Using Partial Pressures to Solve Problems

Cylinder filled with Cylinder being filled water ready to be placed with oxygen gas in the plastic basin 

TABLE 11.5 1 apur Prc.ssuh t)l Wiiicr (Pi t Function of Tempeiature  

By subtracting the partial pressure of water from the total pressure, which is equal to atmospheric pressure, we can determine the partial pressure of oxygen—and thereby determine how many moles are produced by the reaction. We get the partial pressure of water, which depends on temperature, from a table of values. Table 11.5 lists the partial pressure (also known as the vapor pressure) of water at various temperatures. 

Sample Problem 11.13 shows how to use Dalton s law of partial pressures to determine the amount of gas produced in a chemical reaction and collected over water. 

Calcium metal reacts with water to produce hydrogen gas [ W Section 7.7]  

TABLE 11.5 1 Vapor Pressure of Water (/ h.o) as a Function of Temperature  

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The terms adsorption capacity and loading are used generically to express the amount of adsorbate taken up by the adsorbent. To solve problems, it is necessary to express loading quantitatively, e.g., as an explicit function of partial pressure or concentration and temperature ... 

The same procedure applies to Kp. Sample Problem 15.10 shows how to solve an equilibrium problem using partial pressures. 

Follow the procedure used in Example 14.5 and 14.6 (using partial pressures in place of concentrations) to solve the problem. 

Example 12.4 illustrates a principle that you will find very useful in solving equilibrium problems throughout this (and later) chapters. As a system approaches equilibrium, changes in partial pressures of reactants and products—like changes in molar amounts—are related to one another through the coefficients of the balanced equation. 

Therefore, the control loop shown in Fig. 5.28 was developed to solve the problem of symmetry control [121]. Two additional PID control loops are used to control the homogeneity of the reactive gas partial pressure because of appropriate regulation of the threefold gas inlet (top/center/bottom). The... 

The correct answer is (D). This is a partial pressure problem. To solve it, you need to use two equations (both from Chapter 8) ... 

The solution to the problem is given by 2(m- -2) differential equations for the temperature, pressure, degrees of conversion, and for Lagrange multipliers (T, P, k, Xp, kp, and A. ), with partial derivatives of //, where m is the number of reactions between the components. The constant Hamiltonian of this problem was reduced to a solution with constant entropy production. O , in the case of a heat exchange process. Using NET, it was also found that this solution was approximated by a solution with constant driving force, How to realise this in practice, remains to be solved. 

Several methods have been used to solve this problem partially. They can be divided into two major types. In the first a size-dependent physical separation of the clusters is made. In the second the expansion conditions are varied and so cause a change in the composition of the mixture. This is monitored by the change in product formation. If the dependence of the composition on the stagnation pressure can be modeled, this method may provide information on the reaction cross section of each complex. 

One way to solve this problem is to use the numbers of moles given in the problem. Alternatively we could use the partial pressures and the total pressure from Example 12-15. 

We place 10.0 grams of SbCl5 in a 5.00-liter container at 448°C and allow the reaction to attain equilibrium. How many grams of SbCl5 are present at equilibrium Solve this problem (a) using and molar concentrations and (b) using Kp and partial pressures. 

At this point, all the necessary information needed to relate the concentrations of the various defects to the oxygen potential or partial pressure surrounding the crystal is available. In Eqs. (6.23) to (6.27), there are four unknowns [n, p, Vq, Vm] and five equations. Thus in principle, these equations can be solved simultaneously, provided, of course, that all the Ag s for the various reactions are known. Whereas this is not necessarily a trivial exercise, fortunately the problem can be greatly simplified by appreciating that under various oxygen partial pressure regimes, one defect pair will dominate at the expense of all other pairs and only two terms remain in the neutrality condition. How this Brouwer approximation is used to solve the problem is illustrated now ... 

When a gas chromatograph is used for composition measurements, estimates of the partial pressures are given directly. Or rather, estimates are made directly of a constituent vector c, that if properly normalized would give the partial pressures. If, on the other hand, some components of the outlet stream are unmeasured, then it is not immediately clear how to normalize c. In fact we may use a simplified version of the procedure described above to solve this problem for a mass spectrometer. Again we ignore the calibration matrix Mj and the measured peaks vector v (i.e. set Mi equal to the identity matrix in the formulas above), and obtain the following procedure. Partition ... 

This is a (hfficult problem. Express the equilibrium number of moles in terms of the initial moles and the ehange in number of moles (x). Next, ealeulate the mole fraetion of each component. Using the mole fraction, you should come up with a relationship between partial pressure and total pressure for each component. Substitute the partial pressures into the equilibrium constant expression to solve for the total pressure, Pj. 

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