Proper quotient

From equation n. B. 26. above one sees that the proper quotient of molar concentration or mole fractions does depend on pressure. For flame temperature calculations, it is most convenient to write Kp in terms of the nt. The special case of ... 

The argument of the logarithm is called the proper quotient of pressures the numerator is the product of partial pressures of the chemical products each raised to the power of its stoichiometric coefficient, and the denominator is the product of the partial pressures of the reactants, each raised to the power of its stoichiometric coefficient. Ordinarily the quotient is abbreviated by the symbol Qp ... 

Note that the argument of the logarithm is a proper quotient of fugacity and activity for the electrode reaction if the presence of the electrons is ignored in constructing the quotient. From Eq. (17.33) we can calculate the potential, relative to SHE, of a hydrogen electrode at which/h2 and h+ have any values. 

This equation says that is proportional to the proper quotient of partition functions per unit volume. As usual, we have expressed the equilibrium constant as a product of dimensionless ratios. 

The left-hand side of this equation is the proper quotient of equilibrium concentrations, the equilibrium,constant therefore... 

We recognize that cJca Cb = Q, the proper quotient of concentrations for the reaction, and kf/k = K, the equilibrium constant for the reaction. Then we have... 

Qixn consists of a factor for each reactant and product. Each factor is the activity raised to the power of the stoichiometric number Vj. Since the value of v is positive for a product and negative for a reactant, Qrxn is a quotient in which the activities of the products appear in the numerator and those of the reactants appear in the denominator, with each activity raised to a power equal to the corresponding stoichiometric coefficient in the reaction equation. Such a quotient, with quantities raised to these powers, is called a proper quotient. The reaction quotient is a proper quotient of activities. 

The thermodynamic equilibrium constant K is the proper quotient of the activities of species in reaction equilibrium. At typical temperatures and pressures, an activity cannot be... 

On the right side of this equation, the first factor is the proper quotient of fugacity coefficients in the mixture at reaction equilibrium, the second factor is the proper quotient of partial pressures in this mixture, and the third factor is the power of p° needed to make K dimensionless. 

The proper quotient of equilibrium partial pressures is an equilibrium constant on a pressure basis, Kp ... 

We can readily derive a relation between Ks and the molalities of the ions in the saturated solution by treating the dissolved salt as a single solute substance, B. We write the equiUbrium in the form B (s) B(sln), and write the expression for the solubility product as a proper quotient of activities ... 

The first factor on the right side of Eq. 12.5.25, the proper quotient of pressure factors for the reaction B (s) B(sln), will be denoted Er (the subscript r stands for reaction). The value of Er is exactly 1 if the system is at the standard pressure, and is otherwise approximately 1 unless the pressure is very high. 

The subscripts + and — refer to the Ca " " and HCOs ions, and all quantities are for the system at reaction equilibrium. Ft is the proper quotient of pressure factors, given for this... 

Measurements of the true specific heats at low temperatures have been carried out by Eucken, who worked in such a way that to a weighed quantity of the substance in the form of a block, or in a proper isolated vessel, a known quantity of heat was added by means of an electrically heated platinum spiral, the resistance of wThich at the same time served to measure the temperature. The quotient of the electrical energy spent by the rise of temperature gives the specific heat. The correction for cooling (in vacuum of 5 Jo mm.) amounted to 20 per cent., and for heat capacity of the apparatus 5 per cent., yet the results are stated to be accurate to 1 per cent. 

Attach these quotients as subscripts and list the atoms properly. This yields H2O. The compound is water. 

By construction H1lbrtrft) is a quasi-projective scheme. To prove that it is projective it suffices to show that it is proper over k. We will use the valuative criterion of propemess. Let o be a discrete valuation k-algebra with quotient field Q and residue field K, and let... 

Ratio. The quotient of two similar quantities. In physics, the two quantities must have the same units to be similar . Therefore we may properly speak of the ratio of two lengths. But to say the ratio of charge to mass of the electron is improper. The latter is properly called the specific charge of the electron. See specific. 

Plutonium chemists use reaction (1) as the net reaction for reactions (2), (3), and (4). This is clearly documented in the Plutonium Handbook edited by Wick, and in Cleveland s book. The Chemistry of Plutonium. Reaction (1) is an accurate representation of an equilibrium and the equilibrium concentration quotient is the product of the quotients for reactions (2), (3), and (4). Therefore, it is correct to discuss equilibrium concentrations of Pu(IV), Pu(VI), and Pu(III), without Pu(V). Circumstances where the net reaction has not been properly considered are those where concentrations of oxidation states in solutions with low acidity are calculated without consideration of Pu(IV) hydrolysis and polymerization. The distributions of Pu oxidation states (including Pu(V) and Pu(IV) polymer in nitric acid systems) were reported in JINC 609 (1973), and Silver has not included... 

To improve the understanding of THBR tests from different laboratories, the Committee on Nomenclature of the American Thyroid Association has recommended that uptake results for individual patients be normalized to those of a control serum (or reference serum pool) obtained from euthyroid patients who have normal quantities of TBPs. The quotient of these results is proportional to the free fraction of T4 or T3 in serum and is properly known as the THBR ... 

Proposition 3. Suppose f X - Y is proper and R is a valuation ring, with quotient field K. Suppose we are given morphisms , ipo ... 

Notice that at standard state conditions, all activities are unity, the value of the quotient within the parentheses in Equahon 5.39 is 1, and with those conditions, the AG of the reaction is properly the AGi, the standard state value for the free energy change of the reaction. 

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