Two experiments

We consider now the possible interpretations of the results of two experiments on a system for which a single factor, is to be investigated. What can be learned about the effect of the factor x, on the behavior of the system from these two pieces of information  

For the moment, we will investigate the experimental design in which each experiment is carried out at a different level of the single factor. Later, in Section 5.6, we will consider the case in which both experiments are performed at the same level. 

Before we begin, it is important to point out a common misconception that involves the definition of a linear model (Deming and Morgan (1979)]. Many individuals understand the term linear model to mean (and to be limited to) straight line relationships of the form 

This book is limited to models that are linear in the parameters. 

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The first of the two experiments given below illustrates the separation of amino-acids, now an almost classic example of the use of paper chromatography the second illustrates the separation of anthranilic acid and iV-methylanthranilic acid. Both experiments show the micro scale of the separation, and also the fact that a mixture of compounds which are chemically closely similar can be readily separated, and also can be identified by the use of controls. 

The excess of unchanged acetic anhydride is then hydrolysed by the addition of water, and the total free acetic acid estimated by titration with standard NaOH solution. Simultaneously a control experiment is performed identical with the above except that the alcohol is omitted. The difference in the volumes of NaOH solution required in the two experiments is equivalent to the difference in the amount of acetic add formed, i.e., to the acetic acid used in the actual acetylation. If the molecular weight of the alcohol is known, the number of hydroxyl groups can then be calculated. 

Adventitious losses of the reagent, due, e.g., to the chemical action of the alkaline glass vessels, slight absorption by the corks, etc., are almost identical for the actual and the control experiments and therefore do nor affect the difference in result between the two experiments. 

Substituting known values for the two experiments into equation 7.6 gives the following pair of simultaneous equations... 

Two experiments are described in this paper. In the first experiment students determine the %w/w orange oil in a prepared sample by analyzing for d-limonene using anisole as an internal standard. Separations are accomplished using... 

A variation on the use of pseudo-ordered reactions is the initial rate method. In this approach to determining a reaction s rate law, a series of experiments is conducted in which the concentration of those species expected to affect the reaction s rate are changed one at a time. The initial rate of the reaction is determined for each set of conditions. Comparing the reaction s initial rate for two experiments in which the concentration of only a single species has been changed allows the reaction order for that species to be determined. The application of this method is outlined in the following example. 

The order of the rate law with respect to the three reactants can be determined by comparing the rates of two experiments in which the concentration of only one of the reactants is changed. For example, in experiment 2 the [H+] and the rate are approximately twice as large as in experiment 1, indicating that the reaction is first-order in [H+]. Working in the same manner, experiments 6 and 7 show that the reaction is also first-order with respect to [CaHeO], and experiments 6 and 8 show that the rate of the reaction is independent of the [I2]. Thus, the rate law is... 

The checkers obtained, in two experiments, yields of 63 and 73% at this point. The product was white and melted at 233° (corr.). 

Test data are available for two experiments at different impact velocities in this configuration. In one of the tests the projectile impact velocity was 1.54 km/s, while in the second the impact velocity was 2.10 km/s. This test was simulated with the WONDY [60] one-dimensional Lagrangian wave code, and Fig. 9.21 compares calculated and measured particle velocity histories at the sample/window interface for the two tests [61]. Other test parameters are listed at the top of each plot in the figure. 

These two experiments make a number of important points. An <7-HMP will not react with an ortho position as long as a para reaction site is available. A p-HMP will react with unoccupied ortho position at about half the rate that it reacts with a substituted para position. This suggests that there is something special about the repulsion between the phenolic hydroxyls. Since the pH was only 8, it is clear that there was ample opportunity for a salted 2-HMP to find and react with an unsalted 2-HMP. Both species were present. On this basis, we cannot invoke repulsion of like-charged ions. According to Jones salted species probably react with unsalted species and this is one reason that reaction rate drops rapidly when PF pH gets much above 9.0 [147]. Yet the phenolic hydroxyl appears to be the cause of the reduced reactivity of the ortho position. Unfortunately, Jones did much of his work in a carbonate buffer. He did not realize the pH-dependent accelerating effects of carbonate on PF condensation. 

The ratio of third- to second-order piezoelectric constants has also been determined for x-cut quartz with the acceleration pulse loading method [77G05]. Two experiments yielded values for Cm/Cu of 15.0 and 16.6 compared to the ratio of 15.3 [72G03] determined from the fit to the 25 shock loading experiments. 

The standard method to synthesize MWCNTs is based on the electric-arc experiment proposed by Ebbesen and Ajayan [8]. Basically, the production system is similar to the one used by Kratschmer et al. [11] to produce macroscopic quantities of C o and the main difference between the two experiments is the inert gas pressure, that must be rather low (20-100 mbar) for an efficient fullerene production [11], but must be increased to 350-700 mbar to generate nanotubes efficiently [8],... 

