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:
[tex]K = \dfrac{1}{t} \ In ( \dfrac{C_{\infty} - C_o}{C_{\infty} - C_t})[/tex]
where :
K = proportionality constant or the rate constant for the specific reaction rate
t = time of reaction
[tex]C_o[/tex] = initial concentration at time t
[tex]C _{\infty}[/tex] = final concentration at time t
[tex]C_t[/tex] = concentration at time t
To start with the value of t when t = 10 mins
[tex]K_1 = \dfrac{1}{10} \ In ( \dfrac{0.312 - 0}{0.312 - 0.089})[/tex]
[tex]K_1 = \dfrac{1}{10} \ In ( \dfrac{0.312 }{0.223})[/tex]
[tex]K_1 =0.03358 \ min^{-1}[/tex]
[tex]K_1 \simeq 0.034 \ min^{-1}[/tex]
When t = 20
[tex]K_2= \dfrac{1}{20} \ In ( \dfrac{0.312 - 0}{0.312 - 0.153})[/tex]
[tex]K_2= 0.05 \times \ In ( 1.9623)[/tex]
[tex]K_2=0.03371 \ min^{-1}[/tex]
[tex]K_2 \simeq 0.034 \ min^{-1}[/tex]
When t = 30
[tex]K_3= \dfrac{1}{30} \ In ( \dfrac{0.312 - 0}{0.312 - 0.200})[/tex]
[tex]K_3= 0.0333 \times \ In ( \dfrac{0.312}{0.112})[/tex]
[tex]K_3= 0.0333 \times \ 1.0245[/tex]
[tex]K_3 = 0.03412 \ min^{-1}[/tex]
[tex]K_3 = 0.034 \ min^{-1}[/tex]
When t = 40
[tex]K_4= \dfrac{1}{40} \ In ( \dfrac{0.312 - 0}{0.312 - 0.230})[/tex]
[tex]K_4=0.025 \times \ In ( \dfrac{0.312}{0.082})[/tex]
[tex]K_4=0.025 \times \ In ( 3.8048)[/tex]
[tex]K_4=0.03340 \ min^{-1}[/tex]
We can see that at the different time rates, the rate constant of [tex]k_1, k_2, k_3, and k_4[/tex] 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
