Question

The order of reaction for which the units of rate constant are mol dm$^{-3}$ s$^{-1}$ is

• A. 2
• B. 1
• C. 0
• D. 3

Hint:

For a zero-order reaction, the rate of the reaction is completely independent of the concentration of the reactants. Because the concentration term disappears ($\text{Rate} = k \cdot C^0 = k$), the rate constant $k$ inherits the exact same units as the reaction rate itself ($\text{mol dm}^{-3} \text{s}^{-1}$).

Answer 1

The Correct Option is C

Step 1: Write the rate law.
For overall order $n$, $\text{Rate} = k[\text{A}]^n$, so the units of $k$ must make both sides match.
Step 2: State the units of rate.
Rate is concentration over time, so its units are $\text{mol dm}^{-3}\,\text{s}^{-1}$.
Step 3: Use the general unit formula.
Rearranging the rate law gives units of $k = (\text{mol dm}^{-3})^{1-n}\,\text{s}^{-1}$.
Step 4: Set it equal to the given units.
We are told $k$ has units $\text{mol dm}^{-3}\,\text{s}^{-1}$, so $(\text{mol dm}^{-3})^{1-n}\,\text{s}^{-1} = (\text{mol dm}^{-3})^{1}\,\text{s}^{-1}$.
Step 5: Match the exponents.
Comparing the power of concentration: $1 - n = 1$, which gives $n = 0$.
Step 6: Interpret.
The units of $k$ equal the units of rate exactly when concentration has no influence, the signature of a zero-order reaction.
\[ \boxed{n = 0,\ \text{option (3)}} \]