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) \(\Delta \mathrm{H}\) 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: Understanding Column-I and Column-II

In the matching exercise, we need to align the concepts listed in Column-I with the appropriate terms in Column-II. Each item in Column-I has a specific scientific association that can be directly matched with the concepts in Column-II.

Step 2: Matching Variation of Equilibrium Constants with Temperature

The variation of equilibrium constants with temperature is described by Van't Hoff equation, a thermodynamic equation that relates the equilibrium constant ( K ) to temperature ( T ). Thus, (a) matches with (r).

Step 3: Matching 9Delta H of H-Cl9

The enthalpy change ( ΔH ) for the formation of the H-Cl bond has a specific value. Given the options, it is most directly related to the numerical value provided in (s), which is 9-57.2 kJ/equivalent9. Thus, (b) matches with (s).

Step 4: Matching Law of Conservation of Energy

The law of conservation of energy states that energy cannot be created or destroyed, only transformed. In chemistry, Hess's law applies this principle to predict enthalpy changes in reactions. Therefore, (c) matches with (q).

Step 5: Matching Variation of Heat of Reaction with Temperature

The variation of the heat of reaction with temperature is described by Kirchoff's equation, which accounts for changes in reaction heat as temperature changes. Thus, (d) matches with (p).

Step 6: Reviewing Unused Option from Column-II

The Born Haber cycle (t) relates to calculating lattice energies and is not directly associated with any of the concepts in Column-I based on this problem's information. It remains unmatched.

Key Concepts

Van't Hoff equation

The Van't Hoff equation is a foundational concept in thermodynamics that helps us understand how equilibrium constants change with temperature. In chemical reactions, equilibrium denotes a state where the concentrations of reactants and products remain constant. However, when temperature fluctuates, the equilibrium constants often change.The Van't Hoff equation, given as \( \frac{d \ln K}{dT} = \frac{\Delta H^\circ}{RT^2} \), connects the change in temperature with the equilibrium constant \( K \). Here:

• \( \Delta H^\circ \) represents the standard enthalpy change.
• \( R \) is the universal gas constant.
• \( T \) is the temperature in Kelvin.

To utilize the Van't Hoff equation, one needs to understand how enthalpy changes affect the positions of equilibrium.
This equation is particularly useful in predicting the direction of a reaction under varying temperature conditions, showcasing whether products or reactants will be favored as the temperature changes.

Hess's Law

Hess's Law is an essential principle in thermodynamics that describes the idea of conservation of energy in chemical processes. It states that the total enthalpy change during a reaction is the same, regardless of the pathway the reaction takes. This means that whether a reaction occurs in one step or multiple smaller steps, the total heat absorbed or released remains constant. This principle allows chemists to calculate reaction enthalpies for reactions that may not easily occur in a single step. Key applications of Hess's Law include:

• Calculating enthalpy changes for complex reactions.
• Determining the feasibility of a reaction.
• Using known enthalpies to deduce unknown values.

Hess's Law is crucial for simplifying the analysis of reactions and validating the conservation of energy in chemical systems. It exemplifies how energy is transferred during chemical reactions without being lost, upholding the principle that energy in a closed system remains constant.

Kirchhoff's equation

Kirchhoff's equation is a valuable tool in thermodynamics that relates to how the heat of a chemical reaction changes with temperature. In practical terms, as temperature varies, the heat absorbed or released in a reaction can change, and Kirchhoff's equation helps to quantify this change.The equation is expressed as:

• \( \Delta H_T = \Delta H_{T_0} + \int_{T_0}^{T} \Delta C_P \, dT \)

Here:

• \( \Delta H_T \) is the enthalpy change at the new temperature \( T \).
• \( \Delta C_P \) is the change in heat capacity at constant pressure between products and reactants.
• \( T_0 \) is the reference temperature, often 298 K.

Kirchhoff's equation helps chemists understand how reaction enthalpies change beyond standard conditions. It allows the calculation of heats of reaction at different temperatures, thereby providing insights into energy requirements for reactions carried out under varying thermal conditions.
This equation is particularly important for processes occurring at non-standard temperatures, aiding in determining how much heat needs to be provided or removed.

Born Haber cycle

The Born Haber cycle is a theoretical model used in chemistry to analyze the formation of ionic compounds, particularly lattice energies. It employs Hess's Law to breakdown the formation of an ionic solid into a series of individual steps. Through the Born Haber cycle, one can calculate the lattice energy of a crystalline solid, which is the energy required to separate one mole of an ionic solid into gaseous ions. The steps in the Born Haber cycle typically include:

• Sublimation of the metal.
• Dissociation of the diatomic molecule (if applicable).
• Ionization of the gaseous atoms.
• Electron affinity of the non-metal.
• Formation of the solid from gaseous ions.

Each of these steps incurs an enthalpy change, and when combined, they provide the total enthalpy change for forming an ionic compound from its constituent elements.
This approach is essential for understanding the energy considerations involved in the formation of crystals, shedding light on the stability and properties of ionic compounds. By employing the Born Haber cycle, chemists can predict lattice energies, facilitating the study of ionic substances.