Mole calculations using

Calculate, using the data of Fig. III-9a and Eq. III-53, the surface tension versus mole fraction plot for mixtures of cyclohexane and benzene. 

In process engineering, moles are used extensively in performing (lie calculations. A mole is defined as that mass of a substance that is numen cally equal to its molecular weight. Avogadro s Law states that identical volumes of gas at the same temperature and pressure contain equal numbers of molecules for each gas. It can be reasoned that these identical volumes will have a weight proportional to the molecular weight of the gas. If the mass is expressed as... 

Mole fractions of tautomers 14a (Xa) and 14b (2fb) can be calculated using the equation... 

Equilibrium mole fractions calculated using method of Example 7.13. These results are calculated for interest only. They are not needed for the main calculation. The code is specific to initial conditions G = Kthermo PO/P... 

Suppose we pump 4.0 mol of helium into a deep-sea diver s tank. If we pump in another 4.0 mol of He, the container now contains 8.0 mol of gas. The pressure can be calculated using the ideal gas equation, with n = 4.0-1-4.0 = 8.0 mol. Now suppose that we pump in 4.0 mol of molecular oxygen. Now the container holds a total of 12.0 mol of gas. According to the ideal gas model, it does not matter whether we add the same gas or a different gas. Because all molecules in a sample of an ideal gas behave independently, the pressure increases in proportion to the increase in the total number of moles of gas. Thus, we can calculate the total pressure from the ideal gas equation, using n — 8.0 + 4.0 = 12.0 mol. 

Redox reactions may involve solids, solutes, gases, or charge flows. Consequently, you must be prepared for all the various conversions from molar amounts to measurable variables. As a reminder. Table 19-2 lists the four relationships used for mole calculations. 

The isotopic method has been used in conjunction with a flow apparatus by Stranks, to measure the exchange between the cyclopentadienyl complexes of iron (III) and iron (II) in methanol. Separation was based on the insolubility of Fe(C5H5) in petroleum ether at —80 °C. Using Fe(II) and Fe(III) 10 M and short reaction times ( msec), a rate coefficient 8.7 x 10 l.mole .sec at — 75 °C was obtained. The rate of exchange in the presence of chloride ions and inert electrolytes was found to be more rapid. Calculations using Marcus Theory showed reasonable agreement with the experimental observations. In deuterated acetone, line broadening measurements have led to an estimate of this rate coefficient of > 10 l.mole . sec at 26 °C. 

The CHETAH programme used kcal/mole units whereas kJ/mole is used here. Nevertheless, numerous published documents give results using the old units. This is the reason it was decided to provide these group values in both units to be able to make calculations using both systems for comparative purposes. kJ is therefore retained. 

The balanced equation expresses quantities in moles, but it is seldom possible to measure out quantities in moles directly. If the quantities given or required are expressed in other units, it is necessary to convert them to moles before using the factors of the balanced chemical equation. Conversion of mass to moles and vice versa was considered in Sec. 4.5. Here we will use that knowledge first to calculate the number of moles of reactant or product, and then use that value to calculate the number of moles of other reactant or product. 

With molarity and volume of solution, numbers of moles can be calculated. The numbers of moles may be used in stoichiometry problems just as moles calculated in any other way are used. Also, the number of moles calculated as in Chap. 8 can be used to calculate molarities or volumes of solution. 

Randomly - Crosslinked PDMS. The polydimethylsiloxane (PDMS) used to make random networks was obtained from General Electric. Membrane osmometry showed to be 430,000 g/g-mole. The polymer was mixed with various amounts of a free-radical crosslinking agent, dicumylperoxide (Di-Cup R, Hercules Chemical Co.). Samples were then pressed into sheets and crosslinking was effected by heating for 2 h at 150°C in a heated press. Mc values were calculated using equation 2, and are included in Table I. 

Ex 35 Kcal/mole.15 We find that the CO product vibrational distribution calculated using the phase space model with Eav = 35-40 Kcal/mole is in good agreement with our experimental results (Figure 2). Thus, the measured CO vibrational distribution indicates that vibrational energy disposal to the photolysis products is determined at a point on the potential surface where the full reaction exoergicity is available. This suggests that the 351 nm excitation of W(CO)g results in the sequence of events, (2)-(4), where the asterisk denotes vibrational excitation. 

If no KIE is present, the contribution of the derivative atom to the measured 8 value of the derivatised compound can be calculated using a simple mass balance equation (14.2), where n is number of moles of the isotope of interest, F is the fractional abundance of the isotope of interest, c refers to the compound of interest, d refers to the derivative group and... 

Section 6) can be applied to reactions of the non-micellizing ions. The second-order rate constants at the surface of a functionalized micelle and tri-n-octylammonium ion are very similar (Biresaw et al., 1984 Bunton and Quan, 1984). Some examples are given in Table 11. In some reactions mixtures of functional and nonfunctional amphiphile were used and allowance was made for the dilution. The second-order rate constants in Table 11 are calculated using nucleophile concentrations written as mole ratios of nucleophile to quaternary ammonium ion because it is not obvious how a molar volume element of reaction can be estimated for the tri-n-octylammo-nium ions. 

The flux, JA, has units of mol/area-time, the concentration, c, in mol/volume, dif-fusivity, Dab, in length2/time, while the mole fraction, xA, is dimensionless naturally. Concentration can be calculated using from the ideal gas law. 

The value of the quantum yield of fluorescence of TIN in the PMMA film (calculated using the total film absorbance at the excitation wavelength) decreases from 1.2 x 10-3 to 5.0 x 10"4 when the concentration of TIN is increased from 0.07 mole% to 5.0 mole%. This suggests that the TIN molecules are involved in a concentration-dependent, self-quenching process. 

The key to any reaction experiment is moles. The numbers of moles may be calculated from various measurements. A sample may be weighed on a balance to give the mass, and the moles calculated with the formula weight. Or the mass of a substance may be determined using a volume measurement combined with the density. The volume of a solution may be measured with a pipet, or calculated from the final and initial readings from a buret. This volume, along with the molarity, can be used to calculate the moles present. The volume, temperature, and pressure of a gas can be measured and used to calculate the moles of a gas. You must be extremely careful on the AP exam to distinguish between those values that you measure and those that you calculate. 

The moles of any substance in a reaction may be converted to the moles of any other substance through a calculation using the balanced chemical equation. Other calculations are presented in the stoichiometry chapter. 

Once the moles have been calculated (they are never measured), the experiment will be based on further calculations using these moles. 

The mass of the sample is converted to moles by using the molar mass. The moles of titrant may be calculated from a consideration of the moles of sample and the balanced chemical equation. The moles of titrant divided by the liters of solution gives the molarity of the solution. 

Edwards et al. (6) made the assumption that was equal to 4>pure a at the same pressure and temperature. Further theyused the virial equation, truncated after the second term to estimate pUre a These assumptions are satisfactory when the total pressure is low or when the mole fraction of the solute in the vapor phase is near unity. For the water, the assumption was made that <(>w, , aw and the exponential term were unity. These assumptions are valid when the solution consists mostly of water and the total pressure is low. The activity coefficient of the electrolyte was calculated using the extended Debye-Hiickel theory ... 

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