Examples dilution

All of these time correlation functions contain time dependences that arise from rotational motion of a dipole-related vector (i.e., the vibrationally averaged dipole P-avejv (t), the vibrational transition dipole itrans (t) or the electronic transition dipole ii f(Re,t)) and the latter two also contain oscillatory time dependences (i.e., exp(icofv,ivt) or exp(icOfvjvt + iAEi ft/h)) that arise from vibrational or electronic-vibrational energy level differences. In the treatments of the following sections, consideration is given to the rotational contributions under circumstances that characterize, for example, dilute gaseous samples where the collision frequency is low and liquid-phase samples where rotational motion is better described in terms of diffusional motion. 

Many of the reactions of nitric acid are those associated with all strong acids. For example, dilute (6 M) nitric acid can be used to dissolve aluminum hydroxide... 

CdS sols with fluorescence quantum yields close to 100% are obtained by certain surface modification procedures For example, dilution of an aqueous sol with... 

We wish also to mention that solid hydrogen is usually responsible for the block of capillaries in low-temperature apparatus, for example, dilution refrigerators. 

If the test agent is, for example, diluted 1 1,000 from the stock solution, the same dilution of the vehicle is required to... 

When an electrolyte which is without action on vanadium at ordinary temperatures (for example, dilute solutions of mineral acids, of oxalic acid, or of potassium halides) is electrolysed with a vanadium anode, a complex tetravalent vanadium ion is produced. Similarly, electrolysis at 100° C. and in molten chlorides of sodium or zinc gives rise to complex tetravalent vanadium ions. The E.M.F. in each case is found to be independent of the nature of the electrolyte. When, however, solutions of caustic soda or of caustic potash are employed, the vanadium dissolves as a pentavalent ion, irrespective of variations... 

When iron is treated with an acid that has an oxidizing anion—for example, dilute nitric acid—the metal is oxidized directly to iron(III) ... 

The high dilution trident in this example dilutes the diazo ketone solution to 10-3 -10-4 M before it reaches the reaction mixture. 

This expression enhances the fact that the heat release rate is a function of the conversion, but also of the varying volume. The dilution of the reaction mass by the feed will contribute to slow the reaction. Usually with a constant feed rate and as long as the volume varies in the cylindrical part of the reactor, V(t) is a linear function of time. In addition to the pure heat of reaction, the mixing effect of the feed with the reaction mass can be accompanied by thermal effects, for example, dilution enthalpy or mixing enthalpy. 

The addition products are generally unstable and can be dissociated simply by dissolution in solvents, e.g. benzene. They decompose completely into their components when treated with acids. For example, dilute acid causes quantitative separation of the amine from the nitro compound. 

The infrared and Raman spectra of ice is complicated by inter- and intramolecular coupling of vibrations (Bertie, 1968). However, the problem of spectral analysis is simplified by measuring the spectra of, for example, dilute H20 in D20 ice (Homig et al., 1958). In this... 

The first involves sample preparation, for example dilution, weighing and extraction efficiency. We will not discuss these errors in this chapter, but many of the techniques of Chapter 2 have relevance. 

The Action of Acids upon Iron.—As a general rule, when acids act upon iron hydrogen gas is evolved and the metal passes into solution in the form of a ferrous salt. Thus, for example, dilute sulphuric acid solution reacts as follows —... 

Further processing, for example, dilution, derivatization, solvent exchange measurement... 

The precipitation process, the reverse of solid dissolution, is dictated by solution thermodynamics. The solution reaches saturation state when the dissolution rate equals the precipitation rate. Nucleation starts when the solution concentration exceeds the saturation concentration. The solution concentration affects the crystallite size of the precipitated catalyst. For example, diluted solution is beneficial to crystal growth due to slow nucleation and the presence of a few nuclei. In contrast, submicrometer- or even nano-sized amorphous gel or sol can be formed starting with a more concentrated solution. 

When fresh water displaces saline water, dilution occurs. During dilution, divalent ions are preferentially adsorbed in comparison to a monovalent ion. For example, dilution of the solution with distilled water is accompanied by an increase of the monovalent ions (Na ) relative to the divalent cations (Ca ) when the equilibrium with the exchanger is maintained. This effect follows from Eq. 3.19 ... 

Oxidizing solutions (for example diluted solutions of NH4CIO4) have been used for preparing well-defined small particles of chromium dioxide and for stabilizing thermally unstable oxidation states, such as Hg. ... 

The electrolyte must be one that is volatile at the temperature to be used for drying or ignition, and it must not dissolve the precipitate. For example, dilute... 

Polar solvents such as ethers and amines react with organometallic initiators, as well as propagating polystyryl and polydienyl carbanions, to decrease the concentration of active centers [3, 44, 45]. The rate of reaction with ethers decreases in the order Li > Na > K. For example, dilute solutions of poly(styryl)lithium in THF at room temperature decompose at the rate of a few percent each minute. Alkyllithium initiators also react relatively rapidly with ethers the order of reactivity of organolithium compounds with ethers is tertiary RLi > secondary RLi > primary RLi... 

Strained cyclopropenones open more readily, for example dilute sulphuric acid opens the three-membered ring of a cyclohexenocyclo-propenone [90].. ... 

Example— Dilution water is added through an automatic control valve to the circulation tank of a sulphuric acid plant to maintain the strength between 98.2 and 98.6 % with a mean value of 98.4 %. If six consecutive acid samples show... 

If the diffusion Deborah number is small (small moleeular relaxation time or large diffusion time) moleeular relaxation is mueh faster than diffusive transport (in fact, it is almost instantaneous). In this case the diffusion process is similar to simple liquids. For example, diluted solutions and polymer solutions above glass transition temperature fall in fliis category. 

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