The second-order rate constant for an alkaline hydrolysis of...

The second-order rate constant for an alkaline hydrolysis of ethyl formate in $85 \%$ ethanol (aqueous) at $29.86^{\circ} \mathrm{C}$ is $4.53 \mathrm{L} \mathrm{mol}^{-1} \mathrm{s}^{-1}$. (a) If the reactants are both present at $0.001 \mathrm{mol} \mathrm{L}^{-1},$ what will be the half-life of the reaction? $(b)$ If the concentration of one of the reactants is doubled and that of the other is cut in half, how long will it take for one-half the reactant present at the lower concentration to react?

The second-order rate constant for an alkaline hydrolysis of ethyl formate in $85 \%$ ethanol (aqueous) at $29.86^{\circ} \mathrm{C}$ is $4.53 \mathrm{L} \mathrm{mol}^{-1} \mathrm{s}^{-1}$. (a) If the reactants are both present at $0.001 \mathrm{mol} \mathrm{L}^{-1},$ what will be the half-life of the reaction?
$(b)$ If the concentration of one of the reactants is doubled and that of the other is cut in half, how long will it take for one-half the reactant present at the lower concentration to react?

Key Concepts

Second-Order Reactions

In chemical kinetics, a second-order reaction is one where the overall rate is proportional to the product of the concentrations of two reactants (or the square of the concentration of one reactant in cases where they are identical). The rate law typically takes the form rate = k[A][B] (or rate = k[A]^2 for a single reactant), where k is the second-order rate constant. This relationship means that the reaction rate and the time evolution of the reactant concentrations depend significantly on the starting concentrations.

Rate Constant

The rate constant, denoted as k, is a proportionality factor in the rate law that quantifies the speed of a reaction under certain conditions. For a second-order reaction, the units of k are L mol?¹ s?¹. It is determined empirically and reflects the likelihood that reactant molecules will collide with sufficient energy and proper orientation to result in a chemical transformation.

Half-Life in Second-Order Reactions

The half-life of a reaction is the time required for the concentration of a reactant to decrease to half of its initial value. In second-order reactions, the half-life is not constant but depends inversely on the initial concentration. The integrated rate law for second-order kinetics shows that the half-life is given by t?/? = 1/(k[A]?) for reactions where the rate is proportional to the square of a single reactant's concentration, emphasizing that changes in initial concentrations directly affect the time needed to reach half the concentration.

Impact of Concentration Changes on Reaction Kinetics

Altering the concentrations of reactants in a second-order reaction affects the reaction rate and the progression of the reaction. Since the reaction rate is directly proportional to the product of the reactants' concentrations, doubling one concentration or halving the other results in a corresponding change in the rate. This concept is crucial when predicting how changes in conditions, such as varying the amounts of reactants, will influence the time required for a given extent of reaction to occur.

Please give Ace some feedback