The rate constant for a reaction is `10.8 xx 10^(-3) "mol L"^(-1)`. The reaction obeys:

Options

A. First order
B. Zero order
C. Second order
D. All are wrong

Explanation

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

### Step 1: Understand the Units of the Rate Constant
The rate constant (k) is given as \(10.8 \times 10^{-3} \, \text{mol L}^{-1} \, \text{s}^{-1}\). The units of the rate constant depend on the order of the reaction.

### Step 2: Write the General Rate Law Expression
The rate of a reaction can be expressed as:
\[ \text{Rate} = k \cdot [\text{Reactant}]^n \]
where \(k\) is the rate constant, \([\text{Reactant}]\) is the concentration of the reactant, and \(n\) is the order of the reaction.

### Step 3: Identify the Units of Rate and Concentration
- The rate of the reaction is typically expressed in terms of concentration change over time, which has units of:
\[ \text{Rate} = \frac{\text{mol L}^{-1}}{\text{s}} \quad (\text{moles per liter per second}) \]
- The concentration of the reactant is expressed in:
\[ [\text{Reactant}] = \text{mol L}^{-1} \]

### Step 4: Set Up the Equation for Units
From the rate law expression, we can rearrange it to express the units of \(k\):
\[ \text{Rate} = k \cdot [\text{Reactant}]^n \implies k = \frac{\text{Rate}}{[\text{Reactant}]^n} \]
Substituting the units, we get:
\[ k = \frac{\text{mol L}^{-1} \, \text{s}^{-1}}{(\text{mol L}^{-1})^n} \]

### Step 5: Simplify the Units of k
This can be simplified to:
\[ k = \text{mol L}^{-1} \, \text{s}^{-1} \cdot \text{mol}^{-n} \, \text{L}^n = \text{mol}^{1-n} \, \text{L}^{-1+n} \, \text{s}^{-1} \]

### Step 6: Compare the Units
Now, we compare the units of \(k\) with the given units \( \text{mol L}^{-1} \, \text{s}^{-1} \):
\[ \text{mol}^{1-n} \, \text{L}^{-1+n} \, \text{s}^{-1} = \text{mol}^{1} \, \text{L}^{-1} \, \text{s}^{-1} \]
From this comparison, we can set up the following equations:
1. \(1 - n = 1\) (from the mol units)
2. \(-1 + n = -1\) (from the L units)

### Step 7: Solve for n
From the first equation:
\[ 1 - n = 1 \implies n = 0 \]
Thus, the order of the reaction is \(n = 0\).

### Conclusion
The order of the reaction is **0**.

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