Non-NMR Spectroscopies Solutions: #6
6.* (1995 2 6) Uv-vis spectroscopy. A radioactive compound A is dissolved in water to form a solution with initial concentreation c0 at time t = 0. Some of this solution is used to fill a cuvette that is placed inside a single-beam UV-vis spectrophotometer. The wavelength of the spectrophotometer is set at a wavelength at which the compound A absorbs. As time passes, the radioactive compound A decays according to the first-order rate expression c(t) = c0 e(-kt) where k is the rate constant for radioactive decay. Explain how to use Beer's law (I = Ioe(-ecl)) to find k. Discuss whether it is necessary to know the length l of the cuvette or the absorption coefficient e of compound A at the wavelength setting of the spectrophotometer. Plug the expressions for time t = 0 and time t = t into Beer’s law (written in the form ln [I/Io] = -elco), divide the two resulting equations, and solve for k. Note that Io is the initial intensity of the spectrophotometer’s light beam and I(0) is the initial transmitted intensity through the sample. ln [I(0)/Io] = -elco ln [I(t)/Io] = -elcoe(-8k) ______________________________ ln [I(t)/Io / I(0)/Io] = e(-8k) ---> k = -1/t ln {ln [I(t)/Io / I(0)/Io] } sec-1. Note that e and l are not needed to solve the problem. |