Rate constant of a reaction (k) is `2 xx 10^(-3) "litre"^(-1) molsec^(-1)`. What is the order of reaction ?

Options

A. 1
B. 0
C. 3
D. 2

Explanation

To determine the order of the reaction based on the given rate constant (k), we can follow these steps:

### Step 1: Write the rate law expression
The rate of a reaction can be expressed using the rate law:
\[ \text{Rate} = k [A]^x \]
where:
- \( k \) is the rate constant,
- \( [A] \) is the concentration of the reactant,
- \( x \) is the order of the reaction.

### Step 2: Identify the units of the rate
The unit of rate is typically expressed as:
\[ \text{Rate} = \text{mole} \, \text{litre}^{-1} \, \text{second}^{-1} \]

### Step 3: Identify the units of the rate constant (k)
The given unit of the rate constant \( k \) is:
\[ k = 2 \times 10^{-3} \, \text{litre}^{-1} \, \text{mol} \, \text{sec}^{-1} \]

### Step 4: Relate the units of k to the order of the reaction
From the rate law, we can express the units of \( k \) in terms of the order \( x \):
\[ \text{Units of } k = \frac{\text{Units of Rate}}{(\text{Units of Concentration})^x} \]
Substituting the units:
\[ \text{Units of } k = \frac{\text{mole} \, \text{litre}^{-1} \, \text{second}^{-1}}{(\text{mole} \, \text{litre}^{-1})^x} \]

### Step 5: Simplify the units
This can be simplified to:
\[ \text{Units of } k = \text{mole} \, \text{litre}^{-1} \, \text{second}^{-1} \cdot \text{mole}^{-x} \, \text{litre}^{x} \]
\[ = \text{mole}^{1-x} \, \text{litre}^{x-1} \, \text{second}^{-1} \]

### Step 6: Set the units equal to each other
Now, we can set the units of \( k \) equal to the given units:
\[ \text{mole}^{1-x} \, \text{litre}^{x-1} \, \text{second}^{-1} = \text{mole}^{0} \, \text{litre}^{-1} \, \text{second}^{-1} \]

### Step 7: Compare the exponents
From the comparison, we can derive two equations:
1. For mole: \( 1 - x = 0 \) → \( x = 1 \)
2. For litre: \( x - 1 = -1 \) → \( x = 0 \)

### Step 8: Determine the order of the reaction
Since both conditions must be satisfied, we find that:
- The order of the reaction \( x = 0 \).

Thus, the reaction is a **zero-order reaction**.

### Final Answer:
The order of the reaction is **0** (zero order).

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