Problem 139 - A Complete Resource Book in Chemistry for JEE Main

Question

For a zero order reaction, the plot of concentration versus time is linear with (a) positive slope with zero intercept (b) positive slope with non-zero intercept (c) negative slope with non-zero intercept (d) parallel to time axis.

Step-by-Step Solution

Answer

(c) negative slope with non-zero intercept.

Step 1: Understanding a Zero Order Reaction

In a zero order reaction, the rate of reaction is constant and does not depend on the concentration of the reactants. This means that the rate does not change as the reaction progresses.

Step 2: The Rate Equation for a Zero Order Reaction

The rate of a zero order reaction is given by the equation \( r = k \), where \( k \) is the rate constant. This implies that the rate remains constant throughout the reaction.

Step 3: Deriving the Integrated Rate Equation

For a zero order reaction, the integrated rate law is derived as: \( [A] = [A]_0 - kt \). Here, \([A]\) is the concentration of the reactant at time \( t \), \([A]_0\) is the initial concentration, and \( k \) is the rate constant.

Step 4: Analyzing the Concentration-Time Plot

The integrated rate equation \([A] = [A]_0 - kt\) is a linear equation of the form \( y = mx + c \) where \( y \) is \([A]\), \( x \) is \( t \), \( m \) is \(-k\) (the slope), and \( c \) is \([A]_0\) (the y-intercept).

Step 5: Identifying the Slope and Intercept

In the given equation \([A] = [A]_0 - kt\), the slope is \(-k\), which is negative, and the y-intercept is \([A]_0\), which is typically non-zero unless the initial concentration is zero.

Step 6: Conclusion on the Graph Characteristics

The concentration vs time graph is a straight line with a negative slope, corresponding to option (c): negative slope with non-zero intercept.

Key Concepts

Reaction Rate

The reaction rate is a crucial concept in chemistry. In simple terms, it refers to how fast or slow a reaction takes place. For most reactions, the rate depends on the concentration of the reactants involved. However, in a zero order reaction, this is not the case. The reaction rate remains constant regardless of changes in concentration.

This constant nature means that the reaction proceeds at the same speed from start to finish. The scientific reason behind this is that the reaction rate for zero order reactions is determined by external factors, such as catalysts or surface area, rather than the concentration of the reactants.

• The rate of reaction is denoted by the symbol \( r \).
• It is expressed by the formula \( r = k \), where \( k \) is the rate constant.
• For a zero order reaction, \( k \) has units of concentration per time (e.g., M/s).

Concentration vs Time Graph

Understanding the concentration vs time graph can clarify how a zero order reaction behaves over time. In any reaction, this graph plots the concentration of reactants as the reaction proceeds, against time. For a zero order reaction, this results in a straight line, distinct from reactions of other orders.

The equation representing this is \( [A] = [A]_0 - kt \). Here:

• \( [A] \) is the concentration of the reactant at time \( t \).
• \( [A]_0 \) is the initial concentration.
• \( k \) is the rate constant.

The negative slope \( -k \) indicates that the concentration decreases over time. The line is linear with this negative slope and a y-intercept equal to the initial concentration \( [A]_0 \). Note that the line's negative slope confirms the reaction's constant rate of decrease. This behavior makes it easy to predict how quickly a reactant will be consumed.

Integrated Rate Equation

The integrated rate equation is essential for understanding reactions, particularly zero order reactions. Essentially, it provides a formula that expresses the concentration of reactants as a function of time. This equation is derived from the basic rate equation and allows us to predict the concentration at any given point in time.

For zero order reactions, the integrated rate equation is \( [A] = [A]_0 - kt \). This equation is quite straightforward:

• \( [A] \) shows the concentration at a specific time \( t \).
• \( [A]_0 \) is the starting concentration, always serving as the y-intercept in the graph.
• \( kt \) explains how much the concentration has decreased over time \( t \).

The equation reflects that the rate at which concentration changes is linear over time. Knowing this integrated rate equation enables chemists to predict the concentration of a substance at any given moment, significant in both laboratory settings and industrial applications.