The reaction `A+B+Crarr` products is found to obey the rate law, `r=(d[A])/(dt)=K[A]^(2)[B]^((3)/(2))[C]^(-(1)/(2))`. The overall order of the reaction is

Answer

To determine the overall order of the reaction given the rate law \( r = \frac{d[A]}{dt} = K[A]^2[B]^{\frac{3}{2}}[C]^{-\frac{1}{2}} \), we will follow these steps:

### Step 1: Identify the powers of each reactant in the rate law
From the given rate law, we can see the powers of each reactant:
- The power of \( [A] \) is \( 2 \).
- The power of \( [B] \) is \( \frac{3}{2} \).
- The power of \( [C] \) is \( -\frac{1}{2} \).

### Step 2: Calculate the overall order of the reaction
The overall order of the reaction is the sum of the powers of all reactants in the rate law. Therefore, we can calculate it as follows:

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

Substituting the values we identified:

\[ \text{Overall Order} = 2 + \frac{3}{2} - \frac{1}{2} \]

### Step 3: Simplify the expression
Now, we will simplify the expression:

1. Convert all terms to have a common denominator (which is 2):
- \( 2 = \frac{4}{2} \)
- \( \frac{3}{2} \) remains the same
- \( -\frac{1}{2} \) remains the same

2. Now we can add them together:
\[ \text{Overall Order} = \frac{4}{2} + \frac{3}{2} - \frac{1}{2} = \frac{4 + 3 - 1}{2} = \frac{6}{2} = 3 \]

### Conclusion
Thus, the overall order of the reaction is \( 3 \).

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