਀㰀琀椀琀氀攀㸀䄀甀琀漀戀椀漀最爀愀瀀栀礀         ⸀ 吀栀攀 一漀戀攀氀 倀爀椀稀攀 椀渀 䌀栀攀洀椀猀琀爀礀  ਀㰀䴀䔀吀䄀 栀琀琀瀀ⴀ攀焀甀椀瘀㴀䌀漀渀琀攀渀琀ⴀ匀琀礀氀攀ⴀ吀礀瀀攀 挀漀渀琀攀渀琀㴀琀攀砀琀⼀挀猀猀㸀㰀䰀䤀一䬀 栀爀攀昀㴀∀猀琀礀氀攀⸀挀猀猀∀ 琀礀瀀攀㴀琀攀砀琀⼀挀猀猀 爀攀氀㴀猀琀礀氀攀猀栀攀攀琀㸀㰀栀攀愀搀㸀㰀⼀栀攀愀搀㸀 ਀ ਀

਀吀栀攀 一漀戀攀氀 倀爀椀稀攀 椀渀 䌀栀攀洀椀猀琀爀礀  ㄀㤀㔀㘀 㰀⼀栀㈀㸀

਀ SIR CYRIL NORMAN HINSHELWOOD਀ 㰀椀洀最 愀氀椀最渀㴀爀椀最栀琀 戀漀爀搀攀爀㴀㈀ 猀爀挀㴀∀㄀⸀最椀昀∀㸀 ਀㰀䠀㄀㸀 Reaction Mechanism - elementary process਀㰀⼀栀㄀㸀

਀㰀椀洀最 猀爀挀㴀∀⸀⸀⼀昀椀最⼀爀攀愀挀琀椀漀渀⸀最椀昀∀ 眀椀搀琀栀㴀㄀　　 栀攀椀最栀琀㴀㜀㔀 愀氀椀最渀㴀∀爀椀最栀琀∀㸀 A mechanism for a reaction is a collection of elementary਀瀀爀漀挀攀猀猀攀猀 ⠀愀氀猀漀 挀愀氀氀攀搀 攀氀攀洀攀渀琀愀爀礀 猀琀攀瀀猀 漀爀 攀氀攀洀攀渀琀愀爀礀 爀攀愀挀琀椀漀渀猀⤀ that explains how the overall reaction proceeds.਀㰀倀㸀 A mechanism is a proposal from which you can work out a rate law਀琀栀愀琀 愀最爀攀攀猀 眀椀琀栀 琀栀攀 漀戀猀攀爀瘀攀搀 爀愀琀攀 氀愀眀猀⸀ 吀栀攀 昀愀挀琀 琀栀愀琀 愀 洀攀挀栀愀渀椀猀洀 explains the experimental results is not a proof that the mechanism is਀挀漀爀爀攀挀琀⸀ 䄀 洀攀挀栀愀渀椀猀洀 椀猀 漀甀爀 爀愀琀椀漀渀愀氀椀稀愀琀椀漀渀 漀昀 愀 挀栀攀洀椀挀愀氀 爀攀愀挀琀椀漀渀Ⰰ and devising mechanism is an excelent academic exercise.਀㰀倀㸀 The animation here shows an elementary step of two molecules coliding਀眀椀琀栀 攀愀挀栀 漀琀栀攀爀 愀渀搀 攀砀挀栀愀渀最攀 愀 栀礀搀爀漀最攀渀 愀琀漀洀 椀渀 琀栀攀 瀀爀漀挀攀猀猀⸀ Since elementary processes are the language of mechanism, let us first਀搀攀昀椀渀攀 攀氀攀洀攀渀琀愀爀礀 瀀爀漀挀攀猀猀攀猀 漀爀 猀琀攀瀀猀⸀

