Excess fractional

G, T840 + 8.0x, with fuel oil Q L822 + 7.78x, with fuel gas x— fraction excess air... 

The term enantiomeric purity (or optical purity) is defined as the fractional excess of one enantiomer over the other. This is expressed in Equation 19-4 in terms of the moles (or weights) of the two enantiomers, and n2, and is... 

If the supply of air is not infinite, but limited, say, to 1 + (t = fractional excess air) times that theoretically necessary for combustion, Parker and Hottel obtain... 

The Simha-Boyer rule may be derived if it is assumed that the fractional excess volume universal constant for all polymers. In this case we have... 

Even for the largest magnetic fields available for NMR, the energy levels are separated only by mi/Iicalories, and the argument in the exponential is very small except at extremely low temperature. Hence, the high temperature approximation e x 555 1 — x may be employed to show that the fractional excess population in the lower level is... 

For 1H, which has a large magnetic moment, in a field of 7 tesla this fractional excess is only about 5 X 10 5 at room temperature. 

Suppose (nA)feed is the number of moles of an excess reactant. A, present in the feed to a reactor and that (nA)stoich lit stoichiometric requirement of A, or the amount needed to react completely with the limiting reactant. Then (nA)feed ("A)stoich s the amount by which the A in the feed exceeds the amount needed to react completely if the reaction goes to completion. The fractional excess of the reactant is the ratio of the excess to the stoichiometric requirement ... 

In the example above, the stoichiometric amount of oxygen is 2 mol, since that is the amount that would react with the 1 mol of methane. The excess amount of oxygen is 1 mol, which is a percentage excess of 50% or a fractional excess of 0.50. These definitions are employed in the solution below. 

When non-ideal liquid solutions are considered, we use excess thermodynamic functions, which are defined as the differences between the actual thermodynamic mixing parameters and the corresponding values for an ideal mixture. For constant temperature, pressure and molar fractions, excess Gibbs free energy is given as... 

In the experiment, 33 mM labeled DL-proline and 183 mA unlabeled L-proline were incubated with proline racemase and the percent label in D- and L-proline monitored as L-proline was converted to D-proline and the reaction approached chemical and isotopic equilibrium. The percent label in L-proline rose to 65%, then gradually dropped to 50%, showing that there was countertransport of label from D- to L-proline induced by the high flux from l- to D-proline. This countertransport results from the high level of E formed by the reaction E -I- A F -I- E, which increases the rate of the reverse reaction, F -(- E E -I- A. The fractional excess of label in A at any point during the reaction is given by... 

The fractional excess of label in A at the point given by Eq. (58) will be... 

Thus, the countertransport experiment requires that (Ao + P ) be high enough for the exponent x in Eq. (57) to be at least 0.3, if the maximum fractional excess label is to be approximately 0.1. With proline racemase, jc was 1.6, and the maximum excess label was 0.30. It is also necessary that Ao Po in order to observe the maximum possible countertransport (a value of 17 was used with proline racemase). 

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