Q.In the reaction of zinc with dilute hydrochloric acid, the volume of hydrogen gas collected is plotted against time. The curve starts at the origin (zero volume at zero time) and rises, gradually levelling off. Volumes read from the curve are: $V_1$ at $t=20\text{ s}$, $V_2$ at $t=30\text{ s}$, $V_3$ at $t=40\text{ s}$, with larger volumes $V_4$ and $V_5$ near $t=50\text{ s}$. On this basis, mark the correct expression for the average rate of the reaction up to 40 seconds.

Reaction Rate Stoichiometry – From Intuition to Precision

Imagine you are watching a simple reaction:

$2 \text{NO}_2 \rightarrow 2 \text{NO} + \text{O}_2$

As NO₂ disappears, NO appears twice as fast as O₂ appears. Why? Because the balanced equation says: for every 2 molecules of NO₂ that break apart, you get 2 molecules of NO and 1 molecule of O₂. The numbers in front of the species — the stoichiometric coefficients — tell you the relative speeds at which reactants vanish and products appear.

That is the core idea: reaction rate stoichiometry is the relationship between the rates of change of different species in a chemical reaction, dictated by their coefficients in the balanced equation.

The Intuitive Picture

Think of a factory assembly line. The balanced equation is like a recipe:

• 2 units of raw material A → 2 units of product B + 1 unit of byproduct C

If the line runs steadily, every time 2 units of A are consumed, 2 units of B are produced and 1 unit of C is produced. So the rate at which A disappears must be twice the rate at which C appears. The rate at which B appears equals the rate at which A disappears (both have coefficient 2).

The Precise Statement

For a general reaction:

The rate of reaction (often called the rate of the process, $r$) is defined as:

Here:

• $\frac{d[X]}{dt}$ is the instantaneous rate of change of concentration of species X (in mol L⁻¹ s⁻¹).
• The minus sign is used for reactants (their concentration decreases with time).
• The plus sign is used for products (their concentration increases with time).
• Dividing by the coefficient normalises the rate — so $r$ is the same number for every species.

This single value $r$ is the intrinsic rate of the reaction, independent of which species you measure.

How to Use It (Step by Step)

Suppose you are given:

$2 \text{H}_2 + \text{O}_2 \rightarrow 2 \text{H}_2\text{O}$

And you measure that $\frac{d[\text{H}_2]}{dt} = -0.040 \text{ M/s}$ (negative because H₂ is being consumed).

Step 1: Write the rate relation:

Step 2: Plug in the known value:

Step 3: Find the rate for O₂:

Step 4: Find the rate for H₂O:

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