By kobs = ln2 / t1/2 ,
kobs = ln2/ 21.5
= 0.0322 s-1
Semi-log Method
A graph of Z(t) = ln[yt-y∞] against time is plotted.
(The value of ln[yt-y∞] refer to Appendix 3)
Graph 2
From the equation, y= -0.0249x – 1.5439
Slope of graph = -kobs = -0.0249
∴ kobs = 0.0249 s-1
Guggenhein’s Method
Take Δt = 1
A graph of Z(t) = ln[y(t+Δt)-yt] against time is plotted.
(The value of ln[y(t+Δt)-yt] refer to Appendix 3)
Graph 3
From the equation, y= -0.0276x – 4.9105
Slope of graph = -kobs = -0.0276
∴ kobs = 0.0276 s-1
R/RΔ Method (Ratios of Rates)
With pure first-order decays, the successive ratio must remain constant
Where rm is the mean value of the successive ratios Rt/Rt+Δ along the whole kinetic curve.
R = dy/dt
As Δ = 20
Table below is R in Successive 20 s interval
Average of the Rt / Rt+Δ (rm) = 1.66432055
kobs = 0.025s-1
Discussions:
Mercury dithizonates were used in this experiment. Metal dithizonates have several interesting properties including photoactivation by light of wavelength greater than 350nm, reversible colour changes, photochemical forward and fast thermal return reactions, and log term stability to visible and near ultraviolet light.
The colour change accompanies the photoactivation of a cis-trans isomerization within the ligand as shown below.
The orange form of mercury dithizoate is photosensitive because it is ligand-centred with metal-ligand charge transfer character. The photochemical transition proceeds through a rotational movement of the dithizone in its complex with mercury.
In this experiment, dry xylene was used as solvent because the complex is soluble and stable in dry xylene. It can slow down the thermal return rate of the dark reaction.
The half-life was 21.5s. It is much shorter than typical half-time 120s. It is due to the cleanliness of glassware. Dust, water and other surface catalysis may speed up the reaction and shorter the half-life.
4 methods were used in this experiment. Only R/RΔ method does not require linear regression and Y∞. It is a combination of a differential and a time interval method and has several advantages.
- It can be applied directly to the spectrophotometer tracings using simple graphical techniques.
- With a slightly noisy recording, a small portion of the overall curve can be used. Results can thus be obtained quickly.
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The validity of the pseudo-first-order approximation can be tested. It is valid if the R/RΔ values remain constant.
Conclusion:
The rate constants (kobs ) determined by the four methods were
(a) Half-time Method = 0.0322 s-1
(b) Semi-log Method = 0.0249 s-1
(c) Guggenheim’s Method = 0.0276 s-1
(d) R/RΔ Method (ratio of rates) = 0.025s-1
All rate constants (kobs ) determined were in the usual range 5x10-3 < kobs< 5 x 10-2 s-1
Reference:
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R. L. Petersen, G. L. Harris, J. Chem. Educ. 1985, 62, 802.
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A. T. Hutton, J. Chem. Educ. 1986, 63, 888.
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B.Borderie, D. Lavabre, G. Levy, J. C. Micheau, J. Chem. Educ. 1990, 67, 459.
