In the second-order plot, what is the y-intercept of the straight line 1/[A] versus time?

In the second-order plot, what is the y-intercept of the straight line 1/[A] versus time?

• A. 1/[A0]
• B. [A0]
• C. k
• D. 0

Answer: (A)

For a second-order reaction in A, the integrated rate law gives 1/[A] = 1/[A0] + kt. When you plot 1/[A] versus time, you get a straight line where the slope is k and the intercept on the y-axis is the value of 1/[A] at time zero. At t = 0, [A] = [A0], so the intercept is 1/[A0]. The other options don’t fit: [A0] is the initial concentration, not its reciprocal; k is the slope; and 0 would only occur in a special, non-generic case.

For a second-order reaction in A, the integrated rate law gives 1/[A] = 1/[A0] + kt. When you plot 1/[A] versus time, you get a straight line where the slope is k and the intercept on the y-axis is the value of 1/[A] at time zero. At t = 0, [A] = [A0], so the intercept is 1/[A0]. The other options don’t fit: [A0] is the initial concentration, not its reciprocal; k is the slope; and 0 would only occur in a special, non-generic case.