`(dx)/(dt)=K[A]^(0.5)[B]^(0.5)[C]^(0.5)` . What will be the order of the reaction ?

Options

A. 1
B. 1.5
C. Zero
D. 2

Answer

To determine the order of the reaction given by the rate expression:

\[ \frac{dx}{dt} = K[A]^{0.5}[B]^{0.5}[C]^{0.5} \]

we will follow these steps:

### Step 1: Identify the Rate Expression
The rate expression provided is:

\[ \text{Rate} = K[A]^{0.5}[B]^{0.5}[C]^{0.5} \]

### Step 2: Understand the Contribution of Each Reactant
In the rate expression, the concentration of each reactant is raised to a power, which indicates its contribution to the overall reaction rate. Here, the powers are:

- For A: \(0.5\)
- For B: \(0.5\)
- For C: \(0.5\)

### Step 3: Calculate the Overall Order of the Reaction
The overall order of the reaction is the sum of the individual orders with respect to each reactant. Therefore, we can calculate it as follows:

\[ \text{Overall Order} = \text{Order with respect to A} + \text{Order with respect to B} + \text{Order with respect to C} \]

Substituting the values we have:

\[ \text{Overall Order} = 0.5 + 0.5 + 0.5 \]

### Step 4: Perform the Addition
Now, we perform the addition:

\[ \text{Overall Order} = 1.5 \]

### Conclusion
The order of the reaction is \(1.5\).

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