਀䔀氀攀洀攀渀琀愀爀礀 倀爀漀挀攀猀猀攀猀 漀爀 匀琀攀瀀猀

਀䄀渀 㰀䈀㸀攀氀攀洀攀渀琀愀爀礀 瀀爀漀挀攀猀猀㰀⼀䈀㸀 椀猀 愀氀猀漀 挀愀氀氀攀搀 㰀䈀㸀攀氀攀洀攀渀琀愀爀礀 猀琀攀瀀㰀⼀䈀㸀 漀爀 elementary reactions.਀䤀琀 攀砀瀀爀攀猀猀攀猀 栀漀眀 愀挀琀甀愀氀氀礀 洀漀氀攀挀甀氀攀猀 漀爀 椀漀渀猀 爀攀愀挀琀 眀椀琀栀 攀愀挀栀 漀琀栀攀爀⸀ The equation in an elementary step represents the reaction਀愀琀 琀栀攀 洀漀氀攀挀甀氀愀爀 氀攀瘀攀氀Ⰰ 渀漀琀 琀栀攀 漀瘀攀爀愀氀氀 爀攀愀挀琀椀漀渀⸀ Based on numbers of molecules involved in the elementary step, there are਀琀栀爀攀攀 欀椀渀搀猀 漀昀 攀氀攀洀攀渀琀愀爀礀 猀琀攀瀀猀㨀 甀渀椀洀漀氀攀挀甀氀愀爀 猀琀攀瀀 ⠀漀爀 瀀爀漀挀攀猀猀⤀Ⰰ bimolecular process, and trimolecular process.਀㰀倀㸀 An elementary step is proposed to give the reaction rate expression.਀吀栀攀 爀愀琀攀 漀昀 愀渀 攀氀攀洀攀渀琀愀爀礀 猀琀攀瀀 椀猀 愀氀眀愀礀猀 眀爀椀琀琀攀渀 愀挀挀漀爀搀椀渀最 琀漀 琀栀攀 proposed equation. This practice is very different from the derivation਀漀昀 爀愀琀攀 氀愀眀猀 昀漀爀 愀渀 漀瘀攀爀愀氀氀 爀攀愀挀琀椀漀渀⸀

਀圀栀攀渀 愀 洀漀氀攀挀甀氀攀 漀爀 椀漀渀 搀攀挀漀洀瀀漀猀攀猀 戀礀 椀琀猀攀氀昀Ⰰ 猀甀挀栀 愀渀 攀氀攀洀攀渀琀愀爀礀 猀琀攀瀀 椀猀 called a unimolecular step (or process).਀䄀 甀渀椀洀漀氀攀挀甀氀愀爀 猀琀攀瀀 椀猀 愀氀眀愀礀猀 愀 昀椀爀猀琀 漀爀搀攀爀 爀攀愀挀琀椀漀渀⸀ 吀栀攀 昀漀氀氀漀眀椀渀最 examples are given to illustrate this point:਀㰀倀㸀

