For the reaction: `A + B to` product `(dx)/(dt) = k[A]^(a)[B]^(b)`
if `(dx)/(dt) =k`, then the order of the reaction is:

Options

A. 4
B. 3
C. 1
D. 0

Answer

To determine the order of the reaction given the rate equation and the condition that \(\frac{dx}{dt} = k\), we can follow these steps:

### Step 1: Understand the Rate Law Expression
The rate of the reaction is given by the expression:
\[ \frac{dx}{dt} = k[A]^a[B]^b \]
where \(k\) is the rate constant, \([A]\) is the concentration of reactant A, \([B]\) is the concentration of reactant B, and \(a\) and \(b\) are the orders with respect to A and B, respectively.

### Step 2: Analyze the Given Condition
We are given that:
\[ \frac{dx}{dt} = k \]
This implies that the rate of the reaction is equal to the rate constant \(k\).

### Step 3: Set Up the Equation
From the rate law expression, if \(\frac{dx}{dt} = k\), we can equate:
\[ k[A]^a[B]^b = k \]

### Step 4: Simplify the Equation
Dividing both sides by \(k\) (assuming \(k \neq 0\)):
\[ [A]^a[B]^b = 1 \]

### Step 5: Analyze the Implications
For the equation \([A]^a[B]^b = 1\) to hold true, the concentrations \([A]\) and \([B]\) must be such that their contributions to the rate do not depend on their actual values. This can only happen if both \(a\) and \(b\) are equal to zero.

### Step 6: Determine the Order of the Reaction
The order of the reaction is defined as the sum of the powers of the concentration terms in the rate law:
\[ \text{Order} = a + b \]
Since we have established that \(a = 0\) and \(b = 0\):
\[ \text{Order} = 0 + 0 = 0 \]

### Conclusion
Thus, the order of the reaction is **zero**.

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