Assertion: All collision of reactant molecules lead to product formation. Reason: Only those collisions in whi

NCERT Exemplar · Q65

Q. Assertion: All collision of reactant molecules lead to product formation. Reason: Only those collisions in which molecules have correct orientation and sufficient kinetic energy lead to compound formation.

(i) Both assertion and reason are correct and the reason is correct explanation of assertion.

(ii) Both assertion and reason are correct but reason does not explain assertion.

(iii) Assertion is correct but reason is incorrect.

(iv) Both assertion and reason are incorrect.

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Concept understanding — Arrhenius Equation Plot

The Arrhenius Equation Plot: Why Temperature Changes Reaction Speed

You already know that heating things up makes reactions go faster. A cold chai takes forever to dissolve sugar; hot chai does it in seconds. But how much faster? And is there a pattern that holds for every reaction?

That pattern is the Arrhenius equation, and plotting it in a clever way reveals something fundamental about how molecules need to collide to react.

The core idea: an energy barrier

Imagine a ball sitting in a valley. To get to the next valley, it must first be pushed up over a hill. That hill is the activation energy ( $E_a$ ) — the minimum energy two molecules need to have when they collide, for the reaction to happen.

At a low temperature, most molecules move slowly. Only a tiny fraction have enough energy to climb that hill. Raise the temperature, and suddenly many more molecules have the required energy. The fraction of molecules with energy $\ge E_a$ is given by the Boltzmann distribution:

\text{fraction} = e^{-E_a / RT}

where $R$ is the gas constant and $T$ is the absolute temperature (in Kelvin). This exponential is the heart of the story.

The Arrhenius equation (precise statement)

The rate constant $k$ of a reaction depends on temperature as:

k = A \, e^{-E_a / RT}

$k$ = rate constant (how fast the reaction proceeds)
$A$ = pre-exponential factor (frequency of collisions, times a steric factor — how often molecules hit in the right orientation)
$E_a$ = activation energy (J/mol or kJ/mol)
$R$ = 8.314 J/(mol·K)
$T$ = temperature in Kelvin

Important

$k$ is not the reaction rate itself — it's the proportionality constant in the rate law. But for a fixed concentration, a larger $k$ means a faster reaction.

Why plot it? The linear trick

The equation $k = A e^{-E_a / RT}$ is exponential in $1/T$ . That's hard to eyeball. But take the natural logarithm of both sides:

\ln k = \ln A - \frac{E_a}{R} \cdot \frac{1}{T}

This is the equation of a straight line:

y = c + m x

where:

$y = \ln k$
$x = 1/T$
slope $m = -E_a / R$
intercept $c = \ln A$

So if you measure $k$ at several temperatures and plot $\ln k$ versus $1/T$ , you get a straight line — provided the reaction follows Arrhenius behaviour (most do, over moderate temperature ranges).

Tip

Always use Kelvin for $T$ . Celsius will give you a curved mess because $1/T$ is not linear in Celsius.

What the plot tells you

From the slope, you get $E_a$ :

E_a = - (\text{slope}) \times R

A steep negative slope means a large $E_a$ — the reaction is very sensitive to temperature. A shallow slope means a small $E_a$ — temperature doesn't affect it much.

From the intercept, you get $A$ :

A = e^{\text{intercept}}

This tells you about the collision frequency and orientation factor. A high $A$ means molecules are colliding often and in the right geometry.

A typical Arrhenius plot looks like this

$T$ (K)	$k$ (s⁻¹)	$1/T$ (K⁻¹)	$\ln k$
300	0.0012	0.00333	-6.72
310	0.0028	0.00323	-5.88
320	0.0061	0.00313	-5.10
330	0.0125	0.00303	-4.38

Plot $\ln k$ (y-axis) vs $1/T$ (x-axis). The points fall on a straight line. Draw the best-fit line, measure its slope, and compute $E_a$ . …

Why this formula?

