For the reaction 2A + B + 2C ? D + E the following initial rate data was collect

Question

For the reaction

2A + B + 2C ? D + E

the following initial rate data was collected at constant temperature. Determine the correct rate law for this reaction. All units are arbitrary.

Trial             [A]                  [B]                  [C]                  Rate

1                  0.225              0.150              0.350              0.0217

2                  0.320              0.150              0.350              0.0439

3                  0.225              0.250              0.350              0.0362

4                  0.225              0.150              0.600              0.01270

A Rate = k [A][B]^2[C]^-1

B Rate = k [A]^2[B][C]

C Rate = k [A]^2[B][C]^-1

D Rate = k [A][B][C]

E none of these choices is correct

Explanation / Answer

Comparing Trial 1 & 3, Rate increases by 1.66 times when [B] increases 1.66 times while [A] & [C] remain const.

Hence Rate proportional to [B].

Comparing Trials 1 & 4, Rate is multiplied by 0.58 when [C] is multiplied by 1.71 = 1/0.58 while [A] & [B] remain const.

Hence Rate proportional to [C]^-1.

Finally, Comparing 1 & 4, Rate is multiplied by 2.02 when [A] is multiplied by 1.42 = sqrt(2.02) while [B] & [C] remain const.

Hence, rate proportional to [A]^2.

Hence rate equation is Rate = k[A]^2[B][C]^-1..

Answer is C

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