Rate constant for the reaction `2N_(2)O_(5) to 4NO_(2) + O_(2)` is `4.98 xx 10^(-4) s^(-1)`. Find the order of reaction?

Answer

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

### Step 1: Identify the Units of the Rate Constant
The rate constant (K) for the reaction is given as \( 4.98 \times 10^{-4} \, s^{-1} \). The unit of the rate constant is crucial in determining the order of the reaction.

### Step 2: Analyze the Units
The unit \( s^{-1} \) indicates that the rate constant has the dimensions of inverse time. This is characteristic of a first-order reaction.

### Step 3: Relate Units to Reaction Order
For reactions, the units of the rate constant can be related to the order of the reaction:
- For a zero-order reaction: \( K \) has units of \( M \, s^{-1} \) (concentration/time).
- For a first-order reaction: \( K \) has units of \( s^{-1} \).
- For a second-order reaction: \( K \) has units of \( M^{-1} \, s^{-1} \).

Since the unit of the rate constant \( K \) is \( s^{-1} \), we can conclude that the reaction is first-order.

### Step 4: Confirm with the Shortcut
A shortcut to determine the order of the reaction is to analyze the power of the concentration unit in the rate constant:
- If \( K \) has no concentration unit (like \( s^{-1} \)), it implies a zero concentration power.
- Adding 1 to the power gives the order of the reaction. Here, since the concentration power is 0, adding 1 gives us an order of 1.

### Conclusion
Thus, the order of the reaction \( 2N_{2}O_{5} \rightarrow 4NO_{2} + O_{2} \) is **first order**.

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