਀伀㰀匀唀䈀㸀㌀㰀⼀匀唀䈀㸀 㴀 伀㰀匀唀䈀㸀㈀㰀⼀匀唀䈀㸀 ⬀ 伀Ⰰ   㰀䤀㸀刀愀琀攀㰀⼀䤀㸀 㴀 㰀䤀㸀欀㰀⼀䤀㸀 嬀伀㰀匀唀䈀㸀㌀㰀⼀匀唀䈀㸀崀 ਀漀爀 椀渀 最攀渀攀爀愀氀 ਀䄀 㴀 䈀 ⬀ 䌀 ⬀ 䐀Ⰰ 㰀䤀㸀刀愀琀攀㰀⼀䤀㸀 㴀 㰀䤀㸀欀㰀⼀䤀㸀 嬀䄀崀㰀戀爀㸀 A* = X + Y, Rate = k [A*]
਀㰀⼀搀椀爀㸀 A* represents an excited molecule.਀㰀倀㸀 ਀䄀 㰀䈀㸀戀椀洀漀氀攀挀甀氀愀爀 瀀爀漀挀攀猀猀 㰀⼀䈀㸀椀渀瘀漀氀瘀攀猀 琀眀漀 爀攀愀挀琀椀渀最 洀漀氀攀挀甀氀攀猀 漀爀 椀漀渀猀⸀ The rates for these steps are 2nd order, and some examples are given਀琀漀 椀氀氀甀猀琀爀愀琀攀 栀漀眀 礀漀甀 猀栀漀甀氀搀 最椀瘀攀 琀栀攀 爀愀琀攀 攀砀瀀爀攀猀猀椀漀渀⸀ The simulation illustrates a bimolecular process.਀㰀搀椀爀㸀 NO + O3 = NO2 +O2, Rate = k [NO] [O3]
਀   䌀氀 ⬀ 䌀䠀㰀匀唀䈀㸀㐀㰀⼀匀唀䈀㸀 㴀 䠀䌀氀 ⬀ 䌀䠀㰀匀唀䈀㸀㌀㰀⼀匀唀䈀㸀Ⰰ 㰀䤀㸀刀愀琀攀㰀⼀䤀㸀 㴀 㰀䤀㸀欀㰀⼀䤀㸀 嬀䌀氀崀 嬀䌀䠀㰀匀唀䈀㸀㐀㰀⼀匀唀䈀㸀崀㰀戀爀㸀 Ar + O3 = Ar + O3*, Rate = k [Ar] [O3]
਀   䄀 ⬀ 䄀 㴀 䈀 ⬀ 䌀Ⰰ        㰀䤀㸀刀愀琀攀㰀⼀䤀㸀 㴀 㰀䤀㸀欀㰀⼀䤀㸀 嬀䄀崀㰀匀唀倀㸀㈀㰀⼀匀唀倀㸀㰀戀爀㸀 A + B = X + Y, Rate = k [A] [B]
਀㰀⼀搀椀爀㸀 A trimolecular process involves the collision of three molecules.਀䘀漀爀 攀砀愀洀瀀氀攀㨀 ਀   伀 ⬀ 伀㰀匀唀䈀㸀㈀㰀⼀匀唀䈀㸀 ⬀ 一㰀匀唀䈀㸀㈀㰀⼀匀唀䈀㸀 㴀 伀㰀匀唀䈀㸀㌀㰀⼀匀唀䈀㸀 ⬀ 一㰀匀唀䈀㸀㈀㰀⼀匀唀䈀㸀Ⰰ 㰀䤀㸀刀愀琀攀㰀⼀䤀㸀 㴀 㰀䤀㸀欀㰀⼀䤀㸀 嬀伀崀 嬀伀㰀匀唀䈀㸀㈀㰀⼀匀唀䈀㸀崀 嬀一㰀匀唀䈀㸀㈀㰀⼀匀唀䈀㸀崀㰀戀爀㸀 O + NO + N2 = NO2 + N2, Rate = k [O] [NO] [N2]
