For a second-order reaction rate, what is the rate expression in terms of k and [A]?

For a second-order reaction, the rate of reaction depends on the concentration of the reactant squared. This means that the rate expression is formulated as the rate being proportional to the square of the concentration of the reactant.

In the given context, the correct rate expression shows that the rate is equal to k (the rate constant) multiplied by the concentration of substance A squared, which highlights the second-order relationship. This implies that if the concentration of A increases, the rate of reaction will increase exponentially, as it is proportional to the square of that concentration.

In this scenario, the other options do not represent a second-order reaction. One option suggests a first-order reaction, where the rate is proportional to [A] and not its square. Another option incorrectly includes a negative sign, which could imply a decrease in reactant concentration but fails to connect correctly to the rate expression for a second-order process. Finally, one option presents a similar expression but lacks the appropriate power of two, thereby misrepresenting the order of the reaction.

Therefore, the rate expression for a second-order reaction being rate = k[A]^2 accurately captures the essence of how the concentration of reactant influences the rate of the reaction.