Problem 85 - A Complete Resource Book in Chemistry for JEE Main

Question

A graph plotted between concentration of reactant, consumed at any time \((\mathrm{x})\) and time ' \(\mathrm{t}\) ' is found to be a straight line passing through the origin. The reaction is of (a) first-order (b) zero-order (c) third-order (d) second-order

Step-by-Step Solution

Answer

The reaction is of zero-order.

Step 1: Understanding the Problem

The problem gives us a graph of concentration versus time that is a straight line passing through the origin. We need to identify which order of reaction this scenario represents.

Step 2: Identify Characteristics of Reaction Orders

For different reaction orders, the relationship between concentration and time varies. In zero-order reactions, concentration decreases linearly over time, and the graph of concentration vs. time would be a straight line.

Step 3: Relate Graph to Reaction Order

A straight line graph that passes through the origin in concentration versus time indicates a zero-order reaction because the concentration of reactants decreases linearly with time.

Step 4: Conclude Based on Analysis

The given graph characteristics (a straight line through the origin) match the zero-order reaction. Hence, the correct choice is zero-order.

Key Concepts

zero-order reactions

Zero-order reactions are unique in the realm of reaction kinetics. Here, the rate at which the reactant decreases is constant over time. Essentially, the change in concentration of the reactant does not depend on its concentration. This means that the reaction proceeds at a steady pace, regardless of how much reactant is left. This property is what defines a zero-order reaction
and can be described by the rate equation:\[Rate = k\]- **Linear Decrease:** The concentration decreases linearly over time.- **Independent of Concentration:** Because the reaction rate doesn't rely on how much reactant is present, it's constant.- **Graph Representation:** When you plot a graph of concentration vs. time for this reaction, the result is a straight line. This is synonymous with the graph described in the original exercise.Understanding zero-order reactions is crucial for recognizing when a reaction proceeds at a constant rate, which provides critical insight into processing conditions and reaction dynamics.

graph analysis in chemistry

Graph analysis in chemistry is a powerful tool to translate numerical data into visual insights. For a zero-order reaction, plotting concentration against time yields a clear, straight line declining towards the x-axis, confirming the reaction order.
Here's how to interpret such graphs:- **Slope Interpretation:** In a zero-order reaction, the slope of the line represents the negative rate constant \( -k \). This slope is indicative of the speed at which the reactants are consumed.- **Intercept and Origin:** The line passing through the origin signifies that at time zero, the concentration of the reactant starts at its initial value.- **Straight Line Indicators:** The straight line confirms a uniform rate of reaction. Other reaction orders like the first or second will display curves instead.Graph analysis involves interpreting these lines and slopes to make informed conclusions about the reaction kinetics. It's a window into the dynamic world of chemical transformations.

reaction kinetics

Reaction kinetics is the branch of physical chemistry that looks into rates of chemical reactions and how different variables affect them. It's all about understanding how fast or slow reactions happen and what factors influence these speeds. Here’s a simple breakdown: - **Order of Reaction:** This tells us how the rate is affected by the concentration of the reactants. The zero-order, as discussed, is unaffected by concentration changes. - **Rate Constant (k):** This number gives a snapshot of the reaction speed, with higher values indicating quicker reactions. - **Influential Factors:** Factors such as temperature, pressure, and catalysts can significantly impact reaction rates. Relaxing or increasing any of these can accelerate or decelerate reactions. Understanding reaction kinetics is essential because it helps chemists manipulate conditions to control reactions, optimize product yields, or even enhance safety measures during reaction processes. It provides a fundamental framework to predict and control chemical behavior in various industries.