At high pressure the following reaction is zero order. $2NH_3(g) \xrightarrow[\text{Platinum catalyst}]{1130\ K} N_2(g) + 3H_2(g)$ Which of the following options are correct for this reaction? (Two or more than two options may be correct.) (i) Rate of reaction = Rate constant. (ii) Rate of the reaction depends on concentration of ammonia. (iii) Rate of decomposition of ammonia will remain constant until ammonia disappears completely. (iv) Further increase in pressure will change the rate of reaction.

At high pressure the following reaction is zero order. 2NH₃(g) xrightarrow[Platinum catalyst]1130K N₂(g) + 3H₂

NCERT Exemplar · Q50

2NH_3(g) \xrightarrow[\text{Platinum catalyst}]{1130\ K} N_2(g) + 3H_2(g)

(i) Rate of reaction = Rate constant.

(ii) Rate of the reaction depends on concentration of ammonia.

(iii) Rate of decomposition of ammonia will remain constant until ammonia disappears completely.

(iv) Further increase in pressure will change the rate of reaction.

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Concept understanding — Zero Order Kinetics

Zero Order Kinetics: The Drug That Doesn't Care How Much You Give It

Imagine you're filling a bathtub. You turn the tap to a fixed flow rate — say, 5 litres per minute. The amount of water in the tub increases by exactly 5 litres every minute, regardless of whether the tub is empty or already half full. That's the core intuition behind zero order kinetics: a constant amount disappears per unit time, no matter how much is left.

Now contrast this with what you probably expect. Most processes in nature follow first order kinetics: the rate depends on how much is present. If you have 100 molecules, 10 might react per second; if you have 10 molecules, only 1 reacts per second. The fraction lost is constant, but the amount lost per second shrinks as the quantity shrinks. Zero order is the opposite — the amount lost per second is fixed, so the fraction lost actually increases as the quantity drops.

The Precise Statement

-\frac{d[A]}{dt} = k_0

Where $[A]$ is the concentration of the substance (or amount, depending on context), $t$ is time, and $k_0$ is the zero order rate constant with units of concentration per time (e.g., mg/L per hour, or simply mg/hour if we're talking about total amount).

The negative sign indicates the substance is being removed. The key point: the rate does not depend on $[A]$ . It's a flat, constant rate.

The Integrated Form and Half-Life

If you integrate the differential equation, you get a straight line:

[A]_t = [A]_0 - k_0 t

This is the equation of a line with slope $-k_0$ and intercept $[A]_0$ . Plot concentration vs. time, and you get a straight line sloping downward until it hits zero.

The half-life — the time for the concentration to fall to half its initial value — is:

t_{1/2} = \frac{[A]_0}{2k_0}

Notice something crucial: the half-life depends on the initial concentration. Double the starting amount, and the half-life doubles. This is completely different from first order kinetics, where half-life is constant regardless of starting concentration.

Watch out

A common mistake: students assume half-life is always constant. For zero order, it is not. The half-life changes with the starting amount. If you start with 100 mg, half-life might be 5 hours; start with 200 mg, half-life becomes 10 hours.

Where Does Zero Order Kinetics Actually Happen?

In pharmacology, zero order kinetics is most famously seen with ethanol (alcohol) and aspirin at high doses. The reason is saturation of enzymes.

Your body metabolises alcohol using an enzyme called alcohol dehydrogenase. At low alcohol levels, the enzyme works efficiently and the rate depends on how much alcohol is present (first order). But at higher concentrations — say, after a few drinks — the enzyme becomes saturated. It's working at maximum speed, like a factory running at full capacity. Adding more raw material (alcohol) doesn't make it work faster. The rate becomes constant: a fixed amount of alcohol is metabolised per hour, regardless of how much is in your blood.

This is why alcohol elimination follows a straight line when you plot blood alcohol concentration vs. time. A typical person eliminates about 0.015 g/dL per hour — a fixed amount, not a fixed fraction.