Arrhenius Equation Plot: Why It Holds

The Arrhenius equation is not a guess — it emerges from a deep physical picture of how molecules react. Let's build that understanding step by step.

The Core Idea: Molecules Need Energy to React

For a reaction to occur, molecules must collide with enough energy to break existing bonds and form new ones. This minimum energy is called the activation energy ( $E_a$ ).

But not all collisions succeed — only those with kinetic energy $\geq E_a$ lead to a reaction.

The Key Formula

The Arrhenius equation is:

k = A e^{-E_a / (RT)}

Where:

$k$ = rate constant
$A$ = pre-exponential factor (frequency of collisions with correct orientation)
$E_a$ = activation energy (J/mol)
$R$ = gas constant (8.314 J/mol·K)
$T$ = absolute temperature (K)

Why the Exponential Term Appears

Step 1: The Boltzmann Distribution

Molecules in a gas or liquid have a distribution of kinetic energies. The fraction of molecules with energy $\geq E$ is given by the Boltzmann factor:

\text{Fraction} = e^{-E / (k_B T)}

For molar quantities, replace $k_B$ with $R$ :

\text{Fraction} = e^{-E_a / (RT)}

This is not arbitrary — it comes from statistical mechanics. The exponential arises because the probability of a molecule having energy $E$ decreases exponentially as $E$ increases.

Step 2: Rate Depends on This Fraction

The rate constant $k$ is proportional to:

The collision frequency (how often molecules meet)
The fraction of collisions with energy $\geq E_a$

Thus:

k \propto \text{(collision frequency)} \times e^{-E_a / (RT)}

The collision frequency is captured by $A$ , giving:

k = A e^{-E_a / (RT)}

Why the Plot is Linear

Take the natural logarithm of both sides:

\ln k = \ln A - \frac{E_a}{R} \cdot \frac{1}{T}

This is of the form $y = mx + c$ , where:

$y = \ln k$
$x = 1/T$
Slope $m = -E_a / R$
Intercept $c = \ln A$

Thus, plotting $\ln k$ vs $1/T$ gives a straight line — this is the Arrhenius plot.

What the Slope Tells Us

From the slope: …

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The assertion is FALSE — not every collision leads to product formation, only effective collisions do. The reason, however, correctly states the actual condition for a successful collision (correct orientation + sufficient kinetic energy) and is TRUE. This is an "Assertion incorrect, Reason correct" case, which none of the four listed options captures correctly — option (iv) as printed ("Both assertion and reason are incorrect") wrongly implies the reason is also false.

Assertion — "All collisions of reactant molecules lead to product formation" — is FALSE.

By collision theory, only a small fraction of collisions are effective. A collision yields product only when the molecules (i) carry kinetic energy at least equal to the activation energy $E_a$ , and (ii) are correctly oriented. The overwhelming majority of collisions are ineffective.

Reason — "Only those collisions in which molecules have correct orientation and sufficient kinetic energy lead to compound formation" — is TRUE. This is the standard statement of collision theory, and it directly explains why the assertion is false (it describes the actual, narrower condition, contradicting "all collisions"). …

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Here’s a breakdown of the common mistakes students make on this question and how to avoid each.

Common Mistake 1: Misreading the Assertion as True

What students do:

They see the word “collision” and think of the collision theory of chemical reactions. They assume the assertion must be correct because reactions happen when molecules collide.

Why it’s wrong:

The assertion says all collisions lead to product formation. Collision theory clearly states that only a fraction of collisions — those with sufficient energy (≥ activation energy) and correct orientation — are effective. Most collisions are ineffective.

How to avoid:

Read the assertion literally — look for absolute words like “all,” “always,” “never.”
Recall the two conditions for an effective collision:
1. Sufficient kinetic energy (≥ activation energy)
2. Proper orientation
If either condition is missing, no product forms. So “all collisions” is false.

