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The reaction A+B+Crarr products is found...

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

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To determine the overall order of the reaction given the rate law, we will follow these steps: 1. **Identify the Rate Law**: The rate law provided is \( r = \frac{d[A]}{dt} = k[A]^2[B]^{\frac{3}{2}}[C]^{-\frac{1}{2}} \). 2. **Identify the Exponents**: In the rate law, the exponents of the concentration terms represent the order with respect to each reactant: - For \( [A] \), the exponent is \( 2 \). - For \( [B] \), the exponent is \( \frac{3}{2} \). - For \( [C] \), the exponent is \( -\frac{1}{2} \). 3. **Calculate the Overall Order**: The overall order of the reaction is the sum of the individual orders: \[ \text{Overall Order} = \text{Order with respect to } A + \text{Order with respect to } B + \text{Order with respect to } C \] Substituting the values: \[ \text{Overall Order} = 2 + \frac{3}{2} - \frac{1}{2} \] 4. **Simplify the Expression**: - First, calculate \( \frac{3}{2} - \frac{1}{2} = 1 \). - Now add this to \( 2 \): \[ 2 + 1 = 3 \] 5. **Conclusion**: The overall order of the reaction is \( 3 \).
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