STEM 隨筆︰鬼月談化學︰☲ 麗 《光明》‧史

中國傳統服飾-先秦天子冕服

中國結

玉珮

先秦天子冕服有許多象徵意義上衣、象以日夜,故為之青黑下裳,徵之富饒,用中透十二章紋述說一年,上下均分說著夏冬,其數實乃是周易的乾坤。古代上衣下裳的形制,因能方便耕作勞動,也就變成大眾傳統服飾了。

古之讀書人常有配戴玉珮』的習慣,這是因為──

禮記‧聘義

子貢問於孔子曰︰敢問君子貴玉賤媒者,何也?為與?孔子曰︰非為媒之多,故賤之也;玉之寡,故貴之也。夫昔者君子比德於玉焉,溫潤而澤、也,縝密以栗、也,廉而不劌、也,垂之如隊、也,叩之其聲清越以長其終詘然 、也,瑕不掩瑜、瑜不掩瑕、也,孚尹旁達、也,氣如白虹、也,精神見於山川、也,圭璋特達、也。天下莫不貴者、道也云︰言念君子.溫其如玉,故君子貴之也──。

……

周易經傳在數千年的歷史中,不知被『結構』和『解構』過多少次 ,這是為什麼呢?或許是川流不息生命之河,自有它亙古奧秘,也是永恆追求!!誰又能知有沒有『因明』的一天呢? ?如果『詮釋學』使山海經中『夸父追日』的精神,不再那麼飄渺迷茫,也許訴說著人類問著『為什麼』的童年;那中國歷史上最早的一部天文曆算著作《周髀算經》則是『好奇後』的老成,似乎已經揭示了日月星辰的運行規律、四季更替、氣候變化甚至包涵南北有極晝夜相推的道理。可是誰又能一直持有年少時那顆天真好奇之心呢?

假使一個人果能站在前人學問的基石上,又天真好奇孜孜不倦,那就會如孔子在《論語‧子罕》:

後生可畏焉知來者之不如今也。 四十、五十而無 ── ㄨㄣˊ陽關道 ──焉,斯亦不足畏也已。

,裡所說的一樣。甚至要能如下面所引的『一則故事』那樣

歐陽修,一向治學嚴謹,直至晚年,不減當初。他常將自己平生所寫的文章,清理出來進行修改,每字每句反覆推敲,甚是認真。為此,他整天辛苦勞累,有時直忙到深夜。夫人見他年歲已高,還如此盡心費神,恐其操勞過度,影響健康,十分擔心,目前制止。她關切地對丈夫說:『官人,何必如此用功,不惜貴體安康,為這些文字吃這樣多的苦頭,官人已年邁致仕(退休),難道還怕先生責難生氣嗎?』歐陽修回答說:『不怕先生生氣,只怕後生生譏』,『後生可畏耶!』

活到老學到老

── 英特乃者何耶?右尊讀之,是乃特英也,

特英者理念所鑄之祈立人願達人!! ──

─── 《後生可畏!?

 

『概念』實難憑空而生!『創見』偶在夢中出現?

