Question

Identify a type of order of reaction that its unit of rate constant is mol dm\(^{-3}\)s\(^{-1}\) from the following.

• A. Zero-order reaction
• B. First-order reaction
• C. Second-order reaction
• D. Third-order reaction

Hint:

Find the order n for which the unit of k is the same as the unit of rate.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
The rate constant \(k\) connects the rate of a reaction with the concentrations of reactants. Rate is always measured as concentration change per unit time, so its unit is \(\text{mol dm}^{-3}\text{s}^{-1}\) for every reaction.

Step 2: Key Formula or Approach:
For a reaction of order \(n\), \(\text{Rate} = k[\text{A}]^n\). So
\[ k = \frac{\text{Rate}}{[\text{A}]^n} \Rightarrow \text{unit of } k = (\text{mol dm}^{-3})^{1-n}\,\text{s}^{-1} \]

Step 3: Detailed Explanation:
Put \(n = 0\): the unit is \((\text{mol dm}^{-3})^{1}\text{s}^{-1} = \text{mol dm}^{-3}\text{s}^{-1}\). This is the unit given in the question.
For \(n = 1\): \((\text{mol dm}^{-3})^{0}\text{s}^{-1} = \text{s}^{-1}\).
For \(n = 2\): \((\text{mol dm}^{-3})^{-1}\text{s}^{-1} = \text{mol}^{-1}\text{dm}^{3}\text{s}^{-1}\).
For \(n = 3\): \((\text{mol dm}^{-3})^{-2}\text{s}^{-1} = \text{mol}^{-2}\text{dm}^{6}\text{s}^{-1}\).
So the first-order, second-order and third-order reactions each have a different unit, and only the zero-order reaction has the same unit as the rate.

Final Answer:
A zero-order reaction has \(\text{Rate} = k\), so \(k\) has the unit of rate. This is option (A). \[ \boxed{\text{Zero-order reaction (A)}} \]