Question

For a first-order reaction, the unit of rate constant is:

• A. mol \( L^{-1} s^{-1} \)
• B. \( s^{-1} \)
• C. L \( mol^{-1} s^{-1} \)
• D. mol \( L^{-1} \)

Hint:

Zero-order unit: \( \text{mol L}^{-1} s^{-1} \)
First-order unit: \( s^{-1} \)
Second-order unit: \( \text{L mol}^{-1} s^{-1} \)
Identifying the order from the unit of \( k \) is a common exam trick!

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
The rate constant (\( k \)) links the reaction rate to the concentrations of reactants.
Its units change depending on the overall order of the reaction.
Step 2: Key Formula or Approach:
The general unit for a rate constant for a reaction of order \( n \) is:
\[ \text{Units of } k = (\text{concentration})^{1-n} \cdot \text{time}^{-1} \]
Concentration is typically measured in \( \text{mol/L} \) (or M).
Step 3: Detailed Explanation:
For a first-order reaction, \( n = 1 \).
Substituting into the general formula:
\[ \text{Unit} = (\text{mol L}^{-1})^{1-1} \cdot s^{-1} \]
\[ \text{Unit} = (\text{mol L}^{-1})^0 \cdot s^{-1} \]
\[ \text{Unit} = 1 \cdot s^{-1} = s^{-1} \]
Thus, the rate of a first-order reaction depends only on the frequency of the process, and its constant is independent of concentration units.
Step 4: Final Answer:
The unit of the rate constant for a first-order reaction is \( s^{-1} \).