Rough calculations

The free energy of reaction, AG, is derived from the change in enthalpy, AH, and the change in entropy, A5, by the equation  

For rough purposes we can take A and AH as constant for gas-phase reactions, while for many organic reactions, values of AS /R are of the order of 15( —r), less 10 for C—C bond formation with cyclization (at a standard pressure of 1 atm. or 1 bar). We now have a very crude method for assessing feasibility based solely on (gas-phase) heats of formation. 

At low temperatures, In Kp will be positive, but will fall to zero at about 1000 K, above which the reverse reaction becomes possible. In contrast, for the hydration of an olefin AH /R - - 5 500 K) In Kp becomes negative Kp 1) at about 370 K, and the reverse reaction will be significant under all practical conditions. 

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This is a rough calculation, based on direct capital cost and not on interest rates, and needs to be analysed in terms of the general plant economics. It should also be borne in mind that this is based on present-day electricity costs, and a greater saving will be made as fuel costs rise. 

Many modern instruments used in the analytical laboratory are interfaced with a computer and a printer provides a permanent record of the experimental data and the final result may even be given. This printout should be permanently attached to the observations page of the laboratory record book, and it should be regarded as normal practice to perform a rough calculation to confirm that the printed result is of the right order. 

Further to aspects discussed in Section 23.5.1.2, the simplest strategy, if it is practical, is slow decompression. If the pressure can be reduced sufficiently slowly, the gas which is dissolved in the elastomer can diffuse out of the mbber without buUding up sufficient internal pressure to cause damage. The rate of decompression required may be roughly calculated if the diffusion coefficient of the gas and its solubility in the elastomer are known— but in practice it will probably require a laboratory simulation. 

We emphasize that these are rough calculations which depend on validity of approach and assumptions made on the values of mobility of current carriers in zinc oxide. To demonstrate convincingly that there is... 

Consequently, knowledge of the t90 of both coils - for the same applied rf power -allows a rough calculation of the expected signal-to-noise ratio, in agreement with the principle of reciprocity [27]. The sensitivity ratio between the two coils is thus given by... 

The viscosity correction factor is neglected in this rough calculation. 

In addition to the effect of the nonideality of the metal on the electrolyte phase, one must consider the influence of the electrolyte phase on the metal. This requires a model for the interaction between conduction electrons and electrolyte species. Indeed, this interaction is what determines the position of electrolyte species relative to the metal in the interface. Some of the work described below is concerned with investigating models for the electrolyte-electron interaction. Although we shall not discuss it, the penetration of water molecules between the atoms of the metal surface may be related3 to the different values of the free-charge or ionic contribution to the inner-layer capacitance found for different crystal faces of solid metals. Rough calculations have been done to... 

Notebooks/worksheets or other records show the date of analysis, analyst, analyte, sample details, experimental observations, quality control, all rough calculations, any relevant instrument traces and relevant calibration data. 

This rough calculation shows that only a few monolayers are dissolved per year. 

It exhibits a single oxidation process (Ea = + 0.59 V, vs. SCE) affected by some adsorption problems. These adsorption phenomena, which typically affect the electrochemical response of these derivatives, sometimes make it difficult to ascertain by controlled potential coulometry the effective number of electrons involved in the oxidation step. In this case, the (approximate) number of electrons involved per molecule of dendrimer, nd, can be roughly calculated by comparing the cyclic voltammetric responses of the dendrimer with that of the ferrocene monomer using the following empirical equation.27,40... 

Traditional engineering analysis tools will usually be used at some point during the investigation. The investigators will use these methods to support and refute the various theories that are put forth during the investigation. Often rough calculations may be all that is needed to determine if a scenario is possible. For example, even if the entire contents of a tank are released, it may not be sufficient to cause an overflow in another part of the process. This calculation may be sufficient to eliminate certain theories that have been proposed. 

A rough calculation of the overall heat of the reaction according to ... 

These values are shown in Table I. It is to be noted that kcyclic oligomers, while kp>x increases with the increase of x, and kp 2 being very low. Thus the high yield of the dimer at equilibrium is due to concentration by its low reactivity in polymerization. The value of kpjX and kd,x in case of potassium counterion is roughly calculated to be 1000 times larger than the value in Table I. 

By conceiving a model for the dipole layers, it is possible to make some rough calculations for the individual surface potentials (see Section 7.4.30). In this presentation of surface potentials, Xm and Xs were conceived when both phases, the metal and the solution, were taken apart and placed separately in a vacuum. However, when there is a metal in contact with a solution (neither of the phases is in contact with a... 

The worst case will normally be the maloperation that results in the highest rate of temperature and/or pressure rise over the relief range (dependent on whether the system is tempered or untempered). However, this assumes that other parameters used in the relief sizing calculations remain constant, e.g. reactor fill ratio, mass of reacting species, physical properties. Where any of the other parameters used in the calculations are significantly affected by the maloperation under consideration, then this will also have to be taken into account in selecting the worst case. In such cases, it may be necessary to roughly calculate the relief size. 

In fact, the radial parts are somewhat different, but we may use this function in carrying out our rough calculation. 

Alternatively, we might examine the radius ratio of Oj BF and get a crude estimate of = 0.8. The accuracy of our values does not permit us to choose between coordination number 6 and 8, but since the value of the Madelung constant does not differ appreciably between the sodium chloride and cesium chloride structures, a value of 1.75 may be taken which will suffice for our present rough calculations. We may then use the Bom-Lande equation (Eq. 4.13), which provides an estimate of —616 kJ mor1 for the attractive energy, which will be decreased by about 10% (if... 

The final stage in this rough calculation is the introduction of spin-orbit coupling between pure spin states. Setting... 

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