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 1.48- cm sample cell, and the only colored species in the reaction has an extinction coefficient of 5700 cm ^-1 M^-1 at 520 nm. A)find the initial concentration of the colored reacting if the absorbance is .608 at the beginning B)the absorbance falls to .236 at 38.9 minutes. find the rate constant in units of s ^-1 C) Find the Half Life D)how long does it take to fall to .107 abs?

Explanation / Answer

From Beer-Lambert's Law A = Ebc where E(epsilon) = molar absorptivity, b = pathlenght and c = concentration of the analyte. a. 0.537 = 5440 x 1.29 x c Hence c = 0.537/(5440 x 1.29) = 7.65 x10^-5M b. (0.537 - 0.237)/20.20 = 0.015/min = 2.5 x 10^-3/sec. c. Since the recation is 1st order, t(1/2) = ln2/k = 0.6931/(2.5 x 10^-3) = 277sec. d. ln(Ao/At) =kt Hence t = 1/k x ln(Ao/At) = 1/(2.5 x 10^-3) x ln(0.537/0.131) = 564sec

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