If the rate law is rate = k[A]^2[B] and B is doubled with A held constant, by what factor does the rate increase?

• A. 4
• B. 2
• C. 1
• D. 1.414

Answer: (B)

In this rate law, the rate depends on [A] squared and on [B] to the first power. If A is held constant, [A]^2 stays the same, so the rate varies directly with [B]. Doubling [B] therefore doubles the rate, giving a factor of 2. The reason is that B appears with an exponent of 1, so changes in B translate linearly into the rate. If the exponent on B were 2, doubling B would quadruple the rate (factor 4); if B’s influence were the square root (exponent 1/2), doubling B would increase the rate by about 1.414.