਀㰀⼀搀椀爀㸀 The N2 molecules in the above trimolecular elementary steps are involved਀眀椀琀栀 攀渀攀爀最礀 琀爀愀渀猀昀攀爀⸀ 吀栀攀礀 挀愀渀 渀漀琀 戀攀 挀愀渀挀攀氀攀搀⸀ 吀栀攀礀 愀爀攀 眀爀椀琀琀攀渀 in the equation to give an expression for the Rates.਀䤀渀 最攀渀攀爀愀氀Ⰰ 琀爀椀洀漀氀攀挀甀氀愀爀 猀琀攀瀀猀 洀愀礀 戀攀Ⰰ ਀   䄀 ⬀ 䄀 ⬀ 䄀 㴀 瀀爀漀搀甀挀琀猀Ⰰ 㰀䤀㸀刀愀琀攀㰀⼀䤀㸀 㴀 㰀䤀㸀欀㰀⼀䤀㸀 嬀䄀崀㰀匀唀倀㸀㌀㰀⼀匀唀倀㸀㰀戀爀㸀 A + A + B = products, Rate = k [A]2 [B]
਀   䄀 ⬀ 䈀 ⬀ 䌀 㴀 瀀爀漀搀甀挀琀猀Ⰰ 㰀䤀㸀刀愀琀攀㰀⼀䤀㸀 㴀 㰀䤀㸀欀㰀⼀䤀㸀 嬀䄀崀 嬀䈀崀 嬀䌀崀㰀戀爀㸀 ਀吀栀爀攀攀 洀漀氀攀挀甀氀攀猀 挀漀氀氀椀搀攀 愀琀 愀渀 椀渀猀琀愀渀琀 椀猀 爀愀爀攀Ⰰ 戀甀琀 漀挀挀愀猀椀漀渀愀氀氀礀 琀栀攀猀攀 are some of the ways reactions take place.਀

਀䔀氀攀洀攀渀琀愀爀礀 瀀爀漀挀攀猀猀攀猀 愀爀攀 眀爀椀琀琀攀渀 琀漀 猀栀漀眀 栀漀眀 愀 挀栀攀洀椀挀愀氀 爀攀愀挀琀椀漀渀 progresses leading to an overall reaction. Such a collection਀椀猀 挀愀氀氀攀搀 愀 㰀䈀㸀爀攀愀挀琀椀漀渀 洀攀挀栀愀渀椀猀洀㰀⼀䈀㸀⸀ In a mechanism, elementary steps proceed at various speeds. The slowest਀猀琀攀瀀 椀猀 琀栀攀 爀愀琀攀ⴀ搀攀琀攀爀洀椀渀椀渀最 猀琀攀瀀⸀ 吀栀攀 漀爀搀攀爀 昀漀爀 琀栀愀琀 攀氀攀洀攀渀琀愀爀礀 瀀爀漀挀攀猀猀 is the order of a reaction, but the concentrations of reactants in that step਀洀甀猀琀 戀攀 攀砀瀀爀攀猀猀攀搀 椀渀 琀攀爀洀猀 漀昀 琀栀攀 挀漀渀挀攀渀琀爀愀琀椀漀渀猀 漀昀 琀栀攀 爀攀愀挀琀愀渀琀猀⸀

਀䐀攀爀椀瘀椀渀最 刀愀琀攀 䰀愀眀猀 䘀爀漀洀 刀攀愀挀琀椀漀渀 䴀攀挀栀愀渀椀猀洀猀

਀吀栀攀 昀漀氀氀漀眀椀渀最 攀砀愀洀瀀氀攀 椀氀氀甀猀琀爀愀琀攀猀 栀漀眀 攀氀攀洀攀渀琀愀爀礀 猀琀攀瀀猀 愀爀攀 甀猀攀搀 琀漀 represent a reaction mechanism. In particular, a slow step in a਀洀攀挀栀愀渀椀猀洀 搀攀琀攀爀洀椀渀攀猀 琀栀攀 爀愀琀攀 漀昀 愀 爀攀愀挀琀椀漀渀⸀

