The rate of a first-order reaction is followed by spectroscopy, monitoring the a

Question

The rate of a first-order reaction is followed by spectroscopy, monitoring the absorption of a colored reactant at 520 nm. The reaction occurs in a 1.34-cm sample cell, and the only colored species in the reaction has an extinction coefficient of 6100cm?1M?1 at 520 nm.

Part A)

Calculate the initial concentration of the colored reactant if the absorbance is 0.506 at the beginning of the reaction.

= 6.19*10^-5

Part b: The absorbance falls to 0.204 at 38.8min . Calculate the rate constant in units of s?1.

Part C: Calculate the half-life of the reaction.

Part D: How long does it take for the absorbance to fall to 0.102?

Thank you!

Explanation / Answer

From Beer-Lambert's Law
A = Ebc
where E(epsilon) = molar absorptivity,
b = pathlenght and
c = concentration of the analyte.

(a)
0.506 = 6100 x 1.34 x c
Hence c = 0.506/(6100 x 1.34)
c = 6.19 x 10^-5 M

(b)
Rate constant, k = (0.506 - 0.204) / (38.8 * 60)
k = 1.3 x 10^-4 s-1

(c)
Since the recation is 1st order,
t1/2 = ln2/k = 0.6931/(1.3 x 10^-4)
t1/2 = 5342.84 sec = 89.05 min

(d)
ln(Ao/At) =kt
Hence t = 1/k x ln(Ao/At)
t = 1/(1.3 x 10^-4) x ln(0.506/0.102)
t = 12319.72 sec = 205.33 min

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