Problem 113 - A Complete Resource Book in Chemistry for JEE Main

Question

\(\Delta \mathrm{G}^{\circ}\) for the reaction, \(\mathrm{x}+\mathrm{y} \rightleftharpoons \mathrm{z}\) is \(-4.606 \mathrm{kcal}\). The value of equilibrium constant of the reaction at \(227^{\circ} \mathrm{C}\) is (a) \(0.01\) (b 100 (c) 2 (d) 10

Step-by-Step Solution

Answer

Equilibrium constant \(K = 100\).

Step 1: Identify Given Values

We need to find the equilibrium constant, \(K\), given \(\Delta \mathrm{G}^{\circ} = -4.606 \text{ kcal/mol}\) at \(227^{\circ} \mathrm{C}\), which is in Kelvin: \(227 + 273 = 500\, \text{K}.\)

Key Concepts

Equilibrium Constant

The equilibrium constant, denoted as \(K\), is a fundamental concept in chemical reactions that helps predict the direction and extent of a reaction. It is defined for a reaction at equilibrium where the rates of the forward and reverse reactions are equal, maintaining a constant concentration of reactants and products over time. The value of \(K\) is derived from the relationship between Gibbs Free Energy change (\(\Delta G^\circ\)) and the reactants/products' concentrations at equilibrium.

Here’s how it works:

• If \(K\) is much greater than 1, the products are favored at equilibrium.
• If \(K\) is much less than 1, the reactants are favored.
• If \(K\) is around 1, neither reactants nor products are significantly favored.

The equation relating \(\Delta G^\circ\) to \(K\) is given by:\[\Delta G^\circ = -RT \ln K\]where \(R\) is the universal gas constant and \(T\) is temperature in Kelvin. Understanding these concepts and utilizing the equation correctly allows us to predict how a reaction behaves under different conditions.

Temperature Conversion

Temperature conversion is a crucial step in thermodynamic calculations, especially when dealing with Gibbs Free Energy and equilibrium constants. The formula \(\Delta G^\circ = -RT \ln K\) requires temperature to be in Kelvin for accurate calculations. As a standard practice:

• Convert Celsius to Kelvin using the formula: \[ T(\text{K}) = T(\text{°C}) + 273.15 \] This is a straightforward conversion as it requires simply adding 273.15 to the Celsius temperature.

In our given problem, the temperature provided was 227°C. To convert to Kelvin, we calculated:

\[227 + 273 = 500 \text{ K}\]Accurate temperature conversion is essential as many thermodynamic equations rely directly on temperature, affecting equilibrium and reaction dynamics.

Reaction Dynamics

Reaction dynamics refers to the rates and mechanisms by which chemical reactions proceed. At equilibrium, reaction dynamics are perfectly balanced, and the rates of the forward and reverse reactions are equal. The state of equilibrium is still dynamic because reactants and products continue to interconvert, but their concentrations remain unchanged.

Understanding reaction dynamics involves:

• Investigating how temperature, pressure, and concentration affect reaction rates.
• Recognizing that while equilibrium does not alter the ratio (34 Key to investigate how these changes in conditions won't shift the equilibrium unless the system itself changes significantly.

This knowledge is fundamental in chemical thermodynamics and plays a critical role in determining the equilibrium constant and how the changes in reaction conditions can affect a system's overall dynamics.

Thermodynamics

Thermodynamics is the study of energy transformations within chemical systems. It provides tools to understand whether a process or reaction will occur spontaneously. One of the key parameters in thermodynamics is the Gibbs Free Energy (E6T methodology entails understanding how energy is exchanged and how it influences the equilibrium state of a chemical reaction.

Gibbs Free Energy is calculated as:

• \[\Delta G = \Delta H - T \Delta S\]

where \(\Delta H\) is the enthalpy change, \(T\) is the temperature in Kelvin, and \(\Delta S\) is the entropy change. If \(\Delta G\) is negative, the reaction is spontaneous; if positive, it is non-spontaneous. Understanding these principles helps in predicting how energy changes influence a reaction's outcome, the equilibrium position, and the feasibility of processes within chemical industries.