਀倀爀漀戀氀攀洀 ㄀

਀䤀昀 琀栀攀 爀攀愀挀琀椀漀渀 2 NO2 + F2 = 2 NO2F਀昀漀氀氀漀眀猀 琀栀攀 洀攀挀栀愀渀椀猀洀Ⰰ i. NO2 + F2 = NO2F + F (slow)
਀   椀椀⸀   一伀㰀匀唀䈀㸀㈀㰀⼀匀唀䈀㸀  ⬀  䘀   㴀  一伀㰀匀唀䈀㸀㈀㰀⼀匀唀䈀㸀䘀       ⠀昀愀猀琀⤀㰀戀爀㸀 ਀圀漀爀欀 漀甀琀 琀栀攀 爀愀琀攀 氀愀眀⸀

Solution
਀ Since step i is the rate-determining step, the rate law is਀㰀倀爀攀㸀 1 d[NO2]਀     ⴀ ⴀⴀⴀ ⴀⴀⴀⴀⴀⴀ  㴀  㰀䤀㸀欀㰀⼀䤀㸀 嬀一伀㰀匀唀䈀㸀㈀㰀⼀匀唀䈀㸀崀 嬀䘀㰀匀唀䈀㸀㈀㰀⼀匀唀䈀㸀崀 2 dt਀㰀⼀倀爀攀㸀 Addition of i. and ii. gives the overall reaction.਀㰀倀㸀㰀䈀㸀㰀䤀㸀䐀椀猀挀甀猀猀椀漀渀㨀㰀⼀䤀㸀㰀⼀䈀㸀㰀䈀刀㸀 This example illustrates that the overall reaction equation has ਀渀漀琀栀椀渀最 琀漀 搀漀 眀椀琀栀 琀栀攀 漀爀搀攀爀 漀昀 琀栀攀 爀攀愀挀琀椀漀渀⸀ 吀栀攀 攀氀攀洀攀渀琀愀爀礀 瀀爀漀挀攀猀猀 椀渀 the rate-determining step determines the order.਀㰀倀㸀 Other possible elementary steps in this reaction are:਀㰀䐀䤀刀㸀 F + F -> F2
਀䘀 ⬀ 䘀㰀匀唀䈀㸀㈀㰀⼀匀唀䈀㸀 ⴀ㸀 䘀㰀匀唀䈀㸀㈀㰀⼀匀唀䈀㸀 ⬀ 䘀㰀䈀刀㸀 NO2F + F -> F + NO2F
਀㰀⼀䐀䤀刀㸀 but they do not lead to the formation of products.਀㰀⼀䐀䤀刀㸀

਀吀漀 瀀爀漀瀀漀猀攀 愀 洀攀挀栀愀渀椀猀洀 爀攀焀甀椀爀攀猀 琀栀攀 欀渀漀眀氀攀搀最攀 漀昀 挀栀攀洀椀猀琀爀礀 琀漀 最椀瘀攀 plausible elementary processes. A freshman in chemistry will not be਀愀猀欀攀搀 琀漀 瀀爀漀瀀漀猀攀 洀攀挀栀愀渀椀猀洀猀Ⰰ 戀甀琀 礀漀甀 眀椀氀氀 戀攀 愀猀欀攀搀 琀漀 最椀瘀攀 琀栀攀 爀愀琀攀 laws from a given mechanism.