Square brackets concentrations

Tphe equilibrium law (law of mass action) in its logarithmic form gives - simple linear relationships between the activities of the reactants (e.g., Equation 1). In the following text, the curled brackets represent activities, and the square brackets concentrations. 

Molar concentrations are used so frequently that a symbolic notation is often used to simplify its expression in equations and writing. The use of square brackets around a species indicates that we are referring to that species molar concentration. Thus, [Na ] is read as the molar concentration of sodium ions. ... 

The rate of a process is expressed by the derivative of a concentration (square brackets) with respect to time, d[ ]/dt. If the concentration of a reaction product is used, this quantity is positive if a reactant is used, it is negative and a minus sign must be included. Also, each derivative d[ ]/dt should be divided by the coefficient of that component in the chemical equation which describes the reaction so that a single rate is described, whichever component in the reaction is used to monitor it. A rate law describes the rate of a reaction as the product of a constant k, called the rate constant, and various concentrations, each raised to specific powers. The power of an individual concentration term in a rate law is called the order with respect to that component, and the sum of the exponents of all concentration terms gives the overall order of the reaction. Thus in the rate law Rate = k[X] [Y], the reaction is first order in X, second order in Y, and third order overall. 

Hereafter, we shall regularly use the square brackets notation, [ ], to indicate concentration. Thus, we read [Fe+I] as ferric ion concentration. ... 

Square brackets are commonly used for two purposes to denote concentrations and also to include the whole of a complex ion for the latter purpose curly brackets (braces) are sometimes used. With careful scrutiny there should be no confusion regarding the sense in which the square brackets are used with complexes there will be no charge signs inside the brackets. 

Concentrations are indicated by square brackets. Commonly, concentrations rather... 

Square brackets in kinetic equations signify the effective concentrations of the bracketed species, these being the equilibrium forms actually taking part in the rate-determining step. Parentheses are used for stoichiometric concentrations. Thus (ArNH2) is the total amount of an amine present in the system, even if it... 

A note on good practice In chemical kinetics, the square brackets denote molar concentration, with the units mol-L 1 retained. 

When dealing with the kinetic or thermodynamic behaviour of transition-metal systems, square brackets are used to denote concentrations of solution species. In the interests of simplicity, solvent molecules are frequently omitted (as are the square brackets around complex species). The reaction (1.1) is frequently written as equation (1.2). 

Square brackets around a molecular species indicate atmospheric concentration. The rate constants k times the reactant concentration product refers to the rates of the chemical reactions of the indicated number. The photolytic flux term /l4 refers to the photodissociation rate of N02 in Reaction R14, its value is proportional to solar intensity.]. RO2 stands for an organic peroxyl radical (R is an organic group) that is capable of oxidizing NO to NO2. Hydrocarbons oxidize to form a very large number of different RO2 species the simplest of the family is methylperoxyl radical involved in R5, R6 and R8. 

The square brackets refer to the concentration of the species inside. Note that the concentrations are multiplied or divided, not added or subtracted, and the concentrations of the products are in the numerator. The coefficients in the balanced chemical equation have become exponents in this mathematical equation. 

The proportionality constant k, called the rate constant, has a constant value for a given reaction at a given temperature. The terms in square brackets are concentration terms (compare Chap. 14), and x and y are exponents which are often integral. The exponent x is called the order with respect to A, and y is called the order with respect to B. The sum x +y is called the overall order of the reaction. The values for x and y can be 0, 1, 2, 3 or 0.5, 1.5, or 2.5, but never more than 3. These values must be determined by experiment, and do not necessarily equal the values of a and b in the chemical equation. 

Here the square brackets indicate the concentration of the chemical species within the bracket. That is, [A] means the concentration of A, and so forth. [A]" means the concentration of A raised to the a power, where a is the value of the coefficient of A in the balanced equation for the chemical equilibrium. The value of the ratio of concentration terms is symbolized by the letter K, called the equilibrium constant. For example, for the reaction of nitrogen and hydrogen referred to in Sec. 19.3,... 

Bq/m3) thoron progeny Working Level, WL(Tn) 0.15-14 WL. (The square brackets are used here to denote activity concentration.)... 

In this expression, the square brackets refer to the activity of the component although it is more convenient to use its concentration. This approximation is generally satisfactory, except at very high concentrations, and is particularly suitable for analytical use. Where it is necessary to distinguish between the constant obtained using concentrations and the true thermodynamic equilibrium constant Ka the former may be termed the equilibrium quotient and assigned the symbol Q. The exact relation between Ke and Q has been the subject of much investigation and speculation. In this... 

The first two expressions involving the reactants are negative, because their concentrations will decrease with time. The square brackets represent moles per liter concentration (molarity). 

The term in the square bracket is an effective diffusion coefficient DAB. In principle, this may be used together with a material balance to predict changes in concentration within a pellet. Algebraic solutions are more easily obtained when the effective diffusivity is constant. The conservation of counter-ions diffusing into a sphere may be expressed in terms of resin phase concentration Csr, which is a function of radius and time. 

In the equations describing enzyme kinetics in this chapter, the notation varies a bit from other chapters. Thus v is accepted in the biochemical literature as the symbol for reaction rate while Vmax is used for the maximum rate. Furthermore, for simplification frequently Vmax is truncated to V in complex formulas (see Equations 11.28 and 11.29). Although at first glance inconsistent, these symbols are familiar to students of biochemistry and related areas. The square brackets indicate concentrations. Vmax expresses the upper limit of the rate of the enzyme reaction. It is the product of the rate constant k3, also called the turnover number, and the total enzyme concentration, [E]o. The case u, = Vmax corresponds to complete saturation of all active sites. The other kinetic limit, = (Vmax/KM)[S], corresponds to Km >> [S], in other words Vmax/KM is the first order rate constant found when the substrate concentration approaches zero ... 

When a reaction occurs between gaseous species or in solution, chemists usually express the reaction rate as a change in the concentration of the reactant or product per unit time. Recall, from your previous chemistry course, that the concentration of a compound (in mol/L) is symbolized by placing square brackets, [ ], around the chemical formula. The equation below is the equation you will work with most often in this section. 

The square brackets indicate concentrations. The product is in the numerator, and each term is raised to the power of the coefficient in the chemical equation. The coefficient or power of 1 is not written, thus following chemistry conventions. 

We use capital K% to denote thermodynamic equilibrium constants, and we use square brackets to denote concentrations, say, in moles per unit volume. 

The square brackets indicate either concentration or, for oxygen, partial pressure. 

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