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Linear organic molecules, such as acetylene (HC≡CH), are often described by invoking sp orbital hybridization for their carbon centers. Two sp orbitals. According to the VSEPR model (Valence Shell Electron Pair Repulsion model), linear geometry occurs at central atoms with two bonded atoms and zero or three lone pairs (AX 2 or AX 2 E 3) in ...
The names for the degrees may be applied to the polynomial or to its terms. For example, the term 2x in x 2 + 2x + 1 is a linear term in a quadratic polynomial. The polynomial 0, which may be considered to have no terms at all, is called the zero polynomial. Unlike other constant polynomials, its degree is not zero.
Linear pathways follow a step-by-step sequence, where each enzymatic reaction results in the transformation of a substrate into an intermediate product. This intermediate is processed by subsequent enzymes until the final product is synthesized. A linear chain of four enzyme-catalyzed steps. A linear pathway can be studied in various ways.
The Taft equation is a linear free energy relationship (LFER) used in physical organic chemistry in the study of reaction mechanisms and in the development of quantitative structure–activity relationships for organic compounds. It was developed by Robert W. Taft in 1952 [2] [3] [4] as a modification to the Hammett equation. [5]
[18]: 1165 Examples of this include the octacyanomolybdate (Mo(CN) 4− 8) and octafluorozirconate (ZrF 4− 8) anions. [18]: 1165 The nonahydridorhenate ion (ReH 2− 9) in potassium nonahydridorhenate is a rare example of a compound with a steric number of 9, which has a tricapped trigonal prismatic geometry. [13]: 254 [18]
IUPAC has suggested that this name should be replaced by linear Gibbs energy relation, but at present there is little sign of acceptance of this change. [1] The area of physical organic chemistry which deals with such relations is commonly referred to as 'linear free-energy relationships'.
For example, a tungsten complex was shown to alkylate allyl carbonates A and B. The ratio of products A1 and B1 can be attributed to the para substituent, X (Fig. 3). Using Swain–Lupton parameters (σ = 0.2F + 0.8R) a ρ value of -2.5 was found to be the slope. Fig. 3a Allylic alkylation of carbonates. Fig. 3b Graph of Swain–Lupton parameters.
Conversely, every line is the set of all solutions of a linear equation. The phrase "linear equation" takes its origin in this correspondence between lines and equations: a linear equation in two variables is an equation whose solutions form a line. If b ≠ 0, the line is the graph of the function of x that has been defined in the preceding ...
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