The rate of the reaction `A+B+C to` Product is given by: rate `=-(d[A])/(dt)=k[A]^(1//2) [B]^(1//4) [C]^0` The order of reaction is:

Options

A. `1//2`
B. 4
C. `3//4`
D. `3//2`

Answer

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

\[ \text{rate} = -\frac{d[A]}{dt} = k[A]^{1/2}[B]^{1/4}[C]^0 \]

we will follow these steps:

### Step 1: Identify the rate law expression
The rate law expression provided is:

\[ \text{rate} = k[A]^{1/2}[B]^{1/4}[C]^0 \]

### Step 2: Determine the powers of the concentrations
From the rate law expression, we can identify the powers of the concentrations of the reactants:
- The power of \([A]\) is \(1/2\).
- The power of \([B]\) is \(1/4\).
- The power of \([C]\) is \(0\) (since \([C]^0 = 1\), it does not contribute to the order).

### Step 3: Calculate the overall order of the reaction
The overall order of the reaction is the sum of the powers of the concentrations of all reactants that appear in the rate expression:

\[ \text{Order} = \text{power of } [A] + \text{power of } [B] + \text{power of } [C] \]

Substituting the values we found:

\[ \text{Order} = \frac{1}{2} + \frac{1}{4} + 0 \]

### Step 4: Perform the addition
To add these fractions, we need a common denominator. The least common multiple of \(2\) and \(4\) is \(4\):

\[ \frac{1}{2} = \frac{2}{4} \]

Now we can add:

\[ \text{Order} = \frac{2}{4} + \frac{1}{4} + 0 = \frac{2 + 1 + 0}{4} = \frac{3}{4} \]

### Final Answer
Thus, the overall order of the reaction is:

\[ \text{Order} = \frac{3}{4} \]

### Conclusion
The correct option is \( \frac{3}{4} \), which corresponds to option 3.

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