Common Mistake 2: Thinking the Reason is Incorrect

What students do:

They confuse the reason with the assertion. They think the reason says “only those collisions with correct orientation and sufficient energy lead to product formation” is wrong because they remember that sometimes even with correct orientation and energy, a reaction may not occur due to other factors (like steric hindrance).

Why it’s wrong:

The reason is actually correct — it is a standard statement of collision theory. The two conditions (energy + orientation) are necessary for a reaction to occur. The reason does not claim they are sufficient for every possible reaction, but they are the minimum requirements.

How to avoid:

Separate the assertion (a claim) from the reason (an explanation).
The reason is a textbook definition — it is factually correct.
Do not overcomplicate: if the reason matches the standard theory, mark it as correct.

Common Mistake 3: Choosing Option (i) — Both correct, reason explains assertion

What students do:

They see both statements as true and assume the reason explains the assertion. They think: “Since the reason says only some collisions work, that explains why all collisions don’t lead to product formation.”

Why it’s wrong:

The assertion is false (all collisions do not lead to product formation). The reason is true. So the reason cannot explain a false assertion. Option (i) requires both statements to be correct.

How to avoid:

First, decide if the assertion is true or false.
Then decide if the reason is true or false.
Only then check if the reason explains the assertion (only possible if both are true).
Here: Assertion = false, Reason = true → correct answer is (iv).

Common Mistake 4: Choosing Option (ii) — Both correct, reason does not explain

What students do: …

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Same / Similar Concept — real previous-year questions on the same or a closely similar concept, not this exact question.

GSEB Higher Secondary Certificate (HSC) Examination 2024Set ANNUAL1 markMCQ
$Q. What is the slope of plot between lnK -> 1/T according to Arrhenius equation?$
(a) -2.303 Ea / R
(b) K / 2.303
(c) -Ea / R
(d) lnA
›Reveal solutionSolution

The Arrhenius equation in logarithmic form is a straight-line equation whose slope directly gives -Ea/R.

Arrhenius equation: k = A e^(-Ea/RT)

Taking natural log: ln k = ln A - Ea/(RT)

…

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GSEB Higher Secondary Certificate (HSC) Examination 2022Set ANNUAL1 markMCQ
$Q. What is the slope of the graph between ln k and 1/T?$
(a) -Ea/R
(b) -R/Ea
(c) -2.303Ea/R
(d) -2.303R/Ea
›Reveal solutionSolution

The Arrhenius equation k = A·e^(-Ea/RT) becomes linear when written as ln k = ln A - (Ea/R)(1/T).

Plotting ln k (y-axis) against 1/T (x-axis) gives a straight line of the form y = mx + c, where the slope m = -Ea/R and intercept c = ln A. This linear form is how activa …

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GUJCET 2020Set 071 markMCQ
$\log K \to \dfrac{1}{T}$
›Reveal solutionSolution
[!TLDR]

Only the first-order plot $\log\frac{[R]_0}{[R]}$ vs $t$ passes through the origin, so it alone has zero intercept.

Concept

The intercept of a straight-line graph is the value of the y-quantity when the x-quantity is zero; it is zero only if the line passes through the origin.

Solution

Examine each plot's intercept:

(A) Arrhenius: $\log K = \log A - \dfrac{E_a}{2.303RT}$ , so vs $\dfrac{1}{T}$ the intercept is $\log A \neq 0$ . …
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GSEB Higher Secondary Certificate (HSC) Examination 2020Set ANNUAL1 markMCQ
$Q. Which of the following graph for ln k -> 1/T is correct?$
(a) straight line, positive slope, through the origin
(b) horizontal straight line (constant)
(c) straight line, negative slope, decreasing from a positive y-intercept and levelling off
(d) straight line, positive slope, positive y-intercept (not through origin)
›Reveal solutionSolution

The Arrhenius equation, in logarithmic form, is a straight-line equation with slope -Ea/R, so ln k must DECREASE as 1/T increases - only option (c) shows a decreasing plot.

