What does it indicate if the rate of a reaction is first order with respect to reactant A?

If the rate of a reaction is first order with respect to reactant A, it implies that the reaction rate is directly proportional to the concentration of A. This means that if you were to double the concentration of A, the reaction rate would also double. Mathematically, this can be expressed using the rate equation for a first-order reaction, which is typically written as:

Rate = k[A]

where k is the rate constant and [A] is the concentration of A. In this case, if you increase [A] to 2[A], the rate would become:

Rate = k(2[A]) = 2k[A]

This clearly indicates that the rate has doubled when the concentration of A is doubled. This characteristic of first-order reactions, where the rate changes in direct proportion to the concentration of the reactant, is key to understanding this type of reaction kinetics.