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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

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aaregbe

Answer:

C Rate [tex]=k [A]^{2} [B][C]^{-1}[/tex]

Explanation:

In order to determine the correct rate law, let's use Trial 1 as baseline. Therefore:

An increase in [A] in Trial 2 by a factor of [tex]\sqrt{2}[/tex] leads to an increase in the rate of reaction by a factor of 2 (i.e. the reaction rate is doubled). Thus, there is second order in [A].

Similarly,

An increase in [B] in Trial 3 by a factor of 1.667 leads to an increase in the rate of reaction by a factor of 1.667. Thus, there is first order in [B].

Futhermore,

An increase in [C] in Trial 4 by a factor of 1.71 leads to a decrease in the rate of reaction by 1.71. Thus, there is inverse first order in [C].

Therefore, the correct rate law is:

Rate [tex]=k [A]^{2} [B][C]^{-1}[/tex]

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