The reaction 2A + B → C + D goes to completion and follows the rate law -d[A]/dt = K[A]^2[B]. The sum of values of x and y in the following data:
Set 1: [A]0 = 300, [B]0 = 40, Half-life = 62.5
S

Question

The reaction 2A + B → C + D goes to completion and follows the rate law -d[A]/dt = K[A]^2[B]. The sum of values of x and y in the following data:
Set 1: [A]0 = 300, [B]0 = 40, Half-life = 62.5
Set 2: [A]0 = 300, [B]0 = 60, Half-life = x
Set 3: [A]0 = 5, [B]0 = 300, Half-life = 625
Set 4: [A]0 = 10, [B]0 = 300, Half-life = y

Prashant Kotian · Accepted Answer

Correct answer: 0375. In Set 1 & 2, A is in excess, so the reaction is pseudo-first-order in B. Its half-life depends only on [A]^2. Since [A] is 300 in both, x = 62.5. In Set 3 & 4, B is in excess, making it pseudo-second-order in A. For 2nd order, t1/2 = 1/(k_obs [A]0). Set 3 gives 625 = 1 / (K(300)(5)). Set 4 gives y = 1 / (K(300)(10)), which is half of 625, so y = 312.5. Sum x + y = 62.5 + 312.5 = 375. Therefore, correct answer is 0375.

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