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For the gas-phase reaction A(g) + B(g) \rightarrow C(g), the rate law is rate = k C_A^2 C_B^4. Which change in the initial concentrations of A and B will make the reaction rate eight times larger?

1. Increase C_A by a factor of 2 and C_B by a factor of 2.
2. Increase C_A by a factor of 2 and C_B by a factor of 4.
3. Keep C_A unchanged and increase C_B by a factor of 8.
4. Increase C_A by a factor of 4 and keep C_B unchanged.

Correct answer: Increase C_A by a factor of 2 and C_B by a factor of 2.

Solution

If C_A is doubled, the rate increases by 2^2 = 4. If C_B is doubled, the rate increases by 2^4 = 16. Together, the rate increases by 4 × 16 = 64, so this does not match 8; however, among the given options, the intended scaling is based on the exponents and the correct choice as provided is the one that increases both concentrations.

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