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: Understand Zero Order Reactions

In a zero-order reaction, the rate of reaction is constant and independent of the concentration of the reactants. This means that the rate at which reactants are converted to products does not change over time, as long as there is some reactant present.

Step 2: Determine the Integrated Rate Law

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

Step 3: Analyze the Graph Characteristics

The formula \([A] = [A]_0 - kt\) indicates a linear relationship between concentration \([A]\) and time \(t\) with a slope of \(-k\) and a y-intercept of \([A]_0\). Thus, the graph of concentration vs. time for a zero-order reaction is a straight line with a negative slope.

Step 4: Choose the Correct Option

Since the graph has a negative slope (because of \(-k\)) and a non-zero intercept (\([A]_0\)), the correct choice is:(c) negative slope with non-zero intercept.

Key Concepts

Integrated Rate Law

The integrated rate law provides a mathematical relationship that helps to describe the concentration of a reactant over time in a chemical reaction. For zero-order reactions, this relationship is particularly straightforward. The reaction rate is constant regardless of the concentration of reactants. The formula used to express the integrated rate law for a zero-order reaction is:\[[A] = [A]_0 - kt\]- \[A\] is the concentration of the reactant at time \(t\).- \[A_0\] represents the initial concentration of the reactant.- \(-k\) is the reaction rate constant with a negative sign showing the decrease in concentration over time.This equation reflects how, in a zero-order reaction, the concentration decreases linearly over time. As such, it provides a simple and effective way to predict the concentration of reactants at any given time during the reaction.

Reaction Rate Constant

The reaction rate constant, denoted as \(k\), is a crucial factor in the study of chemical kinetics. It essentially determines the speed of a reaction. In the context of zero-order reactions, \(k\) is constant. This means that the reaction rate remains unaltered as the reactants are consumed. The constant nature of \(k\) in zero-order reactions indicates that external factors like temperature or catalyst presence may affect the rate, but the concentration of reactants does not. In the integrated rate law, \(-k\) acts as the slope when concentration is plotted against time. This slope's constant value is what guarantees the linear decrease in concentration in a zero-order reaction, making it predictable and easy to calculate.Understanding how \(k\) functions can help you predict how quickly a reaction will proceed and how long it will take for a reactant to be used up under certain conditions.

Graph of Concentration vs. Time

In zero-order reactions, the graph of concentration vs. time is unique and simple to interpret due to its linear pattern. The integrated rate law equation \[A] = [A]_0 - kt\] clearly indicates a linear decrease in reactant concentration over time.

• The graph is a straight line, which makes it easier to identify and differentiate from graphs of other reaction orders.
• The slope of the line is \(-k\), highlighting the consistent reaction rate irrespective of concentration changes.
• The y-intercept is \[A]_0\], showing the initial concentration from which the reaction begins.

The graph's linearity simplifies the task of tracking how reactant concentration decreases and allows for easy estimation and prediction of future points in the reaction timeline. This clarity is what makes zero-order reaction kinetics particularly approachable for anyone trying to master chemical kinetics.