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The principles of mass and charge conservation apply simultaneously to the disproportionation reactions of plutonium. New formulas for the Pu oxidation number can be generated from a bilinear equation. The new formulas are applied to the analysis of experimental errors in reported oxidation-state distributions for plutonium. Three methods of error analysis are illustrated by examples. [ABSTRACT FROM AUTHOR]

Disproportionation reactions can noticeably change the acidity of a plutonium solution. The estimation of the pH change depends on the the Pu concentration, the initial oxidation-state distribution, the initial pH of the solution, and the values of three equilibrium constants. The method can be used to estimate the minimum Pu concentration that produces a specified change in the solution acidity. The results can be checked. [ABSTRACT FROM AUTHOR]

Equations representing disproportionation reactions should be numerically verifiable. Comprehensive, balanced equations for plutonium disproportionation reactions can be verified in several ways. Overall equations for Pu disproportionation reactions do not meet all the requirements. [ABSTRACT FROM AUTHOR]

Local maxima in the fractions of the trivalent and hexavalent oxidation states are inherent in the algebra of Pu disproportionation reactions. A new method predicts the pH and the oxidation-state fractions at maximum. Tabulated results illustrate the effects of the Pu oxidation number and Pu(IV) hydrolysis on the maxima. This method suggests a new laboratory approach for discovering Pu oxidation-state maxima. [ABSTRACT FROM AUTHOR]

Formulas that estimate the equilibrium constant of the first hydrolysis reaction of tetravalent Pu have recently appeared. Their differential expressions are used to illustrate the effects of errors on the estimates of this constant. Four new formulas that estimate the hydrolysis constant are illustrated. [ABSTRACT FROM AUTHOR]

The equilibrium fractions of soluble tri- and hexavalent Pu depend on the pH and the Pu oxidation number. Both fractions can exhibit maxima as the pH changes at constant N. A fraction at maximum can be used to estimate the equilibrium constant of the first hydrolysis reaction of tetravalent Pu. A new formula that renders least-squares estimates of this constant is illustrated. [ABSTRACT FROM AUTHOR]

The first empirical method for preparing a plutonium predominance-region diagram used horizontal lines to locate the boundaries of the regions of forbidden, unique, and ambiguous oxidation-state distributions. A second approach changes the procedure by using vertical lines to illustrate these regions. In both cases, the boundary lines are determined by the Pu oxidation number and the equilibrium fraction of one oxidation state. [ABSTRACT FROM AUTHOR]

Maxima in the fractions of the trivalent and hexavalent oxidation states of plutonium are inherent in the algebra of its disproportionation reactions. The maxima do not support overall disproportionation equations as satisfactory representations of aqueous plutonium. [ABSTRACT FROM AUTHOR]

The equilibrium constant for the first hydrolysis reaction of tetravalent plutonium is surrounded by uncertainty. A new method illustrates criteria by which the reliabilities of the numerical estimates can be judged. The new formulas are simple, the method is easy to apply, and the results are easy to compare. [ABSTRACT FROM AUTHOR]

The numerical value of the first hydrolysis constant of tetravalent plutonium is uncertain by a factor of about ten. This article illustrates the estimation of that constant by a least squares method applied to simultaneous equations involving all of the Pu oxidation states. [ABSTRACT FROM AUTHOR]

Four new formulas for estimating the first hydrolysis constant of tetravalent plutonium are illustrated. They can be applied with or without an independent estimate of the Pu oxidation number. [ABSTRACT FROM AUTHOR]