Question

Identify the unit of rate constant for a first-order reaction.

• A. \(\text{mol dm}^{-3}\text{s}^{-1}\)
• B. \(\text{s}^{-1}\)
• C. \(\text{mol}^{-1}\text{dm}^3\text{s}^{-1}\)
• D. \(\text{mol dm}^{-3}\)

Hint:

Remember the common units of rate constants:
• Zero order: \[ \text{mol dm}^{-3}\text{s}^{-1} \]
• First order: \[ \text{s}^{-1} \]
• Second order: \[ \text{mol}^{-1}\text{dm}^3\text{s}^{-1} \] The unit changes with reaction order.

Answer 1

The Correct Option is B

Concept: The unit of the rate constant depends upon the order of the reaction. The general rate law is: \[ \text{Rate} = k[A]^n \] where:
• \(k\) = rate constant
• \([A]\) = concentration of reactant
• \(n\) = order of reaction For a first-order reaction: \[ \text{Rate} = k[A] \] The rate of reaction has units: \[ \text{mol dm}^{-3}\text{s}^{-1} \] and concentration has units: \[ \text{mol dm}^{-3} \]

Step 1: Writing the rate law for first-order reaction.
For first order: \[ \text{Rate} = k[A] \] Rearranging: \[ k = \frac{\text{Rate}}{[A]} \]

Step 2: Substituting the units.
\[ k = \frac{\text{mol dm}^{-3}\text{s}^{-1}}{\text{mol dm}^{-3}} \]

Step 3: Cancelling the common concentration units.
\[ k = \text{s}^{-1} \] Thus, the unit of rate constant for a first-order reaction is inverse second.

Step 4: Evaluating the options.

• \(\text{mol dm}^{-3}\text{s}^{-1}\): Unit of reaction rate, not rate constant.
• \(\text{s}^{-1}\): Correct unit for first-order rate constant.
• \(\text{mol}^{-1}\text{dm}^3\text{s}^{-1}\): Unit of second-order rate constant.
• \(\text{mol dm}^{-3}\): Unit of concentration only.

Step 5: Final conclusion.
Therefore, the correct unit is: \[ \boxed{\text{s}^{-1}} \] Hence, the correct option is: \[ \boxed{(2)\ \text{s}^{-1}} \]