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:

Write the rate law for a first order reaction, rate equals k times concentration, then match the units on both sides of the equation to work out the unit of k directly, instead of memorising a general formula.

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 \( s^{-1} \).

Answer 2

Concept:

• For a first order reaction, the rate law is $Rate = k[A]$, so the units of k can be obtained directly by matching the units on both sides of this equation.
• This builds the unit of k from the basic definition of rate, instead of relying on the general formula (concentration) to the power (1-n) times (time) to the power (-1).

Step 1: Write the units of reaction rate.
Rate is expressed as change in concentration per unit time: $mol\,L^{-1}\,s^{-1}$

Step 2: Write the units of concentration.
$[A]$ has units $mol\,L^{-1}$

Step 3: Solve for the units of k from the rate law.
$Rate = k[A]$, so $k = \dfrac{Rate}{[A]}$
$Units\ of\ k = \dfrac{mol\,L^{-1}\,s^{-1}}{mol\,L^{-1}} = s^{-1}$

Final Answer: The unit of the rate constant for a first order reaction is $s^{-1}$.