Answer:
1) The order of the reaction is of FIRST ORDER
2) Rate constant k = 5.667 × 10 ⁻⁴
Explanation:
From the given information:
The composition of a liquid-phase reaction 2A - B was monitored spectrophotometrically.
liquid-phase reaction 2A - B signifies that the reaction is of FIRST ORDER where the rate of this reaction is directly proportional to the concentration of A.
The following data was obtained:
t/min 0 10 20 30 40 ∞
conc B/(mol/L) 0 0.089 0.153 0.200 0.230 0.312
For a first order reaction:
![K = \dfrac{1}{t} \ In ( \dfrac{C_{\infty} - C_o}{C_{\infty} - C_t})](https://tex.z-dn.net/?f=K%20%3D%20%5Cdfrac%7B1%7D%7Bt%7D%20%5C%20In%20%28%20%5Cdfrac%7BC_%7B%5Cinfty%7D%20-%20C_o%7D%7BC_%7B%5Cinfty%7D%20-%20C_t%7D%29)
where :
K = proportionality constant or the rate constant for the specific reaction rate
t = time of reaction
= initial concentration at time t
= final concentration at time t
= concentration at time t
To start with the value of t when t = 10 mins
![K_1 = \dfrac{1}{10} \ In ( \dfrac{0.312 - 0}{0.312 - 0.089})](https://tex.z-dn.net/?f=K_1%20%3D%20%5Cdfrac%7B1%7D%7B10%7D%20%5C%20In%20%28%20%5Cdfrac%7B0.312%20-%200%7D%7B0.312%20-%200.089%7D%29)
![K_1 = \dfrac{1}{10} \ In ( \dfrac{0.312 }{0.223})](https://tex.z-dn.net/?f=K_1%20%3D%20%5Cdfrac%7B1%7D%7B10%7D%20%5C%20In%20%28%20%5Cdfrac%7B0.312%20%7D%7B0.223%7D%29)
![K_1 =0.03358 \ min^{-1}](https://tex.z-dn.net/?f=K_1%20%3D0.03358%20%5C%20%20min%5E%7B-1%7D)
![K_1 \simeq 0.034 \ min^{-1}](https://tex.z-dn.net/?f=K_1%20%5Csimeq%200.034%20%5C%20%20min%5E%7B-1%7D)
When t = 20
![K_2= \dfrac{1}{20} \ In ( \dfrac{0.312 - 0}{0.312 - 0.153})](https://tex.z-dn.net/?f=K_2%3D%20%5Cdfrac%7B1%7D%7B20%7D%20%5C%20In%20%28%20%5Cdfrac%7B0.312%20-%200%7D%7B0.312%20-%200.153%7D%29)
![K_2= 0.05 \times \ In ( 1.9623)](https://tex.z-dn.net/?f=K_2%3D%200.05%20%5Ctimes%20%20%5C%20In%20%28%201.9623%29)
![K_2=0.03371 \ min^{-1}](https://tex.z-dn.net/?f=K_2%3D0.03371%20%5C%20min%5E%7B-1%7D)
![K_2 \simeq 0.034 \ min^{-1}](https://tex.z-dn.net/?f=K_2%20%5Csimeq%200.034%20%5C%20min%5E%7B-1%7D)
When t = 30
![K_3= \dfrac{1}{30} \ In ( \dfrac{0.312 - 0}{0.312 - 0.200})](https://tex.z-dn.net/?f=K_3%3D%20%5Cdfrac%7B1%7D%7B30%7D%20%5C%20In%20%28%20%5Cdfrac%7B0.312%20-%200%7D%7B0.312%20-%200.200%7D%29)
![K_3= 0.0333 \times \ In ( \dfrac{0.312}{0.112})](https://tex.z-dn.net/?f=K_3%3D%200.0333%20%5Ctimes%20%20%5C%20In%20%28%20%5Cdfrac%7B0.312%7D%7B0.112%7D%29)
![K_3= 0.0333 \times \ 1.0245](https://tex.z-dn.net/?f=K_3%3D%200.0333%20%5Ctimes%20%20%5C%201.0245)
![K_3 = 0.03412 \ min^{-1}](https://tex.z-dn.net/?f=K_3%20%3D%200.03412%20%5C%20min%5E%7B-1%7D)
![K_3 = 0.034 \ min^{-1}](https://tex.z-dn.net/?f=K_3%20%3D%200.034%20%5C%20min%5E%7B-1%7D)
When t = 40
![K_4= \dfrac{1}{40} \ In ( \dfrac{0.312 - 0}{0.312 - 0.230})](https://tex.z-dn.net/?f=K_4%3D%20%5Cdfrac%7B1%7D%7B40%7D%20%5C%20In%20%28%20%5Cdfrac%7B0.312%20-%200%7D%7B0.312%20-%200.230%7D%29)
![K_4=0.025 \times \ In ( \dfrac{0.312}{0.082})](https://tex.z-dn.net/?f=K_4%3D0.025%20%5Ctimes%20%20%5C%20In%20%28%20%5Cdfrac%7B0.312%7D%7B0.082%7D%29)
![K_4=0.025 \times \ In ( 3.8048)](https://tex.z-dn.net/?f=K_4%3D0.025%20%5Ctimes%20%20%5C%20In%20%28%203.8048%29)
![K_4=0.03340 \ min^{-1}](https://tex.z-dn.net/?f=K_4%3D0.03340%20%5C%20min%5E%7B-1%7D)
We can see that at the different time rates, the rate constant of
all have similar constant values
As such :
Rate constant k = 0.034 min⁻¹
Converting it to seconds ; we have :
60 seconds = 1 min
∴
0.034 min⁻¹ =(0.034/60) seconds
= 5.667 × 10 ⁻⁴ seconds
Rate constant k = 5.667 × 10 ⁻⁴