Oxygen is available in plenty in air yet fuels do not burn by themselves at room temperature. Explain.

NCERT Exemplar · Q33

Q. Oxygen is available in plenty in air yet fuels do not burn by themselves at room temperature. Explain.

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Concept understanding — Arrhenius Equation

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: 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 picture step by step.

1. The Core Question

Why does reaction rate increase dramatically with temperature?

For many reactions, a 10 °C rise can double or triple the rate. This cannot be explained by simple kinetic energy arguments alone — the relationship is exponential.

2. The Key Insight: An Energy Barrier

Before molecules can react, they must collide — but not all collisions lead to products.

There is a minimum energy threshold called activation energy ( $E_a$ ). Only collisions with energy ≥  $E_a$ can break old bonds and form new ones.

Think of it like pushing a boulder over a hill:

The hilltop is the transition state (activated complex).
$E_a$ is the height of that hill from the reactant valley.

3. The Boltzmann Factor — The "Why" of Exponential Dependence

At temperature $T$ , the fraction of molecules with energy ≥  $E_a$ is given by the Boltzmann distribution:

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

where:

$R$ = universal gas constant (8.314 J mol⁻¹ K⁻¹)
$T$ = absolute temperature (Kelvin)

Why this form?

The Boltzmann distribution tells us that the probability of a molecule having energy $E$ is proportional to $e^{-E/(k_B T)}$ .
For 1 mole of molecules, $k_B$ (Boltzmann constant) becomes $R$ via $R = N_A k_B$ .
So the fraction with energy ≥ $E_a$ is the integral of that distribution from $E_a$ to ∞, which yields $e^{-E_a/(RT)}$ .

Key takeaway: This exponential factor is not arbitrary — it comes directly from statistical mechanics.

4. The Pre-Exponential Factor ( $A$ )

Even if a collision has enough energy, it must also:

Have the correct orientation (steric factor)
Occur with sufficient collision frequency

These are bundled into the pre-exponential factor $A$ (also called the frequency factor):

A = \text{(collision frequency)} \times \text{(orientation factor)}

For simple gas-phase reactions, collision frequency can be calculated from kinetic molecular theory — it's on the order of $10^{10}$  L mol⁻¹ s⁻¹.

5. Putting It Together: The Arrhenius Equation

The rate constant $k$ is proportional to:

The number of effective collisions per second (given by $A$ )
The fraction of collisions with sufficient energy (given by $e^{-E_a/(RT)}$ )

Thus:

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

This is the Arrhenius equation.

6. Why It Works — The Physical Logic

Component	Physical meaning	Why it's there
$A$	Maximum possible rate if every collision worked	Accounts for collision frequency & geometry

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The Arrhenius equation shows that the rate constant $k = A e^{-E_a/RT}$ is extremely small at room temperature because the thermal energy $RT$ is much smaller than the activation energy $E_a$ for combustion. So, even though oxygen is abundant, the reaction rate is negligible — fuels do not burn spontaneously.

The key lies not in the availability of oxygen, but in the energy barrier that must be overcome for the reaction to start. Think of it like a boulder at the top of a hill: it has plenty of gravitational potential energy, but it won’t roll down unless you give it a push past the small lip at the top. That push is the activation energy.

The Arrhenius Equation governs reaction rates. For any chemical reaction, the rate constant $k$ is given by:

k = A e^{-E_a/RT}

where $A$ is the frequency factor (how often molecules collide in the right orientation), $E_a$ is the activation energy (the minimum energy needed for the reaction to occur), $R$ is the gas constant, and $T$ is the absolute temperature.

At room temperature, $RT$ is small.

At $T \approx 298\ \text{K}$ , $RT \approx 2.48\ \text{kJ/mol}$ . For combustion reactions (like burning wood, petrol, or coal), the activation energy $E_a$ is typically in the range of $100$ – $200\ \text{kJ/mol}$ . So the ratio $E_a/RT$ is huge — around $40$ to $80$ .
The exponential factor crushes the rate.

Even a modest $E_a/RT = 40$ gives $e^{-40} \approx 4 \times 10^{-18}$ . That means the rate constant is astronomically small — effectively zero. Billions of oxygen molecules collide with the fuel every second, but almost none have enough energy to cross the barrier.
Why a spark or flame works. …

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Common Mistakes on "Why Fuels Don't Burn at Room Temperature Despite Oxygen Being Present"

The Core Concept

This question tests your understanding of the fire triangle (or combustion triangle) — three essential requirements for combustion:

Fuel (combustible substance)
Oxygen (oxidising agent)
Ignition temperature (minimum temperature to start burning)

All three must be present simultaneously. Oxygen alone is insufficient.

