Problem 136 - A Complete Resource Book in Chemistry for JEE Main

Question

Match the following Column-I (a) Variation of equilibrium constants with temperature (b) \(\Delta \mathrm{H}_{\text {acus }}\) of \(\mathrm{H}-\mathrm{Cl}\) (c) Law of conservation of energy (d) Variation of heat of reaction with temperature Column-II (p) Kirchoff's equation (q) Hess's law (r) Van't Hoff equation (s) \(-57.2 \mathrm{~kJ} /\) equivalent (t) Born Haber cycle

Step-by-Step Solution

Answer

(a) → (r), (b) → (s), (c) → (q), (d) → (p)

Step 1: Analyze Column-I Items

In Column-I, we have four items related to concepts of chemistry: (a) Variation of equilibrium constants with temperature, (b) \(\Delta \mathrm{H}_{\text {acus }}\) of \(\mathrm{H}-\mathrm{Cl}\), (c) Law of conservation of energy, and (d) Variation of heat of reaction with temperature. Each of these needs to be matched with the correct concept from Column-II.

Step 2: Match item (a) from Column-I

For item (a), Variation of equilibrium constants with temperature relates to how temperature affects equilibrium constants in chemical reactions. This concept is explained by the Van't Hoff equation, so (a) matches with (r).

Step 3: Match item (b) from Column-I

Item (b), \(\Delta \mathrm{H}_{\text {acus }}\) of \(\mathrm{H}-\mathrm{Cl}\), represents the enthalpy of reaction for the formation of hydrochloric acid from its ions in solution. The value given is \(-57.2 \mathrm{~kJ} / \text{equivalent}\), directly aligns it with (s) in Column-II.

Step 4: Match item (c) from Column-I

The Law of conservation of energy, indicated by item (c), is related to Hess's law, which states that the total enthalpy change in a reaction is the same regardless of the path taken. Therefore, (c) matches with (q).

Step 5: Match item (d) from Column-I

For item (d), Variation of heat of reaction with temperature is described by Kirchoff's equation, which explains how enthalpy changes with temperature for chemical reactions. Thus, (d) matches with (p).

Step 6: Verify Matches

Check that all items in Column-I have been matched with distinct concepts in Column-II: (a) with (r), (b) with (s), (c) with (q), and (d) with (p). All matches are consistent with their definitions.

Key Concepts

Van't Hoff equation

The Van't Hoff equation is a critical tool in understanding how the equilibrium constant of a chemical reaction changes with temperature. This equation provides a link between thermodynamics and chemical kinetics, highlighting the temperature dependence of reaction equilibria.

Mathematically, the Van't Hoff equation is given as:

• \[ \ln K = -\frac{\Delta H^\circ}{R} \left( \frac{1}{T} \right) + \frac{\Delta S^\circ}{R} \]

Where:

• \(K\) is the equilibrium constant,
• \(\Delta H^\circ\) is the standard enthalpy change of the reaction,
• \(R\) is the universal gas constant,
• \(T\) is the temperature in Kelvin, and
• \(\Delta S^\circ\) is the standard entropy change.

Simply put, as temperature increases, the equilibrium constants change in a way that favors either the forward or reverse reaction, depending on whether the process is exothermic or endothermic. This makes the Van't Hoff equation extremely useful in predicting how a reaction will behave under different temperatures.

Hess's law

Hess's law is an essential principle in thermodynamics, particularly in the domain of chemistry. It states that the total enthalpy change of a chemical reaction is invariant, no matter which path the reaction takes.

This is synonymous with the conservation of energy, where energy is neither created nor destroyed. This means that whether a reaction proceeds in multiple steps or a single step, the overall change in enthalpy remains constant. This provides a robust tool for calculating unknown enthalpy changes using known values.

For instance, consider reactions that can be summed to find the enthalpy change for a larger reaction. By applying Hess's law, one can use the enthalpy changes of individual reactions to determine the total enthalpy change:

• Step 1: \(A \to B\), \(\Delta H_1\)
• Step 2: \(B \to C\), \(\Delta H_2\)
• Total Reaction: \(A \to C\), \(\Delta H = \Delta H_1 + \Delta H_2\)

This law underpins many thermodynamic calculations and is foundational in chemistry education.

Kirchoff's equation

Kirchoff's equation is vital in understanding how the heat of reaction, or enthalpy change, varies with temperature. It offers insight into the temperature dependency of reaction thermodynamics, critical for controlling chemical processes.

Kirchoff’s equation is represented as:

• \[ \Delta H_{T_2} = \Delta H_{T_1} + \int_{T_1}^{T_2} \Delta C_p \, dT \]

Here:

• \(\Delta H_{T_2}\) and \(\Delta H_{T_1}\) represent the enthalpy changes at temperatures \(T_2\) and \(T_1\) respectively,
• \(\Delta C_p\) is the change in heat capacities.

This equation helps predict how heat transfer in reactions changes with temperature and is pivotal in designing reactors and other chemical equipment, illustrating the beauty of thermodynamics in practical chemistry applications.

Enthalpy change

Enthalpy change (\(\Delta H\)) is a key concept in chemistry that reflects the heat absorbed or released during a chemical reaction at constant pressure. It serves as a measure of the total heat content within a system.

Enthalpy change can be:

• Positive (endothermic), where heat is absorbed by the system making \(\Delta H > 0\).
• Negative (exothermic), where heat is released making \(\Delta H < 0\).

This concept is essential because it tells us about the energy changes that accompany chemical reactions, pointing to whether a reaction is likely to occur spontaneously. It is integral to both the Van't Hoff and Kirchoff equations, linking energy changes directly with reaction conditions such as temperature.

Equilibrium constants

Equilibrium constants are fundamental in understanding the balance point of reversible chemical reactions. They represent the ratio of the concentration of products to reactants at equilibrium, giving insight into the extent of a reaction.

Mathematically, an equilibrium constant (\(K\)) is expressed as:

• \[ K = \frac{[C]^c[D]^d}{[A]^a[B]^b} \]

Where:

• \([A]\) and \([B]\) are concentrations of reactants,
• \([C]\) and \([D]\) are concentrations of products,
• \(a\), \(b\), \(c\), and \(d\) are their respective stoichiometric coefficients.

A large \(K\) value indicates a reaction that favors products at equilibrium, whereas a small \(K\) suggests a reaction that favors reactants. Understanding equilibrium constants helps chemists predict how a reaction mixture will behave, guiding the adjustment of conditions to drive reactions toward desired outcomes.