Magnitude guesses

We often need order of magnitude guesses for many things in the environment. This is an important skill, so let us start with a couple of examples. 

This is an extremely small pressure, as you might have guessed from the small magnitude of the equilibrium constant. 

Parameter estimates should not differ by orders of magnitude from those evaluated using well established methods of thermodynamics or known from the literature several rules concerning adsorption phenomena have been worked out by Boudart et al. (1967) the optimal parameter estimates should not differ very much from the initial guesses if the latter were determined in well designed separate dedicated experiments. 

First, initial guesses for the free component concentrations [X, [V] and [Z are made. Naturally, the better the initial guesses the faster and more robustly the correct solution is computed. As it turns out, in equilibrium calculations as described here, the qualify of the initial guesses is often not crucial convergence is fast even for guesses that are several orders of magnitude away from the correct values. 

Plan new measurements predict or guess order of magnitude of experimental result. 

The relatively large magnitude of the correction in (10.33) demonstrates that a calculation of all radiative-recoil corrections of order a Za) m/M)Ep is warranted. The error of the total radiative-recoil correction in the last line in Table 10.2 includes, besides the errors of individual contributions in the upper lines of this Table, also an educated guess on the magnitude of yet uncalculated contributions. 

Explain the difference in the py (0.95 versus 0.75) and log kBH (X = Y = H -1.23 versus -0.22) values obtained for the two solvent systems. Make a guess of the magnitude of px in aqueous solution and estimate the hydrolysis half-life of 4-nitro benzoic acid 4-nitrophenyl ester (X = Y = 4-N02) in water at pH 8.0 and 25°C by assuming that only the base-catalyzed reaction is important. 

Coming to our subject proper, to the intensities of the crystal-field bands, we take our stand on the long established guess or recognition that these are electric dipole transitions assisted by vibrations of the complex. The evidence for this is mainly that as the temperature is varied the magnitude of the intensity follows the famous cotangent law ... 

The only report of experimental determination of noble gas isotopic fractionation upon solution in water is that of Weiss (1970b), who found that 3He is less soluble than 4He by (1.2 0.2)% at 0°C, the fractionation increasing in magnitude by about 0.1% per 10°C. The effect is in the same sense but much larger than the =0.1 % effects found for 02 and N2 by Klots and Benson (1963). On the basis of the reasonably inferred mass dependence, we can guess that isotopic fractionation will be quite small, around 0.1%, for Ne and negligible for the heavier gases. 

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