If the rate law is rate = k[A]^2, by what factor does the rate increase when [A] is doubled?

• A. 4
• B. 2
• C. 1
• D. 8

Answer: (A)

Rate depends on the square of [A], so doubling [A] makes the rate go as (2[A])^2 = 4[A]^2. Since the original rate is k[A]^2, the new rate is 4k[A]^2, four times the original. The constant k cancels when comparing the two rates, confirming the rate increases by a factor of four.