Empirical formula from experimental data

CALCULATING AN EMPIRICAL FORMULA FROM EXPERIMENTAL DATA 

Suppose we decompose a sample of water in the laboratory and find that it produces 3.0 g of hydrogen and 24 g of oxygen. How do we determine an empirical formula from these data  

A Water can be decomjxjsed by an electric current into hydrogen and oxygen. How can we find the empirical formula for water from the masses of its component elements  

We know that an empirical formula represents a ratio of atoms or a raho of moles of atoms, but it does not represent a ratio of masses. So the first thing we must do is convert our data from grams to moles. How many moles of each element formed during the decomposition To convert to moles, we divide each mass by the molar mass of that element. 

From these data, we know there are 3 mol of H for every 1.5 mol of O. We can now write a pseudoformula for water  

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Determining an Empirical Formula from Experimental Data (Section 6.8)... 

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

Obtaining an Empirical Formula from Experimental Data (3.10) Examples 3.17, 3.18 For Practice 3.17, 3.18 Exercises 85-92... 

The empirical formula gives us the least detail. It tells us the simplest ratio of the different types of atoms present in the molecule. For example, an organic compound called propene has the empirical formula CHj. This tells us that it has twice as many hydrogen atoms as carbon atoms in its molecules. We can calculate empirical formulae from experimental data on the mass of each element, and hence the number of moles of each element, in a sample of a compound. 

Empirical and molecular formulas from experimental data... 

Formulas describe the composition of compounds. Empirical formulas give the mole ratio of the various elements. However, sometimes different compounds have the same ratio of moles of atoms of the same elements. For example, acetylene, C2H2, and benzene, CeHe, each have 1 1 ratios of moles of carbon atoms to moles of hydrogen atoms. That is, each has an empirical formula CH. Such compounds have the same percent compositions. However, they do not have the same number of atoms in each molecule. The molecular formula is a formula that gives all the information that the empirical formula gives (the mole ratios of the various elements) plus the information of how many atoms are in each molecule. In order to deduce molecular formulas from experimental data, the percent composition and the molar mass are usually determined. The molar mass may be determined experimentally in several ways, one of which will be described in Chap. 12. 

Empirical and molecular formulas from experimental data Molar masses from gas density, freezing-point, and boiling-point measurements... 

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. 

We could at this point write the empirical formula as Bao.430So.421O1.71, but we know that the empirical formula should be expressed in whole numbers. Consequently, we divide each of the subscripts by the smallest one (0.421), which gives us subscripts of 1.02,1.00, and 4.06. These still are not whole numbers, but because these numbers have been derived from experimental data, which contain errors, we cannot expect the numbers to come out to exact whole numbers. The numbers appear close enough to 1, 1, and 4 to allow us to safely round them off. Hence, the empirical formula of the substance is BaS04. 

In Section 3.5, we will learn how to find the empirical formula for a compound from experimental data. 

Our empirical formula for water, which in this case also happens to be the molecular formula, is H2O. The following procedure can be used to obtain the empirical formula of any compoimd from experimental data. The left column outlines the procedure, and the center and right columns show two examples of how to apply the procedure. 

Of course, any set of experimental data can be described by selecting an appropriate empirical equation with an arbitrary set of constants. However, comparing a vast wealth of the known results of measurements of suspension viscosity, it should be admitted that a universal formula for ther (cp) dependence does not exist, and significant discrepancies may begin already from a linear term, so that physical reasons for exagerated values of the coefficient bt as compared to 2.5 should be looked for. 

To find the empirical formula of vitamin C from the data in Example F.l we must express the ratios of numbers of atoms as the simplest whole numbers. First, we divide each number by the smallest value (3.41), which gives a ratio of 1.00 1.33 1.00. Molecules contain only whole numbers of atoms, and one of these numbers is still not a whole number. Hence, we must multiply each number by the correct factor so that all numbers can be rounded off to whole numbers. Because 1.33 is Vi (within experimental error), we multiply all three numbers by 3 to obtain 3.00 3.99 3.00, or approximately 3 4 3. Now we know that the empirical formula of vitamin C is C3H403. 

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. 

The amphiphilic nature of many emulsifying agents (particularly non-ionic surfactants) can be expressed in terms of an empirical scale of so-called HLB (hydrophile-lipophile balance) numbers222 (see Table 10.1). The least hydrophilic surfactants are assigned the lowest HLB values. Several formulae have been established for calculating HLB numbers from composition data and they can also be determined experimentally - e.g. from cloud-point measurements123,125. For mixed emulsifiers, approximate algebraic additivity holds. 

From the experimental data, determine the empirical formula of copper(II) chloride, and the error in determining the percent of copper. 

The possibility of predicting thermodynamic properties of redox couples and solutes in different solvents is very important. It should be very useful to develop procedures of transferring thermodynamic data such as redox potentials from solvent to solvent. In fact, the correlation found between kinetic and thermodynamic parameters of reactions in solutions, and solvent parameters such as DN, AN, dielectric constant, etc., indicates that it may be quite feasible to draw empirical formulas which predict, for instance, redox potentials in some solvents, based on well-established data obtained experimentally with other solvents. Thus, it may be possible to define transfer parameters (AG , AH , ASf, etc.) reflecting the difference between aqueous and polar aprotic solutions in the thermodynamic properties of solutes. 

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. 

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