Problem 37 - A Complete Resource Book in Chemistry for JEE Main

Question

Pure ammonia is placed in a vessel at a temperature where its dissociation constant \((\alpha)\) is appreciable. At equilibrium (a) \(\alpha\) does not change with pressure (b) concentration of \(\mathrm{NH}_{2}\) does not change with pressure (c) concentration of hydrogen is less than that of nitrogen (d) \(\mathrm{K}_{\mathrm{p}}\) does not changes significantly with pressure

Step-by-Step Solution

Answer

Option (d): \(K_p\) does not change significantly with pressure.

Step 1: Determine the Dissociation Reaction

The dissociation of pure ammonia (H₃) can be represented by the equation: \[\text{NH}_3 (g) \rightleftharpoons \text{N}_2 (g) + \text{H}_2 (g)\] Where ammonia (H₃) dissociates into nitrogen (₂) and hydrogen (H₂) gases.

Step 2: Understand Equilibrium Constant Independence from Pressure

The equilibrium constant \(K_p\) for the dissociation reaction in terms of pressures is defined by the equation: \[K_p = \frac{[\text{N}_2][\text{H}_2]}{[\text{NH}_3]}\] For reactions where the number of moles of products and reactants are equal, \(K_p\) remains mostly unchanged with variations in pressure.

Step 3: Analyze Effect of Pressure on Equilibrium and Concentrations

Increasing the pressure will affect the positions of equilibrium according to Le Châtelier's principle, but the dissociation constant \(\alpha\) represents the ratio of dissociated molecules and is independent of pressure when taken as a percentage of the starting amount. \(\alpha\) and the amount of individual species concentrations may change due to shifts in equilibrium, but the fraction \(\alpha\) will not.

Step 4: Apply Mole Ratio Reasoning for Species Concentrations

As the dissociation reaction proceeds, ammonia breaks down into nitrogen and hydrogen. If the reaction reaches equilibrium, under ideal conditions and if we consider the dissociation to be partial, hydrogen concentration will generally be higher than nitrogen due to stoichiometry.

Step 5: Explanation of Pressure Effects

If pressure affects reaction rates and concentrations, the concentration of \(\text{NH}_2\) will change, but hydrostatic and steady-state architecture does not pertain as much at equilibrium; concentrations might change temporarily but settle back to equilibrium concentrations. \(\text{NH}_2\) not forming separately thus negates its pressure invariance.

Key Concepts

Dissociation Reaction

A dissociation reaction is a specific type of chemical reaction where a compound is broken down into two or more simpler substances. In the context of ammonia, the dissociation reaction involves ammonia ( NH₃ ) splitting into nitrogen ( N₂ ) and hydrogen ( H₂ ) gases. This transformation can be expressed by the equation: \[ \text{NH}_3 (g) \rightleftharpoons \text{N}_2 (g) + \text{H}_2 (g) \] This represents a reversible reaction, meaning it can proceed in both directions. Ammonia decomposes into nitrogen and hydrogen, while nitrogen and hydrogen can recombine to form ammonia.

At the molecular level, the reaction involves the breaking of chemical bonds in ammonia and the formation of new bonds in the resulting molecules. Understanding this process is critical because it sets the stage for exploring further concepts like equilibrium constants and how changes in conditions can affect chemical equilibria.

Equilibrium Constant

The equilibrium constant, denoted as K_p when considering partial pressures, is a fundamental concept in chemistry that quantifies the ratio of product concentrations to reactant concentrations at equilibrium. In the dissociation reaction of ammonia: \[ K_p = \frac{[\text{N}_2][\text{H}_2]}{[\text{NH}_3]} \] The equation shows how the concentration of products (nitrogen and hydrogen) over the concentration of the reactant (ammonia) relates to K_p . An essential aspect of K_p is its independence from pressure changes when the mole numbers on both sides of the equation are equal.

In our reaction, if the number of moles of gas remains constant, an increase in pressure won't significantly affect K_p . This makes equilibrium constants particularly useful for predicting the behavior of gases under varying conditions. K_p allows us to calculate states of equilibrium and understand how changes in pressure, temperature, or concentration gradients can influence the reaction.

Le Châtelier's Principle

Le Châtelier's Principle is a guideline that helps us predict how a system at equilibrium responds to disturbances. It states that a system will adjust itself to counteract any imposed change, and thus reestablish equilibrium. If you increase the pressure on a system involving gases, for instance, the equilibrium will shift to favor the side of the reaction that produces fewer gas molecules.

In our specific example, where ammonia dissociates into nitrogen and hydrogen - increasing the pressure would typically favor a shift towards fewer molecules. However, if both sides of the reaction have an equal number of moles, the effect of pressure becomes minimal. Understanding this principle is crucial for predicting the behavior of chemical systems when subject to external pressures, offering insights into reaction yields and optimal conditions for equilibrium.

• Predictable changes: Allows anticipation of shifts in equilibrium.
• Equilibrium stability: Ensures reactions adapt to maintain balance.

Partial Pressure Independence

Partial pressure refers to the pressure exerted by each individual gas in a mixture of gases. In chemical equilibria involving gases, these pressures help determine concentrations of substances. The concept of partial pressure independence involves understanding that some properties, particularly equilibrium constants K_p , do not vary significantly with changes in total pressure if moles remain consistent on either side of the reaction.

For reactions like the dissociation of ammonia, understanding that K_p remains stable despite shifts in pressure is key. This independence often simplifies calculations and predictions in chemical equilibria. Also, unlike K_p , the actual concentrations of the species involved do depend on pressure changes. Thus, recognizing situations where K_p is pressure-independent helps chemists focus on other variables like temperature or concentration that might affect the reaction further.

• Constant K_p balances reactions despite external changes.
• Focus shifts: Emphasizes importance of variables other than pressure.