁺ ions.
• When these molecules meet, they react and form the salt ammonium chloride (NH₄Cl).

The result is a solid compound, as represented in the equation:
\[ \text{HCl (g)} + \text{NH}_3 (\text{g}) \rightarrow \text{NH}_4\text{Cl (s)} \]

Since the reactants are gases and the product is a solid, this reaction removes gas molecules from the system. This play a crucial role in determining gas pressure equilibrium.

gas pressure equilibrium

Gas pressure is influenced by the number and behavior of gas molecules in a container. Initially, we have two separate vessels:

• One with hydrogen chloride gas at pressure \(p\).
• Another with ammonia gas at pressure \(P\).

Both vessels are of the same volume. When the gases are allowed to mix and react with each other completely, they form solid ammonium chloride. This reaction removes all gas molecules from the system.

Hence, after the reaction, there are no gas molecules left to exert pressure. As a result, the gas pressure in the vessel drops to zero. This illustrates how gas pressure is directly influenced by the presence of gas molecules in a given space.