Which relationship links the rate constant k to the slope m for zero-order or first-order plots?

• A. k = m
• B. k = -m
• C. k = 2m
• D. k = -2m

Answer: (B)

The key idea is that, for both zero-order and first-order plots, the slope represents the rate at which the concentration changes, and that slope is negative because the concentration decreases over time. In a zero-order plot of [A] versus time, the line has slope -k since d[A]/dt = -k. In a first-order plot of ln[A] versus time, the line has slope -k since d/dt[ln A] = -k. So in either case the slope m equals -k, which means k = -m. The negative sign reflects the decreasing quantity as the reaction proceeds.