Problem 51 - A Complete Resource Book in Chemistry for JEE Main

Question

For a zero-order reaction, the plot of concentration vs time is linear with (a) +ve slope and zero intercept (b) -ve slope and zero intercept (c) +ve slope and non-zero intercept (d) -ve slope and non-zero intercept

Step-by-Step Solution

Answer

(d) -ve slope and non-zero intercept.

Step 1: Understanding the Zero Order Reaction

In a zero-order reaction, the rate of reaction is constant and does not depend on the concentration of the reactant. Thus, the rate law expression is given by \( R = k \), where \( k \) is the rate constant.

Step 2: Zero Order Kinetics Equation

For a zero-order reaction, the concentration of the reactant \([A]\) at time \( t \) is given by the equation: \([A] = [A]_0 - kt\), where \([A]_0\) is the initial concentration and \( k \) is the rate constant.

Step 3: Analyzing the Concentration vs Time Plot

The equation \([A] = [A]_0 - kt\) resembles the equation of a straight line \( y = mx + c \), where \( y \) corresponds to \([A]\), \( x \) corresponds to \( t \), \( m \) (the slope) corresponds to \(-k\) (negative because the concentration decreases over time), and \( c \) (the y-intercept) corresponds to \([A]_0\).

Step 4: Determining the Slope and Intercept

From the equation \([A] = [A]_0 - kt\), the slope \(-k\) is negative indicating a negative slope, and the intercept \([A]_0\) is usually non-zero. Thus, for a zero-order reaction, the plot of concentration vs. time has a negative slope with a non-zero intercept.

Step 5: Selecting the Correct Option

Given the explanation above, the plot of concentration vs time for a zero-order reaction has a negative slope (as the concentration decreases) and a non-zero intercept (as determined by \([A]_0\)). Therefore, the correct answer is option (d).

Key Concepts

Rate Law Expression

In chemical kinetics, the rate law expression plays a crucial role in understanding how the rate of a reaction depends on the concentration of reactants. For a zero-order reaction, the rate law is surprisingly straightforward. Unlike first or second-order reactions, where the rate depends on the concentration of reactants, a zero-order reaction means that the rate is constant, regardless of the concentration of any reactant. This can be mathematically represented as:

• \( R = k \)

Here, \( R \) is the rate of the reaction, and \( k \) is the rate constant. Because the rate is unaffected by changes in the concentration of reactants, zero-order reactions often involve scenarios where a catalyst or surface limits the reaction rate, such as in certain enzyme-catalyzed reactions or in gaseous reactions happening on a solid surface.

Concentration vs Time Plot

A zero-order reaction is characterized by its linear concentration vs time plot. When you map concentration against time for zero-order kinetics, you get a straight line. This reflects the simplification that the concentration of reactants decreases at a constant rate over time. Using the equation derived from the zero-order kinetics:

• \([A] = [A]_0 - kt\)

You can identify the features of the plot, much like the equation of a straight line:

• \(y = mx + c\)

Here, \([A]\) is the concentration of the reactant at time \(t\), \([A]_0\) is the initial concentration, \(-kt\) is the term that represents the change in concentration over time, with \(-k\) as the slope indicating a decline in concentration, and \(t\) is the time elapsed. The y-intercept in the concentration vs time plot is the initial concentration, \([A]_0\), which is typically non-zero.

Reaction Kinetics

Understanding reaction kinetics is fundamental when analyzing how reactions proceed over time. In the realm of zero-order reactions, kinetics simplify but reveal particular insights into how reactions behave. In simple terms, in zero-order kinetics,

• The rate of product formation is constant because the reactants are consumed at a uniform rate.
• This generally occurs when a reaction is limited by some external factor, such as a saturated catalyst surface or when all reacting molecules are busy and cannot increase the rate despite an abundance of reactants.

Unlike higher-order reactions where concentration changes alter reaction speed, zero-order kinetics tell us concentrations won't sway the rate. This insight helps in fields like pharmacology, where drug metabolism can often follow zero-order kinetics.

Rate Constant

The rate constant is a pivotal part of the rate law and expresses how quickly a reaction proceeds. In a zero-order reaction, the rate constant \( k \) is especially important because the rate of reaction equals \( k \), as depicted in the equation:

• \( R = k \)

This constancy means that the rate, being independent of reactant concentration, relies solely on \( k \). It represents the amount of reactant transformed per unit time, independent of how much reactant is left. Because zero-order reactions defy typical concentration dependencies, determining \( k \) involves measuring how fast concentration diminishes over certain time intervals. The dimensions of \( k \) also differ from other order reactions:

• It generally has units of concentration/time (e.g., M/s or mol/L/s).

This emphasizes the unique nature of zero-order kinetics and makes the understanding of \( k \) critical for mastering chemical reaction behavior in such scenarios.