Empirical formula calculating, from experimental

The partial pressure of water is determined with the empirical formula from Ref. 21 and is shown in Eq. 14. This relationship enables the partial pressure of water to be calculated from experimental data as the temperature of the DI water into the stack anode varies,... 

If you know the formula of a compound, you can calculate its percent composition. Just the reverse can be done too. If you know the percent composition of a compound, you can calculate a formula for the compound. A formula calculated from percent composition data is called an empirical formula (one calculated from experimental data). The formulas of ionic compounds are always empirical formulas. The formulas of molecular compounds may be the same as their empirical formulas or they may be some whole-number multiple of it. You will learn how to do composition-from-fbrmula and fbrmula-from-composition calculations in this chapter. 

Just as the percentage composition by mass can be calculated from the formula of a compound, the simplest formula of a compound can be found from the percentage composition by mass of each element. The simplest formula is also known as the empirical formula. Here, empirical means obtained from experimental results . To find the simplest formula ... 

Note The assignment of empirical formulae from accurate mass measurements always must be in accordance with the experimentally observed and the calculated isotopic pattern. Contradictions strongly point towards erroneous interpretation of the mass spectrum. 

The critical input parameters are then (1) the grain size, which should be known for each case, (2) the Aci temperature which is calculated from thermodynamics, (3) the effective diffusion activation energy, Qea, and (4) the empirical constants aj for each element. Qea and aj were determined by empirically fitting curves derived using Eq. (11.12) to experimentally observed TTT curves, and the final formula for calculating r was given as... 

As early as 1819, J. L. Gay Lussac proposed to represent the solubility S of potassium chloride in water at a temp. 0 by the formula /S=29-23+0-27380 grms. per 100 grms. of water. Since that time it has been customary to represent solubility curves by empirical formula of the type /S=a+ 0+d02+..., where a, l, c,d,.. . are constants whose numerical values are calculated from the experimental data. Equations of the type S=a- -bO represent straight lines, equations with more terms represent curved lines the solubility equation /S=d+60+c02 represents a portion of a paraboloid curve. The greater the number of terms used in the formula the greater is supposed to be the accuracy of the result. 

Figs. 32a-c illustrate the absorption spectra, calculated, respectively, for water H20 at 27°C, water H20 at 22.2°C, and water D20 at 22.2°C dotted lines show the contribution to the absorption coefficient due to vibrations of nonrigid dipoles. The latter contribution is found from the expression which follows from Eqs. (242) and (255). The experimental data [42, 51] are shown by squares. The dash-and-dotted line in Fig. 32b represents the result of calculations from the empirical formula by Liebe et al. [17] (given also in Section IV.G.2) for the complex permittivity of H20 at 27°C comprising double Debye-double Lorentz frequency dependences. 

Figure 32. Absorption coefficient (a, b, c) and dielectric loss (d, e, f). Water H20 at 27°C (a, d), water H20 at 22.2°C (b, e), and water D20 at 22.2°C (c, f) Solid lines Calculation for the hat-curved model experimental [42, 51] values of absorption (squares) and loss (dashed lines), calculation from empirical formula [17] (dashed-and-dotted lines). Contribution to absorption due to nonrigidity of dipoles is shown by dots.

The empirical formula of a compound can be determined in a laboratory experiment by finding the ratio between the number of moles of the elements in the compound. The number of moles of each element can be calculated from the experimental values of the weights in which the elements combine by dividing by their corresponding atomic weights. If the molecular weight and the empirical formula of the compound are known, then the molecular formula of the compound can be determined. 

The determination of the empirical formula of a compound can be made experimentally, by determining the percentage amounts of elements present in the substance using the methods of quantitative chemical analysis. At the same time the relative molecular mass of the compound has to be measured as well. From these data the empirical formula can be determined by a simple calculation. If, for some reason, it is impossible to determine the relative molecular mass the simplest (assumed) formula only can be calculated from the results of chemical analysis the true formula might contain multiples of the atoms given in the assumed formula. 