Arrhenius equation: k = A e^(-Ea/RT). Taking the natural log: ln k = ln A - Ea/(RT), i.e. ln k = ln A - (Ea/R)(1/T). This is of the form y = c + mx with y = ln k, x = 1/T, intercept c = ln A (a positive constant, since A > 0), and slope m = -Ea/R, which is NEGATIVE (since Ea and R are both positive). So as 1/T (i.e. as T falls) increases, ln k must decrease. Checking the four described graphs: (A) positive slope through origin - wrong sign and wrong intercept; (B) horizontal/constant - implies Ea=0, not general; (D) posit …

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GSEB Higher Secondary Certificate (HSC) Examination 2019Set ANNUAL1 markMCQ
$Q. What is the value of slope in the graph of log10 K against 1/T?$
(a) -Ea / 2.303 R
(b) -Ea / R
(c) -K / 2.303
(d) -K
›Reveal solutionSolution

The Arrhenius equation, written in log10 form, is a straight-line equation whose slope directly gives the activation energy.

Arrhenius equation: k = A e^(-Ea/RT). Taking log10 of both sides:

log10 k = log10 A - Ea/(2.303 R T) …

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GSEB Higher Secondary Certificate (HSC) Examination 2018Set ANNUAL1 markMCQ
$Q. For a reaction, the value of slope of a plot in ln K vs 1/T = ___.$
(a) -Ea
(b) -Ea/2.303
(c) Ea/R
(d) -Ea/2.303R
›Reveal solutionSolution

Arrhenius plot: log k vs 1/T is linear with slope = -Ea/(2.303 R).

Arrhenius equation: k = A e^(-Ea/RT).

Taking natural log: ln k = ln A - Ea/(R T) -> slope of ln k vs 1/T = -Ea/R.

Converting to base-10 log (as commonly plotted): log k = log A - Ea/(2.303 R T) -> slope of log k vs 1/T = -Ea/(2.303 R).

…

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GUJCET 2014Set A1 markMCQ
$\log k \to \frac{1}{T}$
›Reveal solutionSolution
[!TLDR] The slope of a $\log k$ vs $1/T$ plot is $-\dfrac{E_a}{2.303R}$ , option (B).

Concept

The Arrhenius equation relates the rate constant to temperature: $k = A\,e^{-E_a/RT}$ . Converting to base-10 logarithms linearises it, letting us read off the activation energy from a graph.

Solution

Take $\log_{10}$ of both sides: …
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Q.Assertion: All collision of reactant molecules lead to product formation.
Reason: Only those collisions in which molecules have correct orientation and sufficient kinetic energy lead to compound formation.

Concept understanding — Arrhenius Equation Plot

The Arrhenius Equation Plot: Why Temperature Changes Reaction Speed

The core idea: an energy barrier

The Arrhenius equation (precise statement)

Why plot it? The linear trick

What the plot tells you

A typical Arrhenius plot looks like this

Why this formula?

Arrhenius Equation Plot: Why It Holds

The Core Idea: Molecules Need Energy to React

The Key Formula

Why the Exponential Term Appears

Step 1: The Boltzmann Distribution

Step 2: Rate Depends on This Fraction

Why the Plot is Linear

What the Slope Tells Us

Concept: Collision Theory of Chemical Reactions

Method: Statement Analysis Method

Common Mistake 1: Misreading the Assertion as True

Common Mistake 2: Thinking the Reason is Incorrect

Common Mistake 3: Choosing Option (i) — Both correct, reason explains assertion

Common Mistake 4: Choosing Option (ii) — Both correct, reason does not explain

Concept

Solution

Concept

Solution

Q.Assertion: All collision of reactant molecules lead to product formation. Reason: Only those collisions in which molecules have correct orientation and sufficient kinetic energy lead to compound formation.

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Q.Assertion: All collision of reactant molecules lead to product formation.
Reason: Only those collisions in which molecules have correct orientation and sufficient kinetic energy lead to compound formation.

Unlock everything free for 14 days