Chemical reaction rates escape time

Time base Crystal or atomic Oscillator Escapement, motor, tuning fork Pyrotechnic burning rate Oscillator Rate of chemical reaction... 

In terms of chemical reactivity, we can now ask how rapid an intracellnlar reaction must be in order to prevent this escape . To a first approximation, the half-life of such a reaction should be in the range of this escape time, and so we calculate the rate for a reaction with this half-life ... 

If the initial electrode product B undergoes a chemical reaction, the observed ring current, and therefore N, drops to a lower value. The fraction of the B molecules that escape detection at the ring depends on two factors, the rate of the chemical step and the time interval between the generation and detection of B, that is, on (o. Consequently, it can... 

In his seminal work (as it is frequently called), Kramers treated the escape over a potential barrier by a particle undergoing Brownian motion, i.e. thermal noise-assisted escape [1]. Hence, his focus was on the effect of the medium - solvent or bath gas - on the solute reaction rate. While much of the physical chemistry community was at the time focused on the rate of reaction of an isolated molecule -- and would remain so occupied for many years to come, Kramers work was not completed in a vacuum. Indeed, Lindemann, Rice and Ramsperger, Kassel, Slater, Christiansen, and others had already published their collision-rate-based theories of the role of the bath gas in promoting chemical reactions in low-density gases [3, 4]. Thus, one must ask,... 

Here, p is mass density and yk th mass fraction, t is time and div the divergence operator v is local mass flow velocity (vector) and jk the it-th molecular diffusion flux vector, added to the term pykV representing the convection of particles Ck by the motion of a material element as a whole. So the instantaneous local change (increase) of the Ck-concentration (mass per unit volume) equals minus the amount that escapes from a volume element (the divergence term) plus the amount produced by chemical reactions. Physically, the balance makes sense if we know how the flux jk depends on the gradients (most simply by Pick s law), and how the rates of possible reactions depend on the local state of the element. If also the latter information is available then the balance takes the form of convective diffusion equation, possibly with chemical reactions. [If we have no information on the reaction rates, the w -terms can be eliminated from Eqs. (C.2) by an algebraic transformation in the same manner as in Chapter 4 indeed, it is sufficient to substitute for W, in (4.3.2) and to define the components of column vector n as follows from (C.2).] Observe finally that we have... 

The condition in which the concentrations of all reactants and products in a closed system cease to change with time is called chemical equilibrium. Chemical equilibrium occurs when opposing reactions are proceeding at equal rates The rate at which the products are formed from the reactants equals the rate at which the reactants are formed from the products. Eor equilibrium to occur, neither reactants nor products can escape from the system. 

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