It will be seen from these tables that Henry s Law, when expressed in terms of the Ostwald coefficient k, holds over a much wider pressure range than when expressed in terms of k Up to 200 mm k remains constant within the limits of experimental error, and it will be observed, that at the same time the magnitude of the coefficient shows that the concentration of the dissolved gas becomes very considerable Using an empirical formula, Sackur and Stem have calculated with the aid of Hhese absorption coefficients the values of the osmotic pressure of the... 

Table 3 Energy shifts of K- and L-shell electrons in hydrogen-like due to various collective excitations. Upper half The contributions fixim low-lying nuclear states are calculated using experimental energies and transition probabilities [69]. Lower half The contributions from giant resonance states. Excitation energies and corresponding reduced electric transition strengths are again estimated based on empirical formulae. Notations are the same as in Table 2.

It is found j experimentally that the flow rate calculated from Eq. 5.30 is slightly higher than that actually observed. This is due partly to the friction heating in the m eter, which we have assumed to be zero, and partly to the fact that the flow is not entirely uniform across any cross section of the pipe, as we have tacitly assumed. We could attempt to account for these differences by using a more co mplicated formula than Eq. 5.30 the more common approach is to introducej an empirical coefficient into Eq. 5.30. This is called the coefficient of discharge C ... 

Wirtz formula (Eq. 14) in calculating D s when empirical values were not available. As can be seen from Table 10, the D vv values are nearly idential to the experimental values Dg p in hydrocarbon solvents. Spin-statistical factors calculated from the individual slopes in Fig. 12 are all very close to the expected value of Va (Table 11). Of the radicals in Table 10, only the /-propyl radical shows systematic deviations from the theoretical line (166). Since these deviations are outside of the estimated experimental uncertainty (166), and this behavior was not expected a priori, the results for the /-propyl radical are treated in detail below. 

Calculations show that the model of a non-equilibrium surface layer is an alternative to kinetic-controlled adsorption models. On the basis of the purely diffusion-controlled adsorption mechanism the proper consideration of a non-equilibrium diffusion layer leads to a satisfactory agreement between theory and experimental data for various studied systems, systematically demonstrated for the short-chain alcohols [132], The non-equilibrium model is applicable in the concentration range from 10 to 10 mol/cm at different values of the Langmuir constant at- For l < 10 mol/cm a consideration of non-equilibrium layer effects is not necessary. For ai > 10 mol/cm and large surfactant concentration the Ay values calculated from the proposed theory do not compensate the discrepancy to the experimental data so that other mechanisms have to be taken into account. An empirical formula also proposed in [132] for the estimation of the non-equilibrium surface layer thickness leads to a better agreement with experimental data, however this expression restricts the validity of the non-equilibrium surface layer model as alternative to non-diffusional adsorption kinetics. 

In this experiment you will determine the empirical formula of a compound composed of lead and iodine. A weighed quantity of lead is reacted with nitric acid, HNO3, solution. The resulting lead nitrate solution is then reacted with sodium iodide, Nal, solution to form insoluble lead iodide, which is filtered, dried, and weighed. From your experimental data you can calculate the percentage composition and the ratio of moles of lead to moles of iodine in the compound, and then write the empirical formula. 

It is customary in applying normal coordinate theory to use the experimentally observed fundamental frequencies as the basis of the calculation of the quadratic force constants. From a strict viewpoint this is not justifiable inasmuch as the observed fundamental frequencies do not have the same values as they would if the anharmonic terms were zero. In order to calculate the quadratic force constants accurately, it is necessary to use the so-called mechanical frequencies of vibration, which are the frequencies which the molecule would exhibit if the anharmonic terms in V were all zero. When an empirical formula of the type given in (3) has been obtained, the mechanical frequencies can be calculated from the relations... 

CALCULATING AN EMPIRICAL FORMULA FROM EXPERIMENTAL DATA... 

Why is it important to be able to calculate an empirical formula from experimental data ... 

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