Read the passage carefully and answer the questions.

The chemical reactions proceed at different rates which depend on various factors like concentration, temperature, etc. Rate law is an expression which relates the rate of reaction with concentration of various reacting species in the reaction. For a first order reaction, the concentration of the reactant after time $t$ is related with its initial concentration by the relation, $C = C_0e^{-kt}$. The rate constants for different orders have different expressions. For a first order reaction, $k =\frac{2.303}{t}\log\frac{a}{a-x}$, where $a$ is the initial concentration and $x$ is the extent of reaction.

The quantity k in a rate law expression is

independent of reactant concentration

The correct answer is Option (4) → independent of reactant concentration

The quantity k in a rate law expression is the rate constant.

• The rate constant (k) depends only on:
• Temperature
• Nature of reactants
• Presence of catalyst
• Solvent (sometimes)
• k is independent of the concentration of reactants.

The rate of reaction depends on concentration (rate = k [A]ᵐ [B]ⁿ), but the rate constant k itself does not change with concentration.

Why other options are wrong:

• ☀ directly proportional to concentration → Incorrect (Rate is proportional, not k)
• ☀ inversely proportional to concentration → Incorrect
• ☀ doubled on increasing concentration by 10 times → Incorrect (k remains the same; only rate changes)

Hence, the correct statement is: independent of reactant concentration