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 Zero Order Reaction

In a zero-order reaction, the rate of reaction is constant and does not depend on the concentration of the reactants. The rate law for a zero-order reaction is given by \( r = k \), where \( r \) is the rate of reaction and \( k \) is the rate constant.

Step 2: Expressing Concentration-Time Relationship

For a zero-order reaction, the relationship between concentration \([A]\) and time \(t\) is given by the equation \([A] = [A_0] - kt\), where \([A_0]\) is the initial concentration and \(k\) is the rate constant. This equation shows that the concentration decreases linearly over time.

Step 3: Analyzing the Plot

The equation \([A] = [A_0] - kt\) is in the form of \(y = mx + b\), where \(m = -k\) is the slope and \(b = [A_0]\) is the y-intercept. Since the slope \(-k\) is negative, this implies that the concentration versus time plot will have a linear, negative slope starting from the initial concentration \([A_0]\) (non-zero intercept).

Step 4: Identifying the Correct Answer

From the analysis, the line has a negative slope and a non-zero intercept, matching option (c) of the provided answer choices.

Key Concepts

Understanding Concentration-Time Relationship in Zero Order Reactions

In a zero-order reaction, the concentration-time relationship is straightforward. The concentration of the reactant decreases linearly over time. This simplicity occurs because the rate of reaction is constant, as it does not depend on the concentration of the reactant. Thus, irrespective of how much reactant you start with, the speed at which it is consumed remains the same.

To express this concentration-time relationship mathematically, the formula is given by:

• \([A] = [A_0] - kt\)

Here, \([A]\) is the concentration at time \(t\), \([A_0]\) is the initial concentration, and \(k\) is the reaction rate constant. As time increases, the term \(kt\) also increases, leading to a decrease in \([A]\) over time. This relationship is crucial for understanding how a zero-order reaction progresses, showing a clear linear decline in concentration.

Exploring the Reaction Rate Constant

The reaction rate constant, denoted as \(k\), plays a pivotal role in zero-order reactions. Unlike other orders of reactions where \(k\) might vary with concentration, in zero-order reactions \(k\) remains unaffected by the concentration of the reactants. This means whether you start with a large or small amount of reactant, \(k\) dictates the rate at which the reaction proceeds at a constant pace.

The value of \(k\) provides insight into how fast a reaction occurs. In the concentration-time equation, \(k\) represents the negative slope, signifying how fast the concentration decreases over time. Therefore, if \(k\) has a higher value, the reaction will proceed at a faster rate, and the concentration will drop quickly. Conversely, a smaller \(k\) means a slower reaction, with concentrations depleting at a languid pace.

• Zero-order reactions have a constant rate \(k\)
• The magnitude of \(k\) affects how steep the concentration-time plot will be

Understanding \(k\) enables you to predict reaction dynamics efficiently.

Linear Graph Analysis of Zero Order Reactions

Analyzing a graph of concentration versus time for zero-order reactions involves understanding its linear nature. The plot expresses the equation \([A] = [A_0] - kt\), where it's in the format of \(y = mx + b\). This indicates a straight line with a clear slope \(-k\) and intercept \([A_0]\).

On this graph:

• The y-axis represents concentration \([A]\)
• The x-axis represents time \(t\)
• The slope (\(m\)) is \(-k\), showcasing a negative incline
• The y-intercept \([A_0]\) is the initial concentration

This linearity indicates a predictable decrease in concentration over time. By analyzing this graph, one can extrapolate crucial details such as the time required to reach a certain concentration or estimate the initial concentration based on the intercept. Thus, a linear graph not only confirms the zero-order kinetics but also provides a visual representation of the reaction's consistent rate.