਀㰀䠀㌀㸀 Summary਀㰀⼀䠀㌀㸀 The number of particle involved in an elementary step is called the਀㰀䈀㸀洀漀氀攀挀甀氀愀爀椀琀礀㰀⼀䈀㸀Ⰰ 愀渀搀 椀渀 最攀渀攀爀愀氀Ⰰ 眀攀 挀漀渀猀椀搀攀爀 漀渀氀礀 琀栀攀 洀漀氀攀挀甀氀愀爀椀琀礀 漀昀 1, 2, and 3. Types of elementary steps are summarized below.਀䤀渀 琀栀攀 琀愀戀氀攀Ⰰ 䄀Ⰰ 䈀Ⰰ 愀渀搀 䌀 爀攀瀀爀攀猀攀渀琀 爀攀愀挀琀愀渀琀猀Ⰰ 椀渀琀攀爀洀攀搀椀愀琀攀猀Ⰰ 漀爀 products in the elementary process. ਀㰀倀㸀 ਀㰀吀刀㸀㰀吀䠀㸀䴀漀氀攀挀甀氀愀爀椀琀礀 㰀吀䠀㸀䔀氀攀洀攀渀琀愀爀礀 猀琀攀瀀 㰀吀䠀㸀刀愀琀攀 氀愀眀
1 A -> products rate = k [A]਀㰀吀刀㸀㰀吀䠀㸀㈀ 㰀吀䐀㸀䄀 ⬀ 䄀 ⴀ㸀 瀀爀漀搀甀挀琀猀㰀䈀刀㸀 䄀 ⬀ 䈀 ⴀ㸀 瀀爀漀搀甀挀琀猀 rate = k [A]2
rate = k [A] [B]਀㰀吀刀㸀㰀吀䠀㸀㌀ 㰀吀䐀㸀䄀 ⬀ 䄀 ⬀ 䄀 ⴀ㸀 瀀爀漀搀甀挀琀猀㰀䈀刀㸀 䄀 ⬀ ㈀ 䈀 ⴀ㸀 瀀爀漀搀甀挀琀猀㰀䈀刀㸀䄀 ⬀ 䈀 ⬀ 䌀 ⴀ㸀 瀀爀漀搀甀挀琀猀 		rate = k [A]3
rate = k [A] [B]2
਀㰀䤀㸀爀愀琀攀 㴀 欀㰀⼀䤀㸀 嬀䄀崀 嬀䈀崀 嬀䌀崀
਀ ਀匀椀爀 䌀礀爀椀氀 一漀爀洀愀渀 䠀椀渀猀栀攀氀眀漀漀搀 眀愀猀 戀漀爀渀 椀渀 䰀漀渀搀漀渀 漀渀 䨀甀渀攀 ㄀㤀Ⰰ ㄀㠀㤀㜀⸀ 䠀攀 眀愀猀 攀搀甀挀愀琀攀搀 愀琀 圀攀猀琀洀椀渀猀琀攀爀 䌀椀琀礀 匀挀栀漀漀氀 愀渀搀 伀砀昀漀爀搀 唀渀椀瘀攀爀猀椀琀礀 眀栀攀爀攀 栀攀 最愀椀渀攀搀 䴀愀猀琀攀爀 漀昀 䄀爀琀猀 愀渀搀 䐀漀挀琀漀爀 漀昀 匀挀椀攀渀挀攀 搀攀最爀攀攀猀⸀ 䠀攀 栀攀氀搀 猀甀挀挀攀猀猀椀瘀攀 昀攀氀氀漀眀猀栀椀瀀猀 愀琀 䈀愀氀氀椀漀氀Ⰰ 吀爀椀渀椀琀礀Ⰰ 愀渀搀 䔀砀攀琀攀爀 䌀漀氀氀攀最攀猀㬀 栀攀 眀愀猀 琀甀琀漀爀 漀昀 吀爀椀渀椀琀礀 䌀漀氀氀攀最攀 昀爀漀洀 ㄀㤀㈀㄀ 琀漀 ㄀㤀㌀㜀 愀渀搀 猀椀渀挀攀 ㄀㤀㌀㜀 栀攀 栀愀猀 戀攀攀渀 䐀爀⸀ 䰀攀攀✀猀 倀爀漀昀攀猀猀漀爀 漀昀 䌀栀攀洀椀猀琀爀礀Ⰰ 唀渀椀瘀攀爀猀椀琀礀 漀昀 伀砀昀漀爀搀⸀ 䠀攀 椀猀 