For a reaction A + B → products, the following data were collected. Experiment Number Initial Concentration of A (M) Initial Con
centration of B (M) Observed Initial Rate (M/s) 1 3.40 4.16 1.82 ✕ 10−4 2 4.59 4.16 3.32 ✕ 10−4 3 3.40 5.46 1.82 ✕ 10−4 Calculate the rate constant for this reaction.
1 answer:
Answer:
Rate constant k = 1.57*10⁻⁵ s⁻¹
Explanation:
Given reaction:

Expt [A] M [B] M Rate [M/s]
1 3.40 4.16 1.82*10^-4
2 4.59 4.16 3.32*10^-4
3. 3.40 5.46 1.82*10^-4
![Rate = k[A]^{x}[B]^{y}](https://tex.z-dn.net/?f=Rate%20%3D%20k%5BA%5D%5E%7Bx%7D%5BB%5D%5E%7By%7D)
where k = rate constant
x and y are the orders wrt to A and B
To find x:
Divide rate of expt 2 by expt 1
![\frac{3.32*10^{-4} }{1.82*10^{-4} } =\frac{[4.59]^{x} [4.16]^{y} }{[3.40]^{x} [4.16]^{y} }\\\\x =2](https://tex.z-dn.net/?f=%5Cfrac%7B3.32%2A10%5E%7B-4%7D%20%7D%7B1.82%2A10%5E%7B-4%7D%20%7D%20%3D%5Cfrac%7B%5B4.59%5D%5E%7Bx%7D%20%5B4.16%5D%5E%7By%7D%20%7D%7B%5B3.40%5D%5E%7Bx%7D%20%5B4.16%5D%5E%7By%7D%20%7D%5C%5C%5C%5Cx%20%3D2)
To find y:
Divide rate of expt 3 by expt 1
![\frac{1.82*10^{-4} }{1.82*10^{-4} } =\frac{[3.40]^{x} [5.46]^{y} }{[3.40]^{x} [4.16]^{y} }\\\\y =0](https://tex.z-dn.net/?f=%5Cfrac%7B1.82%2A10%5E%7B-4%7D%20%7D%7B1.82%2A10%5E%7B-4%7D%20%7D%20%3D%5Cfrac%7B%5B3.40%5D%5E%7Bx%7D%20%5B5.46%5D%5E%7By%7D%20%7D%7B%5B3.40%5D%5E%7Bx%7D%20%5B4.16%5D%5E%7By%7D%20%7D%5C%5C%5C%5Cy%20%3D0)
Therefore: x = 2, y = 0
![Rate = k[A]^{2}[B]^{0}](https://tex.z-dn.net/?f=Rate%20%3D%20k%5BA%5D%5E%7B2%7D%5BB%5D%5E%7B0%7D)
To find k
Use rate for expt 1:
![k = \frac{Rate1}{[A]^{2} } =\frac{1.82*10^{-4}M/s }{[3.40]^{2} } =1.57*10^{-5} s-1](https://tex.z-dn.net/?f=k%20%3D%20%5Cfrac%7BRate1%7D%7B%5BA%5D%5E%7B2%7D%20%7D%20%3D%5Cfrac%7B1.82%2A10%5E%7B-4%7DM%2Fs%20%7D%7B%5B3.40%5D%5E%7B2%7D%20%7D%20%3D1.57%2A10%5E%7B-5%7D%20s-1)
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