The rate constant of a reaction is found to be `3 xx 10^(-3) "mol" L^(-1) "min"^(-1)`. The order of the reaction is

Options

A. zero
B. `1`
C. `2`
D. `1.5`

Explanation

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

### Step 1: Understand the relationship between rate, rate constant, and concentration.
The rate of a reaction can be expressed as:
\[ r = k \cdot [A]^n \]
where:
- \( r \) = rate of the reaction
- \( k \) = rate constant
- \( [A] \) = concentration of the reactant
- \( n \) = order of the reaction

### Step 2: Identify the units of the rate constant.
The given rate constant \( k \) has the value:
\[ k = 3 \times 10^{-3} \, \text{mol L}^{-1} \text{min}^{-1} \]
The units of \( k \) can help us determine the order of the reaction.

### Step 3: Write the units of the rate.
The unit of the rate \( r \) is:
\[ \text{mol L}^{-1} \text{min}^{-1} \]

### Step 4: Relate the units of \( k \) to the order \( n \).
From the equation \( r = k \cdot [A]^n \), we can express the units of \( k \) in terms of the units of \( r \) and the concentration \( [A] \):
\[ \text{Units of } k = \frac{\text{Units of } r}{\text{Units of } [A]^n} \]

The unit of concentration \( [A] \) is:
\[ \text{mol L}^{-1} \]

Thus, the units of \( [A]^n \) will be:
\[ \text{(mol L}^{-1})^n = \text{mol}^n \text{L}^{-n} \]

### Step 5: Set up the equation for the units.
Now we can set up the equation for the units:
\[ \text{mol L}^{-1} \text{min}^{-1} = \frac{\text{mol L}^{-1} \text{min}^{-1}}{\text{mol}^n \text{L}^{-n}} \]

### Step 6: Equate the units.
This leads to:
\[ \text{mol L}^{-1} \text{min}^{-1} = \text{mol}^{1-n} \text{L}^{-1+n} \text{min}^{-1} \]

### Step 7: Solve for \( n \).
For the units to be equal, the powers of each unit must match:
1. For mol: \( 1 = 1 - n \) → \( n = 0 \)
2. For L: \( -1 = -1 + n \) → \( n = 0 \)
3. For min: This is already equal.

### Conclusion: Determine the order of the reaction.
Since we found \( n = 0 \), the order of the reaction is:
\[ \text{Order} = 0 \]

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

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