愀 搀攀氀攀最愀琀攀 漀昀 琀栀攀 䌀氀愀爀攀渀搀漀渀 倀爀攀猀猀 愀渀搀 栀攀 栀愀猀 猀攀爀瘀攀搀 愀猀 愀 洀攀洀戀攀爀 漀昀 猀攀瘀攀爀愀氀 䄀搀瘀椀猀漀爀礀 䌀漀甀渀挀椀氀猀 漀渀 猀挀椀攀渀琀椀昀椀挀 洀愀琀琀攀爀猀 琀漀 琀栀攀 䈀爀椀琀椀猀栀 䜀漀瘀攀爀渀洀攀渀琀⸀ 䠀攀 眀愀猀 攀氀攀挀琀攀搀 䘀攀氀氀漀眀 漀昀 琀栀攀 刀漀礀愀氀 匀漀挀椀攀琀礀 椀渀 ㄀㤀㈀㤀Ⰰ 猀攀爀瘀椀渀最 愀猀 䘀漀爀攀椀最渀 匀攀挀爀攀琀愀爀礀 昀爀漀洀 ㄀㤀㔀　 琀漀 ㄀㤀㔀㔀Ⰰ 愀渀搀 愀猀 倀爀攀猀椀搀攀渀琀 昀爀漀洀 ㄀㤀㔀㔀 琀漀 ㄀㤀㘀　⸀ 䠀攀 眀愀猀 欀渀椀最栀琀攀搀 椀渀 ㄀㤀㐀㠀 愀渀搀 愀瀀瀀漀椀渀琀攀搀 琀漀 琀栀攀 伀爀搀攀爀 漀昀 䴀攀爀椀琀 椀渀 ㄀㤀㘀　⸀ ਀䠀椀猀 攀愀爀氀礀 猀琀甀搀椀攀猀 漀昀 洀漀氀攀挀甀氀愀爀 欀椀渀攀琀椀挀猀 氀攀搀 琀漀 琀栀攀 瀀甀戀氀椀挀愀琀椀漀渀 漀昀 吀栀攀爀洀漀搀礀渀愀洀椀挀猀 昀漀爀 匀琀甀搀攀渀琀猀 漀昀 䌀栀攀洀椀猀琀爀礀 愀渀搀 吀栀攀 䬀椀渀攀琀椀挀猀 漀昀 䌀栀攀洀椀挀愀氀 䌀栀愀渀最攀 椀渀 ㄀㤀㈀㘀Ⰰ 琀栀攀 氀愀琀攀猀琀 ⠀昀漀甀爀琀栀⤀ 攀搀椀琀椀漀渀 漀昀 琀栀攀 氀愀琀琀攀爀 愀瀀瀀攀愀爀椀渀最 椀渀 ㄀㤀㐀　Ⰰ 愀渀搀 栀攀 猀甀戀猀攀焀甀攀渀琀氀礀 眀漀爀欀攀搀 漀渀 挀栀攀洀椀挀愀氀 挀栀愀渀最攀猀 椀渀 琀栀攀 戀愀挀琀攀爀椀愀氀 挀攀氀氀Ⰰ 瀀爀漀搀甀挀椀渀最 瀀栀礀猀椀挀漀挀栀攀洀椀挀愀氀 攀砀瀀氀愀渀愀琀椀漀渀猀 昀漀爀 琀栀攀 戀椀漀氀漀最椀挀愀氀 爀攀猀瀀漀渀猀攀猀 漀昀 戀愀挀琀攀爀椀愀 琀漀 挀栀愀渀最攀猀 椀渀 攀渀瘀椀爀漀渀洀攀渀琀⸀ 䠀椀猀 昀椀渀搀椀渀最猀 瀀爀漀瘀攀搀 琀漀 戀攀 漀昀 最爀攀愀琀 椀洀瀀漀爀琀愀渀挀攀 椀渀 氀愀琀攀爀 爀攀猀攀愀爀挀栀 眀漀爀欀 漀渀 愀渀琀椀戀椀漀琀椀挀猀 愀渀搀 琀栀攀爀愀瀀攀甀琀椀挀 愀最攀渀琀猀Ⰰ 愀渀搀 栀椀猀 戀漀漀欀 漀渀 琀栀攀 琀漀瀀椀挀 吀栀攀 䌀栀攀洀椀挀愀氀 䬀椀渀攀琀椀挀猀 漀昀 琀栀攀 䈀愀挀琀攀爀椀愀氀 䌀攀氀氀 眀愀猀 瀀甀戀氀椀猀栀攀搀 椀渀 ㄀㤀㐀㘀⸀ 䠀攀 栀愀猀 挀漀渀琀爀椀戀甀琀攀搀 愀 最爀攀愀琀 渀甀洀戀攀爀 漀昀 漀爀椀最椀渀愀氀 瀀愀瀀攀爀猀 愀渀搀 爀攀瘀椀攀眀猀 琀漀 樀漀甀爀渀愀氀猀 漀昀 氀攀愀爀渀攀搀 猀漀挀椀攀琀椀攀猀 愀渀搀 琀漀 漀琀栀攀爀 猀挀椀攀渀琀椀昀椀挀 瀀攀爀椀漀搀椀挀愀氀猀Ⰰ 愀渀搀 