Activities and Standard States An Overall View

Thus CaCOj in the form of calcite and aragonite at 3737 bars, although having the same chemical potential, has two different activities because there are two different standard states. Recalling that activity is the ratio fjf , we see too that the physical meaning of an activity of calcite of 261 is that the fugacity (which vapor pressure) of calcite is increased by a factor of 261 when it is squeezed from 1 bar to 3737 bars. We know this without knowing either / at 3737 bars or /° at one bar for calcite. 

If we now consider systems having more and more B in the solid solution (and hence in the other two phases), but always at equilibrium, the histogram bars stay where they are (because we are not changing standard states) but the level of the (absolute) chemical potential of A is lowered, increasing the distance between the top of the histogram bar for each phase and the level of Ua, that is, increasing the (negative) value of jXp — /xD as the activity of A is lowered. 

This diagram is worth careful thought. It illustrates several things that are useful in understanding activities, chemical potentials, and standard states, such as the absolute nature of chemical potentials and the necessity of using differences, the equality of chemical potentials in each phase, and the arbitrary nature of the standard state. 

So probably it is better to stick to having different standard states and different activities in each phase. 

Another way to think about standard states is to consider how to change from one to another. For example, let s say we have a real system consisting of a 

(b) The top part of the histogram of chemical potentials in kilocalories. The length of the bar for each phase is fixed when the standard state is chosen, and the chemical potential of A in the equilibrium system is represented by a line across the histogram at a level depending on the amount of B in the system. The lengths of the bars shown on the left represent traditional standard states, but any position for the top of the bar could be chosen, such as the one shown on the right, thus defining a new standard state. 

This diagram is worth careful thought. It illustrates several things that are useful in understanding activities, chemical potentials, and standard states, such as the absolute nature of chemical potentials and the necessity of using differences, the equality of chemical potentials in each phase, and the arbitrary nature of the standard state. To further illustrate the la.st point, suppose we choose a new energy level for the standard state more or less at random, such that (/xa — when Xa is 0.5 is 5000 cal mol . This implies a value of oa of 10 and this in turn defines the physical 

If it is used for the solid phase, then because a mole fraction of A of 0.5 has an activity of 10 , a mole fraction of 1.0 has an activity of twice this, or 10 . This implies that the standard state is hypothetical solid A having a fugacity 0.00043 times the normal fugacity of pure crystalline A. 

These weird standard states have one very attractive feature, which is that because they all have the same value of the activity of A would always be the same in all three phases at equilibrium. The three standard states could also coexist at equilibrium, if they could exist at all. As mentioned earlier, there is no reason why other concentrations or pressures could not be chosen for the standard states, that is, other than one molal or one bar, as long as ideal behavior is still part of the definition. But these other concentrations or pressures would then appear in all activity calculations and all equilibrium constants, and we would have to give up the convenience of being able to think of gaseous activities as approximate or thermodynamic pressures, and of aqueous activities as approximate or thermodynamic concentrations. It seems generally more convenient to add a little diversity to standard states, and keep activity expressions simple, as is the present custom. 

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Quality control is defined as an overall system of technical activities that measures the attributes and performance of a process, item, or service against defined standards to verify that they meet the stated requirements established by the client or customer. QA is a management function, whereas QC can be viewed as a laboratory function. A laboratory must have a written QA document on file, whereas a record of certified reference standards that are properly maintained implies that QC is in place. Much of what has been discussed in this chapter falls under the definition of QA. 

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