The rate of certain hypothetical reaction
`A+B+C rarr` Products, is given by
`r = -(dA)/(dt) = k[A]^(1//2)[B]^(1//3)[C]^(1//4)`
The order of a reaction is given by

Options

A. 1
B. 2
C. 13/12
D. 5/4

Answer

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

\[ r = -\frac{dA}{dt} = k[A]^{\frac{1}{2}}[B]^{\frac{1}{3}}[C]^{\frac{1}{4}} \]

we follow these steps:

### Step 1: Identify the powers of concentration terms
The rate expression includes the concentrations of reactants A, B, and C raised to certain powers:
- The power of A is \( \frac{1}{2} \)
- The power of B is \( \frac{1}{3} \)
- The power of C is \( \frac{1}{4} \)

### Step 2: Sum the powers
To find the overall order of the reaction, we need to sum the powers of all the concentration terms:

\[ \text{Order} = \left(\frac{1}{2}\right) + \left(\frac{1}{3}\right) + \left(\frac{1}{4}\right) \]

### Step 3: Find a common denominator
The least common multiple (LCM) of the denominators 2, 3, and 4 is 12. We will convert each fraction to have this common denominator:

- \( \frac{1}{2} = \frac{6}{12} \)
- \( \frac{1}{3} = \frac{4}{12} \)
- \( \frac{1}{4} = \frac{3}{12} \)

### Step 4: Add the fractions
Now we can add these fractions together:

\[ \text{Order} = \frac{6}{12} + \frac{4}{12} + \frac{3}{12} = \frac{6 + 4 + 3}{12} = \frac{13}{12} \]

### Conclusion
Thus, the overall order of the reaction is:

\[ \text{Order} = \frac{13}{12} \]

### Final Answer
The order of the reaction is \( \frac{13}{12} \).

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