The overall order of a reaction which has the rate expression.

Rate \(= k [A]^{2/4}[B]^2\) will be

\(\frac{5}{2}\)

The correct answer is option 2. \(\frac{5}{2}\).

To determine the overall order of a reaction given its rate expression, we need to sum the exponents of the concentration terms in the rate law.

Given the rate expression:

\(\text{Rate} = k [A]^{2/4}[B]^2 \)

Steps to Determine the Overall Order:

For \( [A] \), the exponent is \( \frac{2}{4} \).

For \( [B] \), the exponent is \( 2 \).

Calculate the overall order by adding the exponents of all concentration terms.

\(\text{Overall order} = \left(\frac{2}{4}\right) + 2\)

Simplify \( \frac{2}{4} \) to \( \frac{1}{2} \).

\(\text{Overall order} = \frac{1}{2} + 2 = \frac{1}{2} + \frac{4}{2} = \frac{5}{2}\)

Conclusion

The overall order of the reaction is \( \frac{5}{2} \). Therefore, the correct answer is: 2. \(\frac{5}{2}\)