Mistake #1: Saying "Oxygen is not reactive enough at room temperature"

Why it's wrong: Oxygen is actually quite reactive — it causes rusting, tarnishing, and slow oxidation of many materials at room temperature. The issue is not oxygen's reactivity, but the energy barrier for combustion.

How to avoid: Remember that combustion is a rapid oxidation reaction that produces heat and light. At room temperature, the fuel molecules don't have enough kinetic energy to overcome the activation energy barrier. The reaction is thermodynamically possible but kinetically slow.

Mistake #2: Confusing "ignition temperature" with "boiling point" or "melting point"

Why it's wrong: Ignition temperature is a specific property — the minimum temperature at which a substance catches fire and continues to burn. It has nothing to do with phase changes.

Example: Paper's ignition temperature is about $233^\circ\text{C}$ , while its boiling point is irrelevant (paper decomposes before boiling).

How to avoid: Define ignition temperature clearly in your answer: "The minimum temperature to which a fuel must be heated so that it catches fire and sustains combustion."

Mistake #3: Giving only a one-line answer

Why it's wrong: Many students write: "Because ignition temperature is needed." This is incomplete — you must explain why ignition temperature matters.

How to avoid: Structure your answer in three parts:

State the fire triangle — fuel, oxygen, ignition temperature
Identify what's missing — at room temperature, ignition temperature is not reached
Explain the mechanism — below ignition temperature, the rate of heat generation is less than heat loss to surroundings, so combustion cannot sustain itself

Mistake #4: Using vague terms like "energy" or "heat" without specificity

Why it's wrong: Saying "Fuels need energy to burn" is too vague. The precise concept is activation energy — the minimum energy required for the reaction to start.

How to avoid: Use the correct terminology:

At room temperature, fuel molecules lack sufficient kinetic energy to overcome the activation energy barrier of the combustion reaction. Once heated to the ignition temperature, the reaction becomes self-sustaining because the heat released exceeds the heat lost.

Mistake #5: Forgetting to mention that some fuels do burn at room temperature

Why it's wrong: This shows incomplete understanding. Substances like white phosphorus (ignition temperature $\approx 30^\circ\text{C}$ ) and liquefied petroleum gas (LPG) (if a spark is present) can ignite near room temperature.

How to avoid: Add a qualifying statement: …

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

TG EAPCET 2024Set eng-2024-05-11-FN1 markMCQ
$Q. At what temperature will the RMS velocity of sulphur dioxide molecules at 400 K be the same as the most probable velocity of oxygen molecules? (A) 600 K (B) 200 K (C) 400 K (D) 300 K$
›Reveal solutionSolution

Equating $v_{rms}(\text{SO}_2, 400\,\text{K})$ with $v_{mp}(\text{O}_2, T)$ gives $T = 300$ K.

$v_{rms} = \sqrt{\frac{3RT_1}{M_1}}, \qquad v_{mp} = \sqrt{\frac{2RT_2}{M_2}}.$
With $M(\text{SO}_2) = 64$ , $T_1 = 400$ K, and $M(\text{O}_2) = 32$ , set the two speeds equal:

$\frac{3RT_1}{M_1} = \frac{2RT_2}{M_2}$ …
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TG EAPCET 2021Set ap-2021-08-10-AN1 markMCQ
$^\circ$
›Reveal solutionSolution
The temperature coefficient (Q₁₀ = 2) tells us the rate constant halves for every 10 °C drop. From 25 °C to 15 °C is a 10 °C decrease, so the rate constant at 15 °C is half of $1 \times 10^{-3}$ min⁻¹, i.e., $5 \times 10^{-4}$ min⁻¹.

Concept & Intuition

The temperature coefficient (often denoted $Q_{10}$ ) is defined as the factor by which the rate constant increases when the temperature is raised by 10 °C.

Here $Q_{10} = 2$ means:

Increase temperature by 10 °C → rate constant doubles.

Decrease temperature by 10 °C → rate constant halves.

We are moving down from 25 °C to 15 °C, a drop of exactly 10 °C. So the rate constant at the lower temperature is simply $k_{15} = k_{25} / 2$ .

