Use of Partial Pressure

The concentration c, in equation 4.1-3, the rate law, is usually expressed as a molar volumetric concentration, equation 2.2-7, for any fluid, gas or liquid. For a substance in a gas phase, however, concentration may be expressed alternatively as partial pressure, defined by 

The partial pressure p, is related to c by an equation of state, such as 

For the gas-phase reaction 2A + 2B - C 4- 2D taking place in a rigid vessel at a certain T, suppose the measured (total) pressure P decreases initially at a rate of 7.2 kPa min 1. At what rate is the partial pressure of A, pA, changing State any assumptions made. 

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Up to this point, we have emphasized the use of partial pressures for specifying the composition of a gas mixture. However, this is not the only possibility. 

For quite a number of gases, Henry s law holds very well when the partial pressure of the solute is less than about 100 kPa (I atm). For partial pressures of the solute gas greater than 100 kPa, H seldom is independent of the partial pressure of the solute gas, and a given value of H can be used over only a narrow range of partial pressures. There is a strongly nonlinear variation of Heniy s-law constants with temperature as discussed by Schulze and Prausnitz [2nd. Eng. Chem. Fun-dam., 20,175 (1981)]. Consultation of this reference is recommended before considering temperature extrapolations of Henry s-law data. 

Characteristic of most equations for surface-controlled kinetics, as opposed to diffusion-controlled kinetics, are a number of partial pressure terms, often to high powers. When large changes in partial pressures are made, differences between the observed and the calculated reaction can easily equal a factor of 1000 or more. When diffusion-type kinetics are used, one seldom finds differences exceeding a factor of two or three. While this may not seem very accurate, comparison of the two methods is rather startling. 

Using Dalton s law of partial pressures to express p, in terms of p gives... 

There are also other routes to esters of phosphorous acid. Esterification of phosphorous acid is possible but this reaction is not economical. A third route is provided by simultaneous reaction of alcohol, phosphorous, and oxygen, often using different partial pressure of oxygen see Eqs. (24) and (25). 

SOLUTION First convert the units of partial pressures to bars using 1 bar = 105 Pa P i7 = 4.2 X 10 8 bar, Pcli = 8.3 X 10 8 bar. Write the expression for the equilibrium constant from the chemical equation given. 

Partial pressure in the exit gas at 95 per cent recovery = 60.8 x 0.05 = 3.04 mm Hg Over this range of partial pressure the equilibrium line is essentially straight so Figure 11.40 can be used to estimate the number of stages needed. 

The first method of interpreting rate of reaction in terms of partial pressure uses the verbal definition given by equation 1.4-2 for rs. By analogy with equation 4.1-3, we write the rate law (for a reactant i) as... 

Use the gven data of rate of reaction as a function of partial pressure to check te validity of these rate equations. 

Note You could also solve this problem using equilibrium partial pressures of the gases ... 

Background Avogadro s law (Vin2 = V2ni), where moles, n = mw (grams/mole) exPresses the relationship between molar mass, the actual mass and the number of moles of a gas. The molar volume of a gas at STP, VSTP is equal to the volume of the gas measured at STP divided by the number of moles VSTp = pp. Dalton s Law of Partial Pressure (Ptotai = Pi + P2 + P3 +. ..) and the derivation, Pi = pp Ptotai will also be used in this experiment to predict the volume occupied by one mole of hydrogen gas at STP. 

This is Dalton s Law of partial pressures. The total pressure of the gang is equal to the sum of their individual efforts. Here, A could be the isopropyl alcohol and B the isobutyl, (it doesn t matter) but PTotal must be the atmospheric pressure, Patm. So a special version of Dalton s Law of partial pressures for use in fractional distillation will be... 

Well, at 99.6°C, quinoline contributes 10 torr to the total vapor pressure, and water must make up the difference (750 torr) in order to satisfy Dalton s Law of partial pressures to make PTotal 760 torr at boiling. Using the relationships for the composition of the vapor over a liquid, we can calculate the quinoline/water ratio coming over. 

Equilibrium constants involving each compound were evaluated using the partial pressures by the third law method. Accepting the heats of formation of WF5 and WF obtained from bomb calorimetry, the values for WF (n = 1 to 4) could be extracted by iterative fitting to partial pressure data. The W/02/F2 and W/S/F2 systems were also examined to give heats of formation of tungsten oxo- and thiofluorides. This experimentally simple technique yields thermodynamic data on high-temperature species inaccessible to conventional calorimetry. 

E—This problem depends on the ideal gas equation PV = nRT. R, V, and T are known, and by using the partial pressure for a gas, the number of moles of that gas may be determined. To convert from moles to mass, the molar mass of the gas is needed. 

Once again we use subscript T to indicate that the reaction enthalpy and entropy may not refer to 298.15 K. The subscript p in the equilibrium constant indicates that we are accepting the perfect gas model and therefore Kp is defined in terms of partial pressures, not fugacities. 

Of the problems presented, correlation of the NH3-CO2-H2S-H2O system is most important. Data that might be used for direct empirical correlation of partial pressures or fugacities with total concentrations of ammonia, carbon dioxide, and hydrogen sulfide in the liquid are available for relatively limited ranges... 

A few gases may be involved in some enzyme reactions, e.g., C02 and 02 as used by carbonic anhydrase and produced by catalase, respectively. If the presence of such dissolved gases affects rates and equilibria at ordinary pressure, their importance will increase at higher pressure. Henry s law says that the partial pressure of a gas above a solution is proportional to its mole fraction in the solution. At high pressure it is more correct to speak of the fugacity / of a gas, instead of partial pressure, in the same sense that one uses activity instead of concentration in solution calculations. In dilute solutions, the fugacity of the dissolved gas is given by... 

Concentration is the most common means for describing the composition of a solution in biochemistry. Enzyme kinetic expressions are typically expressed in these concentration units. Unless otherwise noted, this is the method used throughout this text. Nevertheless, other methods for describing compositions are utilized. For example, mole fractions are often used in Job plots. Gases in solution are commonly measured in terms of partial pressures. Below is a brief description of a few of these other conventions or methods. 

Another convention in catalytic reactions at surfaces is to use the partial pressure Pj rather than the concentration Cj in describing densities in the bulk phase above catalyst surfaces, although there are of course many situations where the reactants and products are in the liquid phase. These are simply related for ideal gases by the expression Cj = Pj/RT. 

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