Acetaldehyde decomposes to methane and carbon monoxide. Initial rates are 2.06 x 10^-11 at 1.75 x 10^-3 M, 8.24 x 10^-11 at 3.50 x 10^-3 M, and 3.30 x 10^-10 mol/L/s at 7.00 x 10^-3 M. What is the rate law?
Arate = k[CH3CHO]^2
Brate = k[CH3CHO]
Crate = k[CH3CHO]^3
Drate = k, a constant
Answer & Solution
Correct answer: A. rate = k[CH3CHO]^2
1. Compare trials in which only the acetaldehyde concentration changes.
2. From 1.75 x 10^-3 M to 3.50 x 10^-3 M the concentration doubles.
3. The rate climbs from 2.06 x 10^-11 to 8.24 x 10^-11 mol per litre per second, a factor of four.
4. Doubling giving a fourfold rate means the order is 2, since 2^2 = 4.
5. Check with the third trial: four times the first concentration gives 16 times the first rate, and 2.06 x 10^-11 x 16 = 3.30 x 10^-10.
6. The rate law is rate = k[CH3CHO]^2.
7. First order would only double the rate on doubling, and zero order would leave it unchanged.
8. Third order would multiply the rate by eight on doubling, which the data rule out.
_Source: OpenStax Chemistry (CC BY 4.0), Ch 12 "Kinetics", section 12.3 Rate Laws_
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