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 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.