Question

The unit of rate and rate constant is same for which order of reaction?

• A. First
• B. Second
• C. Third
• D. Zero

Hint:

Unit of \( k \) is \( mol^{1-n}L^{n-1}s^{-1} \); set it equal to the rate unit \( mol\,L^{-1}s^{-1} \).

Answer 1

The Correct Option is D

Step 1: The rate of a reaction is measured as change in concentration per unit time, so its unit is always \( mol\,L^{-1}\,s^{-1} \).
Step 2: For a reaction of order \( n \), rate \( = k[A]^n \), so \( k = \dfrac{\text{rate}}{[A]^n} \) and the unit of \( k \) is \( \dfrac{mol\,L^{-1}\,s^{-1}}{(mol\,L^{-1})^n} = mol^{1-n}\,L^{n-1}\,s^{-1} \).
Step 3: The unit of \( k \) equals the unit of rate only when \( 1-n=1 \), i.e. \( n=0 \).
Step 4: For a zero order reaction, rate \( = k[A]^0 = k \), so \( k \) carries the same unit \( mol\,L^{-1}\,s^{-1} \) as the rate. (First order \( k \) is \( s^{-1} \); second order \( L\,mol^{-1}\,s^{-1} \); third order \( L^2\,mol^{-2}\,s^{-1} \), all different from the rate unit.)
Answer: Zero order.