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 expression:

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

we will follow these steps:

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

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

### Step 2: Determine the Exponents
From the rate expression, we can identify the exponents of the concentration terms:

- For \(A\), the exponent is \(1/2\).
- For \(B\), the exponent is \(1/4\).
- For \(C\), the exponent is \(0\) (which means it does not affect the rate).

### Step 3: Calculate the Overall Order of the Reaction
The overall order of the reaction is the sum of the exponents of all reactants in the rate expression:

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

Substituting the values we identified:

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

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

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

### Step 5: State the Final Answer
Thus, the overall order of the reaction is:

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

### Conclusion
The order of the reaction is \(\frac{3}{4}\).

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