Question

The values of enthalpies of reactants and products are \(x\) and \(y \mathrm{~J} / \mathrm{mol}\), respectively. If the activation energy for the backward reaction is \(z \mathrm{~J} / \mathrm{mol}\), then the activation energy for forward reaction will be (in \(\mathrm{J} / \mathrm{mol}\) ) (a) \(x-y-z\) (b) \(x-y+z\) (c) \(y-x-z\) (d) \(y-x+z\)

Short answer

(b) \(x-y+z\)

Step-by-step solution

Understand Activation Energy

Activation energy is the minimum energy required to initiate a chemical reaction. The activation energy for the forward reaction is the energy needed to reach the transition state from the reactants, while for the backward reaction, it's the energy needed to go from the products to the transition state.

Calculate Activation Energy for Forward Reaction

To find the activation energy for the forward reaction, we must consider that the total energy to reach the transition state would be the enthalpy of the reactants plus the activation energy for the backward reaction, since the backward reaction starts from the products state. Therefore, the activation energy for the forward reaction is enthalpy of the reactants (x) plus the activation energy for the backward reaction (z) minus the enthalpy of the products (y), which is given by the equation: activation energy for forward reaction = x + z - y.

Identify the Correct Option

The correct option that represents the activation energy for the forward reaction in terms of x, y, and z is x + z - y, which matches option (b) \(x-y+z\).

Key concepts

Enthalpy of Reaction

The enthalpy of reaction, commonly symbolized as \(\Delta H\), is a measure of the heat change during a chemical reaction, occurring at constant pressure. It's vital in understanding whether a reaction is endothermic (absorbing heat) or exothermic (releasing heat). In the provided exercise, the enthalpy of reactants is denoted as \('x'\) and that of the products as \('y'\).

This concept is crucial when predicting the energy exchanged with the surroundings during a reaction. Students often struggle to correlate these thermodynamic values with the practical aspects of energy and how it influences a reaction's progress. When \(\Delta H\) is positive, the reaction absorbs energy, indicating that it is endothermic. Conversely, a negative \(\Delta H\) signifies that the reaction is exothermic, hence releasing energy. Remember, the enthalpy of reaction links closely to the overall stability and feasibility of chemical processes.

Physical Chemistry for Competitive Examinations

Physical chemistry covers a broad range of topics concerned with the physical properties of molecules, the forces that act upon them, and the interactions among them. It's a field peppered with both conceptual inquiries and quantitative calculations, which can be daunting for students preparing for competitive exams.

To conquer such challenges, it's essential to grasp core concepts like thermodynamics, quantum mechanics, and kinetics – which relate directly to exercises involving enthalpy and activation energy. The exercise at hand is an illustration of a question that might appear in a competitive setting, where the understanding of these concepts must be applied logically and numerically. For success in competitive exams, a clear comprehension of these principles, accompanied by regular practice with pertinent problems, is indispensable.

Chemical Kinetics

Chemical kinetics focuses on the rates of chemical reactions and the steps through which they occur. Students learn about factors that affect reaction rates, such as concentration, temperature, and the presence of catalysts. In the context of the textbook solution, chemical kinetics is the framework within which we examine the activation energy – the threshold energy that must be exceeded to produce a chemical reaction.

It's important for students to recognize that although the term 'activation energy' might seem abstract, it has real implications. For instance, activation energy dictates how fast a reaction will proceed under certain conditions. Understanding this concept aids students in predicting the behavior of reactions and designing experiments accordingly. The exercise presented provides a practical example of calculating the activation energy, an exercise that reinforces the learners' grasp of chemical kinetics in a tangible way.