Mixing quantity

It should be stressed that the pH value of an actual buffer solution prepared by mixing quantities of the weak acid or base and its conjugate base or acid based on the calculated ratio will likely be different from what was calculated. The reason for this is the use of approximations in the calculations. For example, the molar concentration expressions found in Equations (5.23) to (5.30), e.g., [H+], are approximations. To be thermodynamically correct, the activity of the chemical should be used rather than the concentration. Activity is directly proportional to concentration, the activity coefficient being the proportionality constant ... 

A series of experiments were run to find the probable cause of these explosive events. A 20-liter bucket was placed on the ground and a second bucket placed on a stand above it with a remotely actuated tipping device. In alternate experiments, water was poured on LNG and LNG on water. Foamed ice was formed, but no explosions occurred. The tests were extended by adding either additional LNG or water after the initial mixing of LNG and water had taken place. The further addition of LNG had no effect. However, when water was added to an already mixed quantity of LNG and water, an explosive event occurred which threw the contents of the bucket upward about 5 m. 

A fodder to be used as a substitute for oats is described, being prepared by mixing quantities of rye, barley, oats, maize, potatoes, rice, grass, clover, malt germs, food potatoes, topinambur (Helianthus tuberosus), horse chestnuts, straw, dried beet, linseed cake, and rape cake. 

We can also interpret (38) as the equation for the covariant derivative of the mixed quantity whose indices are related to the tangent space or rather to the five-dimensional space. 

This holds as long as the batch is larger than the critical mixing quantity. See e.g. Hall and Nioholls (1980) or Cafaro and Cerda (2004). 

In practice, many of the extensive functions (IJ, S, H, G), and their corresponding partial molar quantities, can only be determined up to an additive constant—absolute values of U, H, and can be obtained from simulation, but these then depend on the model of choice. Hence, their values are typically expressed with respect to a set of defined reference or standard states. These are usually taken as the pure solutions of each component at the same T and p. One can then define a series of mixing quantities such that... 

Obtaining the derivatives on the right-hand side requires a fitting equation for the excess mixing quantities. The Wilson, Redlich-Kister, and nonrandom two liquid (NRTL) model equations are some of the most commonly used (Poling, Praunitz, and O Connell 2000). Some additional practical considerations are also provided in Section 1.3.9 and Section 4.2 in Chapter 4. 

A general method to evaluate the partial molar quantities Xa and Xb in a binary mixtore is based on the variant of the method of intercepts described in Sec. 9.2.3. The molar mixing quantity AX(mix)/n is plotted versus xb, where AX(mix) is (X—nAX —n X ). On this plot, the tangent to the curve at the composition of interest has intercepts equal to Xa—X ... 

Following the same procedure for an extensive state function X, we derive the following general relation for its molar mixing quantity ... 

When the mixture formed is an ideal mixture (gas, liquid, or solid), and the pure constituents have the same physical state as the mixture, the expressions for various molar mixing quantities are particularly simple. An ideal molar mixing quantity will be indicated... 

We obtain expressions for other molar mixing quantities by substituting formulas for partial molar quantities of constituents of an ideal mixture derived in Sec. 9.4.3 into Eq. 11.1.5. From Si = S — R Inxj (Eq. 9.4.9), we obtain... 

Figure 11.2 Molar mixing quantities for a binary ideal mixture at 298.15 K.

An excess molar quantity X is the excess quantity divided by , the total amount of all constituents of the mixture. Examining the dependence of excess molar quantities on composition is a convenient way to characterize deviations from ideal-mixture behavior. Excess molar quantities are related to molar mixing quantities as follows ... 

The contributions of the various PSP terms in mixing quantities in the case of bulk phases have been discussed in References 14-16. In Reference 14 it was shown that the van der Waals and the... 

The changes in properties when a solution is formed from its components are described by the mixing quantities. The partial molar mixing quantities for each component are given by... 

To indicate that the current is expressed as a multiple of the capacity, it is often written as CA or C(A) , to indicate that C does not mean a capacity in Ah but a corresponding current in A. In regard to the dimensions, Eq. (53) is not correct, since it mixes quantities with units (i in A, Cr in Ah, m without dimensions). But in the battery field, this description of discharging and charging currents is well established and understood. It is also used in the lEC standard for secondary cells and batteries containing alkaline or other nonacid electrolytes (20). 

The excess enthalpy and the excess volume are equal to the mixing quantities, since A//mix and Ay ix both vanish for an ideal solution. 

ATmix Symbol used to stand for a general mixing quantity such as the change in Gibbs energy on mixing, AGmix, etc. 

Let us first assume that 6 = 6 = p = 0. Then g , A and s are given by (17.6.3), (17,6.4) and (17.6.5). However for high polymer solutions thepartial molar quantities are more suitable than the excess functions. From (17.6,3)-(I7.6.5) we easily obtain (we use here mixing quantities instead of excess functions)... 

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