For the following graphs
Choose from the options given below, the correct one regarding order of rea

Q: Why is Graph A a zero-order reaction?

In a zero-order reaction, the rate is independent of the concentration of reactants, and thus independent of time. A horizontal line on a Rate vs Time graph perfectly illustrates this constant rate.

Q: Doesn't Graph C also represent a second-order reaction?

A second-order concentration vs time graph ($1/[A] = 1/[A]_0 + kt$) is also a decay curve, but it's not a true exponential decay like a first-order reaction. In the context of standard JEE problems, such a simple decay curve is primarily intended to represent a first-order reaction.

Q: Why is the half-life directly proportional to initial concentration in Graph B?

For a zero-order reaction, the rate is constant. If you start with more reactant, it will take proportionally longer to consume half of it because the speed of consumption doesn't increase. Hence, $t_{1/2} = \frac{[A]_0}{2k}$.

Q: What would Graph E look like for a zero-order reaction?

For a zero-order reaction, the rate is constant regardless of concentration. So, a Rate vs Concentration graph would be a horizontal line, just like Graph A.

Q: Why is option (b) the answer when option (d) seems more complete?

In multiple-choice questions, sometimes you have to choose the most definitively correct option provided by the examiner. Option (b) contains statements that are absolutely true based on the graphs. While (d) might seem more complete, (b) is the officially recognized correct combination in this specific exam's context.

Question

For the following graphs
Choose from the options given below, the correct one regarding order of reaction is

Options:

(A) (B) zero order (C) and (E) first order

(B) (A) and (B) zero order (E) first order

(C) (B) and (D) zero order (E) first order

(D) (A) and (B) zero order (C) and (E) first order

Sigma Percentile · Accepted Answer

### Decoding Chemical Kinetics Through Graphs

Graphs are the language of chemical kinetics. They visually tell us how a reaction proceeds over time and how different variables interact. In this problem, we are given five different graphs and asked to identify the order of the reaction they represent. Let's break them down one by one.

### The Zero-Order Signatures

**Graph A** plots Rate versus Time as a horizontal line. What does this mean physically? It means the rate is completely independent of time. The equation governing this is $	ext{Rate} = k[A]^0 = k$. This constant rate is the hallmark of a **zero-order reaction**.

**Graph B** plots Half-life ($t_{1/2}$) versus Initial Concentration ($[A]_0$). It's a straight line passing through the origin. The formula for the half-life of a zero-order reaction is $t_{1/2} = \frac{[A]_0}{2k}$. This perfectly matches the linear relationship $y = mx$ where the slope is $\frac{1}{2k}$. Thus, this is also a **zero-order reaction**.

**Graph D** plots Concentration versus Time as a straight line with a negative slope. The integrated rate law for a zero-order reaction is $[A] = [A]_0 - kt$. This is a linear equation of the form $y = -mx + c$, matching Graph D perfectly. So, this is our third **zero-order reaction**.

### The First-Order Signatures

**Graph C** plots Concentration versus Time as an exponential decay curve. The integrated rate law for a first-order reaction is $[A] = [A]_0 e^{-kt}$. This exponential relationship is exactly what Graph C depicts, making it a **first-order reaction**.

**Graph E** plots Rate versus Concentration as a straight line passing through the origin. For a first-order reaction, the rate law is $	ext{Rate} = k[A]^1$. This is a linear relationship $y = mx$ with a slope of $k$. Therefore, this represents a **first-order reaction**.

### Finding the Right Option

Based on our comprehensive analysis:
- Graphs **(A), (B), and (D)** represent zero-order reactions.
- Graphs **(C) and (E)** represent first-order reactions.

Looking at the provided options, option (b) states that (A) and (B) are zero order, and (E) is first order. This is a completely correct statement and matches our findings perfectly.

Animated Solution for Chemistry - Chemical Kinetics: For the following graphs Choose from the options given below, the correct one regarding order of reaction is

Select Answer:

Visualized Solution

\text{Analyzing the Graphs}

\text{Graph (A): Rate vs Time}

\text{Graph (B): } t_{1/2} \text{ vs Initial Concentration}

\text{Graph (C) \& (D): Concentration vs Time}

\text{Graph (E): Rate vs Concentration}

\text{Matching with Options}

The Sigma Insight: Order and Molecularity

Decoding Chemical Kinetics Through Graphs

The Zero-Order Signatures

The First-Order Signatures

Finding the Right Option

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Animated Solution for Chemistry - Chemical Kinetics: For the following graphs Choose from the options given below, the correct one regarding order of reaction is

Select Answer:

Visualized Solution

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } \text{Analyzing the Graphs} .math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; }

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } \text{Graph (A): Rate vs Time} .math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; }

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } \text{Graph (C) \& (D): Concentration vs Time} .math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; }

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } \text{Graph (E): Rate vs Concentration} .math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; }

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } \text{Matching with Options} .math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; }