栀椀猀 氀愀琀攀猀琀 戀漀漀欀Ⰰ 吀栀攀 匀琀爀甀挀琀甀爀攀 漀昀 倀栀礀猀椀挀愀氀 䌀栀攀洀椀猀琀爀礀 愀瀀瀀攀愀爀攀搀 椀渀 ㄀㤀㔀㄀⸀ ਀匀椀爀 䌀礀爀椀氀 眀愀猀 倀爀攀猀椀搀攀渀琀 漀昀 琀栀攀 䌀栀攀洀椀挀愀氀 匀漀挀椀攀琀礀 昀爀漀洀 ㄀㤀㐀㘀 琀漀 ㄀㤀㐀㠀Ⰰ 愀渀搀 倀爀攀猀椀搀攀渀琀 漀昀 琀栀攀 䘀愀爀愀搀愀礀 匀漀挀椀攀琀礀 昀爀漀洀 ㄀㤀㘀㄀ 琀漀 ㄀㤀㘀㈀Ⰰ 愀渀搀 椀渀挀氀甀搀攀搀 愀洀漀渀最猀琀 琀栀攀 洀愀渀礀 愀眀愀爀搀猀 栀攀 栀愀猀 最愀椀渀攀搀 愀爀攀 䰀愀瘀漀椀猀椀攀爀 䴀攀搀愀氀Ⰰ 匀漀挀椀琀 䌀栀椀洀椀焀甀攀 搀攀 䘀爀愀渀挀攀Ⰰ ㄀㤀㌀㔀㬀 䐀愀瘀礀 䴀攀搀愀氀Ⰰ 刀漀礀愀氀 匀漀挀椀攀琀礀Ⰰ ㄀㤀㐀㌀㬀 刀漀礀愀氀 䴀攀搀愀氀Ⰰ ㄀㤀㐀㜀㬀 䰀漀渀最猀琀愀昀昀 䴀攀搀愀氀Ⰰ 䌀栀攀洀椀挀愀氀 匀漀挀椀攀琀礀Ⰰ ㄀㤀㐀㠀㬀 䜀甀氀搀戀攀爀最 䴀攀搀愀氀Ⰰ 伀猀氀漀 唀渀椀瘀攀爀猀椀琀礀Ⰰ ㄀㤀㔀㈀㬀 䘀愀爀愀搀愀礀 䴀攀搀愀氀Ⰰ ㄀㤀㔀㌀㬀 䄀瘀漀最愀搀爀漀 䴀攀搀愀氀Ⰰ 䄀挀挀愀搀攀洀椀愀 搀攀椀 䰀椀渀挀攀椀Ⰰ 刀漀洀攀Ⰰ ㄀㤀㔀㘀㬀 愀渀搀 䰀攀瘀攀爀栀甀氀洀攀 䴀攀搀愀氀Ⰰ 刀漀礀愀氀 匀漀挀椀攀琀礀Ⰰ ㄀㤀㘀　⸀ ਀䠀漀渀漀爀愀爀礀 搀攀最爀攀攀猀 挀漀渀昀攀爀爀攀搀 漀渀 匀椀爀 䌀礀爀椀氀 椀渀挀氀甀搀攀 䐀漀挀琀漀爀 漀昀 䌀椀瘀椀氀 䰀愀眀 ⠀伀砀昀漀爀搀⤀ 愀渀搀 琀栀攀 䐀漀挀琀漀爀 漀昀 匀挀椀攀渀挀攀 搀攀最爀攀攀猀 漀昀 䈀爀椀猀琀漀氀Ⰰ 䌀愀洀戀爀椀搀最攀Ⰰ 䐀甀戀氀椀渀Ⰰ 䠀甀氀氀Ⰰ 䰀攀攀搀猀Ⰰ 䰀漀渀搀漀渀Ⰰ 匀栀攀昀昀椀攀氀搀Ⰰ 圀愀氀攀猀Ⰰ 愀渀搀 伀琀琀愀眀愀 唀渀椀瘀攀爀猀椀琀椀攀猀⸀ 䠀攀 栀漀氀搀猀 栀漀渀漀爀愀爀礀 洀攀洀戀攀爀猀栀椀瀀猀 漀昀 琀栀攀 洀愀樀漀爀 猀挀椀攀渀琀椀昀椀挀 猀漀挀椀攀琀椀攀猀 漀昀 洀愀渀礀 挀漀甀渀琀爀椀攀猀⸀ ਀匀椀爀 䌀礀爀椀氀 椀猀 甀渀洀愀爀爀椀攀搀⸀ 䠀攀 椀猀 昀氀甀攀渀琀 椀渀 洀愀渀礀 氀愀渀最甀愀最攀猀 愀渀搀 栀椀猀 洀愀椀渀 栀漀戀戀椀攀猀 愀爀攀 瀀愀椀渀琀椀渀最Ⰰ 挀漀氀氀攀挀琀椀渀最 䌀栀椀渀攀猀攀 瀀漀琀琀攀爀礀Ⰰ 愀渀搀 昀漀爀攀椀最渀 氀椀琀攀爀愀琀甀爀攀 ਀ ਀ ਀ ਀ ਀ ਀ ਀ ਀ ਀ ਀ ਀ ਀ sponsors link òþíèíã àâòî
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