(a) For the generic reaction A S B what quantity, when graphed versus time, will yield a straight line for a first-order reaction?

Verified step by step guidance

1. Identify the order of the reaction given in the problem, which is a first-order reaction.
2. Recall that for a first-order reaction, the rate of reaction is directly proportional to the concentration of one reactant. The rate law can be expressed as: \(rate = k[A]\), where \(k\) is the rate constant and \([A]\) is the concentration of reactant A.
3. Understand that for a first-order reaction, the natural logarithm of the concentration of the reactant versus time will yield a straight line. This is derived from the integrated rate law for a first-order reaction: \(\ln[A] = -kt + \ln[A]_0\), where \([A]_0\) is the initial concentration of A.
4. Set up the graph with time (t) on the x-axis and the natural logarithm of the concentration of A (\(\ln[A]\)) on the y-axis.
5. Plot the data points for \(\ln[A]\) versus time and draw the best fit line. The slope of this line will be equal to \(-k\), and the y-intercept will be \(\ln[A]_0\).

Key Concepts

First-Order Reactions

First-order reactions are chemical reactions where the rate is directly proportional to the concentration of one reactant. This means that as the concentration of the reactant decreases, the rate of reaction also decreases in a linear fashion. The mathematical representation of a first-order reaction is given by the equation: rate = k[A], where k is the rate constant and [A] is the concentration of reactant A.

Integrated Rate Law

The integrated rate law for a first-order reaction relates the concentration of the reactant to time. It is expressed as ln[A] = -kt + ln[A]₀, where [A]₀ is the initial concentration, k is the rate constant, and t is time. When plotted, a graph of ln[A] versus time yields a straight line with a slope of -k, indicating that the reaction follows first-order kinetics.

Graphing Reaction Kinetics

Graphing is a crucial tool in analyzing reaction kinetics. For first-order reactions, plotting the natural logarithm of the concentration of the reactant (ln[A]) against time results in a straight line. This linear relationship allows chemists to determine the rate constant (k) and understand the reaction's behavior over time, providing insights into the reaction mechanism and dynamics.