The reaction A +2B → products. = k[A][B]3. How will the factor rateRxn increase when [A] is doubled and [B] is trippled?

Method 1 :

Rate = k [A] [B]³

When [A] = a and [B] = b: Rate = R
R = k a b³

When [A] = 2a and [B] = 3b:
Rate = k (2a) (3b)³ = 54 k a b³ = 54 R

The rate increases 54 times.

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Method 2 :

Times that the rate increases = 2 × 3³ = 54