Which of the following linear plots do you expect for a reaction A → products if the reaction follows first-order kinetics?

• A. 1/[A] vs. time
• B. ln[A] vs. time
• C. [A] vs. time
• D. Rate vs. [A]

Answer: (B)

Verified step by step guidance

1. Understand that first-order kinetics means the rate of reaction is directly proportional to the concentration of one reactant.
2. Recall the integrated rate law for a first-order reaction: \( \ln[A] = -kt + \ln[A]_0 \), where \( [A] \) is the concentration of reactant A at time t, \( k \) is the rate constant, and \( [A]_0 \) is the initial concentration.
3. Recognize that the integrated rate law equation \( \ln[A] = -kt + \ln[A]_0 \) is in the form of a straight line \( y = mx + c \), where \( y = \ln[A] \), \( m = -k \), \( x = t \), and \( c = \ln[A]_0 \).
4. Identify that plotting \( \ln[A] \) versus time \( t \) will yield a straight line with a slope of \(-k\) and a y-intercept of \( \ln[A]_0 \).
5. Conclude that for a first-order reaction, the correct linear plot is \( \ln[A] \) versus time, as it will produce a straight line, confirming the reaction order.