Note

The same saturation principle applies to some drug transporters in the kidneys. When the transport proteins are working at maximum capacity, drug excretion becomes zero order. This is why high doses of certain drugs (like phenytoin) can lead to unexpectedly long elimination times — the system is overwhelmed.

A Quick Comparison Table

Property	Zero Order	First Order
Rate depends on	Nothing (constant)	Concentration
Rate equation	$-\frac{d[A]}{dt} = k_0$	$-\frac{d[A]}{dt} = k_1[A]$

Why this formula?

Zero Order Kinetics: Why the Formula Holds

Let's build this from the ground up — understanding the why before the what.

The Core Idea

Zero order kinetics describes a process where the rate is constant — it does not depend on the concentration of the reactant.

This is the definition, but why would that ever happen?

Why the Rate is Constant

Imagine a reaction happening on a solid surface (like a catalyst or a tablet dissolving). The reactant molecules must first adsorb onto the surface before reacting.

If the surface is saturated with reactant molecules, adding more reactant in solution doesn't help — the surface is already full.
The reaction proceeds at a fixed speed determined by how fast the surface can process the adsorbed molecules.

Key insight: The rate is limited by the surface, not by how much reactant is floating around.

Deriving the Zero Order Rate Law

Step 1: Write the rate definition

For a reaction $A \rightarrow \text{products}$ , the rate of disappearance of $A$ is:

-\frac{d[A]}{dt} = k

where $k$ is the zero order rate constant (units: concentration/time, e.g., $\text{mol L}^{-1} \text{s}^{-1}$ ).

Notice: No $[A]$ term on the right side — that's the signature of zero order.

Step 2: Separate variables and integrate

-d[A] = k \, dt

Integrate from initial time $t=0$ (concentration $[A]_0$ ) to time $t$ (concentration $[A]_t$ ):

-\int_{[A]_0}^{[A]_t} d[A] = k \int_0^t dt

-[A]_t + [A]_0 = kt

Step 3: Rearrange to the familiar form

\boxed{[A]_t = [A]_0 - kt}

This is the integrated rate law for zero order kinetics.

What This Formula Tells Us

Linear decrease: Concentration falls linearly with time (not exponentially like first order).
Slope = $-k$ : A plot of $[A]_t$ vs. $t$ gives a straight line with slope $-k$ .
Half-life depends on initial concentration:

Set $[A]_t = \frac{[A]_0}{2}$ :

\frac{[A]_0}{2} = [A]_0 - k t_{1/2}

\boxed{t_{1/2} = \frac{[A]_0}{2k}}

Critical exam point: Unlike first order (where $t_{1/2}$ is constant), zero order half-life increases with higher initial concentration.

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For a zero-order reaction, the rate is constant and independent of reactant concentration — so the rate equals the rate constant, and decomposition proceeds at a steady pace until the reactant is exhausted. Options (i) and (iii) are correct.

This is a classic zero-order kinetics problem, but it’s wrapped in a high-pressure context that can confuse students. Let’s unpack why.

The core idea: What does “zero order” actually mean?

A zero-order reaction has a rate that does not depend on the concentration of the reactant. The rate law is:

\text{Rate} = k[\text{NH}_3]^0 = k

That’s it — the rate is just the rate constant $k$ , a fixed number at a given temperature. No matter how much ammonia is left, the reaction chugs along at the same speed until the ammonia runs out.

Why would a reaction be zero order? At very high pressure, the platinum catalyst surface gets completely covered with ammonia molecules. Adding more ammonia gas can’t increase the number of molecules reacting per second — the surface is already saturated. So the rate is limited by the catalyst’s capacity, not by how much ammonia is floating around.

Now let’s test each option.

Option (i): Rate of reaction = Rate constant.

From the rate law above, this is literally true for a zero-order reaction. The rate is $k$ , and $k$ is the rate constant. So (i) is correct.
Option (ii): Rate depends on concentration of ammonia.

