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Any non-linear differentiable function, (,), of two variables, and , can be expanded as + +. If we take the variance on both sides and use the formula [11] for the variance of a linear combination of variables (+) = + + (,), then we obtain | | + | | +, where is the standard deviation of the function , is the standard deviation of , is the standard deviation of and = is the ...
[1] The change in the extent of reaction is then defined as [2] [3] = where denotes the number of moles of the reactant or product and is the stoichiometric number [4] of the reactant or product. Although less common, we see from this expression that since the stoichiometric number can either be considered to be dimensionless or to have units ...
This approach was the first reported use of standard addition, and was introduced by a German mining chemist, Hans Hohn, in 1937. [3] In his polarography practical book, titled Chemische Analysen mit dem Polargraphen, Hohn referred this method as Eizhusatzes , which translates to "calibration addition" in English.
a A + d D → b B, a A + d D → c C. In this case, K eq can be defined as ratio of B to C rather than the equilibrium constant. When B / C > 1, B is the favored product, and the data on the Van 't Hoff plot will be in the positive region. When B / C < 1, C is the favored product, and the data on the Van 't Hoff plot will be in ...
D&H say that, due to the "mutual electrostatic forces between the ions", it is necessary to modify the Guldberg–Waage equation by replacing with , where is an overall activity coefficient, not a "special" activity coefficient (a separate activity coefficient associated with each species)—which is what is used in modern chemistry as of 2007.
The 3 × 3 symmetric matrix is called the effective reciprocal inertia tensor. If all q s were zero (rigid molecule) the Eckart frame would coincide with a principal axes frame (see rigid rotor ) and μ {\displaystyle {\boldsymbol {\mu }}} would be diagonal, with the equilibrium reciprocal moments of inertia on the diagonal.
The elements of an arithmetico-geometric sequence () are the products of the elements of an arithmetic progression (in blue) with initial value and common difference , = + (), with the corresponding elements of a geometric progression (in green) with initial value and common ratio , =, so that [4]
In theoretical chemistry, Marcus theory is a theory originally developed by Rudolph A. Marcus, starting in 1956, to explain the rates of electron transfer reactions – the rate at which an electron can move or jump from one chemical species (called the electron donor) to another (called the electron acceptor). [1]