For the reaction A Products, it is found that the rate of reaction increases by a factor of 6.25, when the concentration of A is increased by a factor of 2.5. The order of reaction with respect to A is:

2

The correct answer is option 3. 2.

The order of the reaction with respect to A, denoted as "n," can be determined by the given information:

\(\frac{\text{rate}_2}{{\text{rate}_1}} = \left(\frac{{[\text{A}]_2}}{{[\text{A}]_1}}\right)^n\)

Substituting the values provided:

\(\frac{{6.25}}{{1}} = \left(\frac{{2.5}}{{1}}\right)^n\)

Simplifying the equation:

\(2.5^n = 6.25\)

Taking the logarithm of both sides:

\(n \log(2.5) = \log(6.25)\)

Solving for "n":

\(n = \frac{{\log(6.25)}}{{\log(2.5)}}\)

Using a calculator, we find \(n \approx 2\).

Hence, the order of the reaction with respect to A is 2.