Step-by-step reasoning

Identify the given data

$k_{25} = 1 \times 10^{-3}$ min⁻¹

Temperature coefficient $Q_{10} = 2$

Temperature change: from 25 °C to 15 °C = −10 °C

Apply the definition of temperature coefficient

The relationship is:

$\frac{k_{T+10}}{k_T} = Q_{10}$
So for a 10 °C decrease:
$\frac{k_{15}}{k_{25}} = \frac{1}{Q_{10}} = \frac{1}{2}$

Calculate the unknown rate constant $k_{15} = k_{25} \times \frac{1}{2} = (1 \times 10^{-3}) \times \frac{1}{2} = 0.5 \times 10^{-3} = 5 \times 10^{-4} \text{ min}^{-1}$ …
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TG EAPCET 2021Set ap-2021-08-10-FN1 markMCQ
$25^\circ \mathrm{C}$
›Reveal solutionSolution
The temperature coefficient (Q₁₀ = 2) tells us the rate constant halves for every 10°C drop. Going from 25°C to 15°C is a 10°C decrease, so the rate constant at 15°C is half of the given value: $5 \times 10^{-4}~\mathrm{min}^{-1}$ .

Concept & Intuition

The temperature coefficient (often denoted $Q_{10}$ ) is the factor by which the rate constant changes when the temperature is raised by 10°C. Here $Q_{10} = 2$ means that for every 10°C increase, the rate constant doubles; conversely, for every 10°C decrease, it halves. Since we are moving from 25°C down to 15°C (a drop of exactly 10°C), we simply divide the given rate constant by 2.

Step-by-step reasoning

Identify the temperature change

The given rate constant $k_{25} = 1 \times 10^{-3}~\mathrm{min}^{-1}$ is at $25^\circ\mathrm{C}$ . We need $k_{15}$ at $15^\circ\mathrm{C}$ .

The difference: $25^\circ\mathrm{C} - 15^\circ\mathrm{C} = 10^\circ\mathrm{C}$ .

Apply the definition of the temperature coefficient

The temperature coefficient $Q_{10}$ is defined as

$Q_{10} = \frac{k_{T+10}}{k_T}$
Here $Q_{10} = 2$ , so for a 10°C increase the rate constant multiplies by 2. For a 10°C decrease, we use the reciprocal:
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TG EAPCET 2021Set eng-2021-08-05-AN1 markMCQ
$Q. When salt is added to water, which of the following statement is true? (A) Boiling point decreases (B) Boiling point increases (C) Boiling point remain constant (D) Freezing point increases$
›Reveal solutionSolution
Adding salt to water raises its boiling point and lowers its freezing point — a colligative effect. The correct statement is that the boiling point increases.

The question tests your understanding of colligative properties — properties that depend only on the number of solute particles, not their chemical identity. When salt (sodium chloride, NaCl) dissolves in water, it dissociates into Na⁺ and Cl⁻ ions, increasing the total number of particles in the solution. This changes two key physical properties of water: its boiling point and its freezing point.

Why does this happen? At the boiling point, the vapour pressure of the liquid equals the atmospheric pressure. Adding a non-volatile solute like salt lowers the vapour pressure of the solvent (water). To make the vapour pressure reach atmospheric pressure again, you need to supply more heat — hence the boiling point rises. For freezing, the solute particles disrupt the orderly arrangement of water molecules into ice, so a lower temperature is needed to freeze the solution — hence the freezing point drops.

Let’s examine each option step by step.

Boiling point behaviour

The boiling point elevation is given by $\Delta T_b = i \cdot K_b \cdot m$ , where $i$ is the van’t Hoff factor (for NaCl, $i \approx 2$ ), $K_b$ is the ebullioscopic constant of water, and $m$ is the molality. Since $\Delta T_b > 0$ , the boiling point increases. This eliminates option (A) and (C).

Freezing point behaviour …
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←Previous questionQ32 — Why does the rate of a reaction increase with rise in temperature?→Next questionQ34 — Why is the probability of reaction with molecularity higher than three…

Q.Oxygen is available in plenty in air yet fuels do not burn by themselves at room temperature. Explain.

Concept understanding — Arrhenius Equation

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: Why It Holds

1. The Core Question

2. The Key Insight: An Energy Barrier

3. The Boltzmann Factor — The "Why" of Exponential Dependence

4. The Pre-Exponential Factor ( $A$ )

5. Putting It Together: The Arrhenius Equation

6. Why It Works — The Physical Logic

Concept: Activation Energy in Chemical Reactions

Method: Energy Barrier Explanation

Common Mistakes on "Why Fuels Don't Burn at Room Temperature Despite Oxygen Being Present"

The Core Concept

Mistake #1: Saying "Oxygen is not reactive enough at room temperature"

Mistake #2: Confusing "ignition temperature" with "boiling point" or "melting point"

Mistake #3: Giving only a one-line answer

Mistake #4: Using vague terms like "energy" or "heat" without specificity

Mistake #5: Forgetting to mention that some fuels do burn at room temperature

Q.Oxygen is available in plenty in air yet fuels do not burn by themselves at room temperature. Explain.

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