Response to a Change in Mole Number

In the previous two sections we presented those simple derivative relations that characterize changes of state in closed systems or systems of constant composition. But engineering practice is more often concerned with open multicomponent systems— systems of variable composition. In those situations the behavior of our system is affected by the kinds and amounts of components that are present. 

In this section we consider how thermod)mamic properties are affected by changes in the amounts of components. Such changes promote a response that is governed by the partial molar properties. In what follows, we apply the calculus and define certain useful quantities, but no new thermodynamics is introduced. 

Consider any extensive property F for a mixture that contains C components whose mole numbers are N, N2,. .., Th mixture is a single homogeneous phase with no internal constraints, so (3.1.7) indicates that F depends on (C + 2) independent variables  

Note that the list of independent variables contains both intensive and extensive properties this is legitimate because F is extensive. 

Now let the intensive analog of F be/= F/N, where N is the total number of moles in the mixture. In special cases (revealed in Chapters 4 and 5) F can be computed by a mole-fraction average of the pure-component propertiesj. But in general 

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For a reaction with positive gas mole change, Eq. (47) indicates that Kx decreases with pressure. Because ce is a monotonically increasing function of Kx, the equilibrium extent of a reaction with positive Avgas always decreases as pressure is increased. This is an example of Le Chatelier s principle, which states that a reaction at equilibrium shifts in response to a change in external conditions in a way that moderates the change. In this case, because the reaction increases the number of moles of gas and thus the pressure, the reaction shifts back to reactants. The isothermal compressibility of a reactive system can, therefore, be much greater than that of a nonreactive system. This effect can be dramatic in systems with condensed phases. For example, in the calcium carbonate dissociation discussed in Example 12, if the external pressure is raised above the dissociation pressure of C02, the system will compress down to the volume of the solid. Of course, a similar effect is observed in simple vaporization or sublimation equilibrium. As the pressure on water at 100°C is increased above 1.0 atm, all vapor is removed from the system. 

Since P > 0, the response of to a change in pressme is determined by a that is, by whether the reaction increases or decreases the number of moles. If a < 0, then the number of moles decreases during the reaction, and we increase conversion by increasing P. Inversely, if a > 0, then the number of moles increases during the reaction, and we increase conversion by decreasing P. If o = 0, then the number of moles is conserved by the reaction, and a change in pressure has little effect on conversion. 

With electrochemical methods, we determine thermodynamic potentials of components in systems which contain a sufficiently large number of atomic particles. Since the systematic investigation of solid electrolytes in the early 1920 s, it is possible to change the mole number of a component in a crystal via the corresponding flux across an appropriate electrolyte (1 mA times 1 s corresponds to ca. 10 s mol). Simultaneously, the chemical potential of the component can be determined with the same set-tip under open circuit conditions. Provided both the response time and the buffer capacity of the galvanic cells are sufficiently small, we can then also register the time dependence of the component chemical potentials in the reacting solids. ... 

The correct answer is (C). The equation in choice (C) is the only one in which the number of moles of products is the same as the number of moles of reactants. As a result, it won t shift in response to pressure changes due to changes in volume. 

To measure the response of the biotinylated protein sample, add 3 ml of the (strept)avidin solution plus 75 pi of the HABA dye to a cuvette. Mix well and measure the absorbance of the solution at 500 nm. Next, add a small amount of sample to this solution and mix. Record the absorbance at 500 nm. If the change in absorbance due to sample addition was not sufficient to obtain a significant difference from the initial (strept)avidin-HABA solution, add another portion of sample and measure again. Determine the amount of biotin present in the protein sample by using the standard curve. The number of moles of biotin divided by the moles of protein present gives the number of biotin modifications on each protein molecule. 

Amperometric detection refers to a detection method in which the current is proportional to the concentration of the species generating the current. It consists of two electrodes, a working electrode and a reference electrode, across which a DC voltage is applied. A redox reaction is induced at the working electrode when analyte solution flows in between two electrodes and the current change is monitored. The current response is directly proportional to the number of moles of analyte oxidized or reduced at the working electrode surface as described by Faraday s law ... 

The objective of the ECD and NIMS experiments is to measure the molar response of different compounds as a function of temperature. From these data the fundamental kinetic and thermodynamic properties of the reaction of thermal electrons with molecules and negative ions can be determined. The measurement is carried out in the same manner as the calibration of any detector. Known amounts of a compound are injected into the chromatograph and purified on a column, they then enter the detector. The response of the detector is normalized to the number of moles injected. When obtaining physical parameters, the detector temperature is changed and the procedure repeated. Since the molar response can vary by three to four orders of magnitude, the concentrations of the test molecule and the conditions in the detector at different temperatures must be taken into account. 

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