Experiments on the detonability of nonhomogeneous mixtures are scarce. Two experiments reported in the literature may shed some light on this matter. Bull et al. (1981) investigated the transmission of detonation across an inert region in hydrocarbon-air mixtures under unconfined conditions. The transmission of a hydrocarbon-air detonation across an inert region in a tube was studied by Bjerketvedt and Sonju (1984) and Bjerketvedt, Sonju, and Moen (1986). 

In 1606 Gioavanni Battista della Porta of Naples performed two experiments that formed the basis for steam engines. He proved that steam could develop pressure by expelling water from a sealed container. In the next experiment a steam-filled flask was inrmersed neck down in water. As the cooling steam condensed, water flowed upward into the flask, proving that a vacuum had been created. 

Ip = hG/c y is the Planck length. Since c6t < 6x, A and B are outside of each other s light cone and local field theory assures us that these two experiments can be performed completely independently of one another. Heisenberg s uncertainty principle, however, asserts that these two measurements will also yield an energy fluctuation on the order of AE > Ip. We know that the gravitational... 

Strategy The key to solving this problem is to realize that because P, T, and V are the same in the two experiments, the number of moles ofAr and X effusing into the flask is the same ... 

Notice that the beryllium atom has no unpaired electrons, the boron atom has one, and the carbon atom two. Simple valence bond theory would predict that Be, like He, should not form covalent bonds. A boron atom should form one bond, carbon two. Experience tells us that these predictions are wrong. Beryllium forms two bonds in BeF2 boron forms three bonds in BF3. Carbon ordinarily forms four bonds, not two. 

Strategy To find the order of the reaction with respect to (CH3)3CBr, choose two experiments, perhaps 1 and 3, where [OH-] is constant. A similar approach can be used to find n compare experiments 2 and 5, where [(CH3)3CBr] is constant. To write the rate expression, use the calculated reaction orders. 

Figure 7-6 depicts the relative concentrations in two experiments, one starting with pure trans isomer, the other cis. In the first of these [m] actually rises higher than [trans] before both fall nearly to zero. Microscopic reversibility comes into play because the rate constants for this triangular scheme are related by... 

A piston confines 0.100 mol Ar(g) in a volume of 1.00 L at 25°C. Two experiments are performed. In one, the piston is allowed to expand through 1.00 L against a constant pressure of 1.00 atm. In the second, it is allowed to expand reversibly and isothermally to the same final volume. Which process does more work ... 

Experiments on the sky. Two experiments have been carried out at the sky, using two laser installations built for the American and French programmes for Uranium isotope separation, respectively AVLIS at the Lawrence Livermore Nat l Lab (California) in 1996 and SILVA at CEA/Pierrelatte (Southern France) in 1999. The average power was high pa 2 x 175 W, with a pulse repetition rate of 12.9 and 4.3 kHz, a pulse width of 40 ns and a spectral width of 1 and 3 GHz. Polarization was linear. The return flux was < 5 10 photons/m /s (Foy et al., 2000). Thus incoherent two-photon resonant absorption works, with a behavior consistent with models. But we do need lower powers at observatories ... 

It is to be hoped that specifically designed experiments may, in the next few years, lead to an answer to this dilemma. Two experiments which are being contemplated are the following ... 

These two experiments, which are being extended, show quite definitely that (in these compounds, at least) pure translational recoir is not sufficient to cause the reactions described in this review. 

Due to technical difficulties in measurement, experimental results for the local film thickness and pressure distributions caused by asperities are quite limited that only two experiment cases recently have been reported which are employed here as the comparison reference. 

Figure 38 shows the contact ratios from two experiments in which the values of the combined roughness of the glass disk and ball are 17 nm and 32 nm, respectively. 

In fact viscosity reduction of diene elastomer blends with QDI show an optimum based on mixer discharge temperature. Figure 16.13 shows the results of two experiments done on the 16 L scale. The viscosities represent the viscosity of the fourth stage of a multistage mixing experiment. These compounds were 60/40 blends of either BR or SBR with NR and contained 50 phr of N-234 carbon black. 

Two experiments have been performed by varying the reactant flow rates and subsequently the residence time in the reactor. Details of each experiment are shown in Table 12.8. 

Figure 2. Potency of anatoxin-a analogs to induce contracture in frog rectus abdominis muscle. The data from two experiments are combined in this figure. In one, anatoxinmethylester was found to be equipo-tent with carbamylcholine. In the other, the anatoxin isomers were assayed against ACh [after cholinesterse inhibition by diisopropylfluoro-phosphate (DFP) followed by washing of the preparation] (19). Maximal contracture was measured by depolarization with KCl at the end of each experiment.

The basic INEPT spectrum cannot be recorded with broad-band proton decoupling, since the components of multiplets have antiphase disposition. With an appropriate increase in delay time, the antiphase components of the multiplets appear in phase. In the refocussed INEPT experiment, a suitable refocusing delay is therefore introduced that allows the C spin multiplet components to get back into phase. The pulse sequences and the resulting spectra of podophyllotoxin (Problem 2.21) from the two experiments are given below ... 

P 66] No details of the electrical field are given in [65] other than mentioning the average charge densities. These amoimt for two experiments to 1 and 5 A m. ... 

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