If the rate expression for a reaction is `(dx)/(dt)=k[A]^(1//2)[B]^(2//3)`, the overall order of the reaction is :

Options

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

Answer

To determine the overall order of the reaction given the rate expression \((dx)/(dt) = k[A]^{1/2}[B]^{2/3}\), we will follow these steps:

### Step 1: Identify the individual orders of the reactants
In the rate expression, the concentration of reactant A is raised to the power of \(1/2\) and the concentration of reactant B is raised to the power of \(2/3\).

### Step 2: Write down the individual orders
- The order with respect to A is \(1/2\).
- The order with respect to B is \(2/3\).

### Step 3: Calculate the overall order
The overall order of the reaction is the sum of the individual orders:
\[ \text{Overall Order} = \text{Order with respect to A} + \text{Order with respect to B} \]
Substituting the values we found:
\[ \text{Overall Order} = \frac{1}{2} + \frac{2}{3} \]

### Step 4: Find a common denominator
To add these fractions, we need a common denominator. The least common multiple of \(2\) and \(3\) is \(6\).
- Convert \(\frac{1}{2}\) to sixths:
\[ \frac{1}{2} = \frac{3}{6} \]
- Convert \(\frac{2}{3}\) to sixths:
\[ \frac{2}{3} = \frac{4}{6} \]

### Step 5: Add the fractions
Now we can add the two fractions:
\[ \text{Overall Order} = \frac{3}{6} + \frac{4}{6} = \frac{7}{6} \]

### Conclusion
The overall order of the reaction is \(\frac{7}{6}\).

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