For zero order, the rate is independent of $[\text{NH}_3]$ . The exponent is zero — concentration doesn’t appear in the rate expression. So (ii) is wrong.
Option (iii): Rate of decomposition of ammonia will remain constant until ammonia disappears completely.

Yes — that’s the hallmark of zero-order kinetics. The rate is constant, so the concentration decreases linearly with time. The reaction keeps going at the same speed until the last molecule is gone. (iii) is correct.
Option (iv): Further increase in pressure will change the rate of reaction. …

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Common Mistakes in Zero Order Kinetics (NH₃ Decomposition)

Mistake 1: Confusing "Rate = k" with "Rate is constant"

The error: Students think (i) is wrong because they believe rate always depends on concentration.

Why it happens: They memorise "rate depends on concentration" without understanding the zero order exception.

The correct understanding:

For zero order: $\text{Rate} = k[\text{NH}_3]^0 = k$
This means rate = rate constant numerically (option A is correct)
The rate does not change as [NH₃] decreases

How to avoid: Remember the order = exponent rule:

Zero order → exponent 0 → concentration term = 1 → Rate = k

Mistake 2: Selecting option (ii) — "Rate depends on concentration"

The error: Students apply first-order thinking to a zero-order reaction.

Why it happens: They don't check that "high pressure" means surface of catalyst is saturated — all active sites are occupied.

The correct understanding:

At high pressure, catalyst surface is fully covered with NH₃ molecules
Adding more NH₃ (higher concentration) cannot increase the reaction rate
Rate depends only on how fast the surface reaction occurs → constant rate

How to avoid: For heterogeneous catalysis:

Low pressure → rate ∝ concentration (first order)
High pressure → rate independent of concentration (zero order)

Mistake 3: Rejecting option (iii) — "Rate remains constant until NH₃ disappears"

The error: Students think rate must slow down as reactant is used up.

Why it happens: They apply homogeneous kinetics logic to a surface reaction.

The correct understanding:

In zero order: $-\frac{d[\text{NH}_3]}{dt} = k$
This means constant slope on a concentration vs. time graph
Rate stays constant as long as the condition (high pressure) holds
When NH₃ becomes very low, pressure drops → reaction may shift from zero order

How to avoid: Draw the concentration-time graph:

Zero order → straight line with constant negative slope
First order → curved line with decreasing slope

Mistake 4: Selecting option (iv) — "Further increase in pressure changes rate"

The error: Students think "more pressure always means faster reaction." …

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Q.At high pressure the following reaction is zero order.
$2NH_3(g) \xrightarrow[\text{Platinum catalyst}]{1130\ K} N_2(g) + 3H_2(g)$
Which of the following options are correct for this reaction? (Two or more than two options may be correct.)

Concept understanding — Zero Order Kinetics

Zero Order Kinetics: The Drug That Doesn't Care How Much You Give It

The Precise Statement

The Integrated Form and Half-Life

Where Does Zero Order Kinetics Actually Happen?

A Quick Comparison Table

Why this formula?

Zero Order Kinetics: Why the Formula Holds

The Core Idea

Why the Rate is Constant

Deriving the Zero Order Rate Law

Step 1: Write the rate definition

Step 2: Separate variables and integrate

Step 3: Rearrange to the familiar form

What This Formula Tells Us

The core idea: What does “zero order” actually mean?

Method: Zero Order Kinetics — Definition & Direct Application

Step 1 — Recall the defining equation of zero order kinetics

Step 2 — Apply to the given reaction

Step 3 — Interpret "constant rate until disappearance"

Common Mistakes in Zero Order Kinetics (NH₃ Decomposition)

Mistake 1: Confusing "Rate = k" with "Rate is constant"

Mistake 2: Selecting option (ii) — "Rate depends on concentration"

Mistake 3: Rejecting option (iii) — "Rate remains constant until NH₃ disappears"

Mistake 4: Selecting option (iv) — "Further increase in pressure changes rate"

The core idea: What does “zero order” actually mean?

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