What is the sign of the slope m for a first-order plot of ln[A] versus time?

• A. m > 0
• B. m < 0
• C. m = 0
• D. m depends on initial concentration

Answer: (B)

In first-order kinetics, the integrated rate law is ln[A] = ln[A]0 − kt. This means plotting ln[A] versus time gives a straight line with slope equal to −k. Since the rate constant k is positive, the slope is negative. So as time increases, ln[A] decreases, reflecting that [A] is diminishing exponentially. The initial concentration affects the intercept ln[A]0, not the slope. Therefore the slope must be negative.