當人們在『夢中』喃喃自語,人們真的說了些什麼嗎?若是講有人『記下』了『夢中』所憶︰

pi@raspberrypi ~ python3 Python 3.2.3 (default, Mar  1 2013, 11:53:50)  [GCC 4.6.3] on linux2 Type "help", "copyright", "credits" or "license" for more information. >>>  >>>  >>> from pyDatalog import pyDatalog >>> pyDatalog.create_terms('T萬物, 有力, 長生') >>> +有力('聖人', '能力') >>> +有力('大盜', '能力') >>> 長生(T萬物, '難死') <= 有力(T萬物, '能力') 長生(T萬物,'難死') <= 有力(T萬物,'能力') >>> print(長生(T萬物,'難死')) T萬物 --- 聖人  大盜  >>> print(有力(T萬物,'能力')) T萬物 --- 大盜  聖人  >>> >>> pyDatalog.create_terms('有死') >>> pyDatalog.create_terms('定律') >>> 定律(T萬物, '會死') <= 有死(T萬物, '人') 定律(T萬物,'會死') <= 有死(T萬物,'人') >>> +有死('聖人', '人') >>> +有死('大盜', '人') >>> print(有死(T萬物,'人')) T萬物 --- 聖人  大盜  >>> print(定律(T萬物,'會死')) T萬物 --- 大盜  聖人  >>> >>> print((有死(T萬物, '人')) & ~(定律(T萬物, '會死')))  [] >>> >>> print((T萬物 == '聖人') & ~(定律(T萬物, '會死'))) [] >>> print((T萬物 == '大盜') & ~(定律(T萬物, '會死'))) [] >>> print((定律('聖人', '會死')) & ~(定律('大盜', '會死')))  [] >>></pre>    <span style="color: #008080;">那麼是否應該『設想』他可能『證明』了『聖人不死,大盜不止』的呢?然後在考察『邏輯』之後,『認同』他真的……的耶??</span>  <span style="color: #008080;">也許與『清醒』的人談論『真、假』以及『是、非』都未必可信,那又將怎麽說那『夢中』之事?真的有誰知此『夢』會不會是一個『夢中之夢』!還不曉那人哪時方將『醒來』的哩!!雖說你不能『證明』上帝『存在』,那你能說祂『不存在』的嗎?反之你不能『證明』上帝『不存在』,那你就能說祂『存在』的耶??此所以</span><span style="color: #ff9900;">《<a href="http://cls.hs.yzu.edu.tw/hlm/read/text/text.asp">紅樓夢</a>》講︰世間事終難定。</span><span style="color: #008080;">因為『<a style="color: #008080;" href="http://www.freesandal.org/?p=1969">時間矛盾</a>』早已經在那裡了 ,這又與『知或不知』有什麼關係的呢?於是『邏輯』與『宇宙』的關係到底是什麼??!!也許真正困惑的是『人世間』正在追求之『價值』的方向的吧!!??</span>  <span style="color: #008080;">有的人以疏落的觀點看待『語言』,認為『凡是可以詮釋的現象,都是大自然之言說』。如是一沙一石皆有所說,更別講鳥語花香,以至於『動物語言』的哩!這樣的人是否更容易了解『程式語言』的呢?也有人以嚴格之想法處理『語言』,認為『只有人類的語言才能稱得上言語』。因此海豚雖可溝通,卻不會講話,動物吼叫聲除了警示意謂,了無它意,若說到花草的榮枯根本毫無意義的勒!這樣的人是否更容易了解『程式語言』的嗎?那麼什麼是『語言』的呢?什麼又是『程式語言』的哩?假使給個『定義』是否就能將之釐定清楚,大家都講同家話的耶!考之於歷史,此事希望渺茫,難保不正因這種『多樣性』開拓了視野,加深了認識的嗎??也許還是多些『兩極對話』的好!!</span>  <span style="color: #808080;">─── 摘自《<a style="color: #808080;" href="http://www.freesandal.org/?p=37117">勇闖新世界︰ 《 PYDATALOG 》 導引《五》</a>》</span>     <span style="color: #666699;">所以孔子喜夢周公乎??一代大哲<a style="color: #666699;" href="http://www.freesandal.org/?p=37117">熊十力</a>斷言</span>  <span style="color: #ff99cc;">真積力,久則入。</span>  <span style="color: #666699;">也!!</span>  <span style="color: #666699;">如斯者,</span>  <span style="color: #666699;">可以讀『史』︰</span> <h1 id="firstHeading" class="firstHeading" lang="en"><span style="color: #008080;"><a style="color: #008080;" href="https://en.wikipedia.org/wiki/Law_of_mass_action">Law of mass action</a></span></h1> <span style="color: #008080;">In chemistry, the <b>law of mass action</b> is the proposition that the <a style="color: #008080;" title="Reaction rate" href="https://en.wikipedia.org/wiki/Reaction_rate">rate</a> of a <a style="color: #008080;" title="Chemical reaction" href="https://en.wikipedia.org/wiki/Chemical_reaction">chemical reaction</a> is directly proportional to the product of the <a class="mw-redirect" style="color: #008080;" title="Activity (chemistry)" href="https://en.wikipedia.org/wiki/Activity_(chemistry)">activities</a> or <a style="color: #008080;" title="Concentration" href="https://en.wikipedia.org/wiki/Concentration">concentrations</a> of the <a style="color: #008080;" title="Reagent" href="https://en.wikipedia.org/wiki/Reagent">reactants</a>.<sup id="cite_ref-ÉrdiTóth1989_1-0" class="reference"><a style="color: #008080;" href="https://en.wikipedia.org/wiki/Law_of_mass_action#cite_note-ÉrdiTóth1989-1">[1]</a></sup> It explains and predicts behaviors of <a class="mw-redirect" style="color: #008080;" title="Solutions" href="https://en.wikipedia.org/wiki/Solutions">solutions</a> in <a style="color: #008080;" title="Dynamic equilibrium" href="https://en.wikipedia.org/wiki/Dynamic_equilibrium">dynamic equilibrium</a>. Specifically, it implies that for a chemical reaction mixture that is in equilibrium, the ratio between the concentration of reactants and <a style="color: #008080;" title="Product (chemistry)" href="https://en.wikipedia.org/wiki/Product_(chemistry)">products</a> is constant.<sup id="cite_ref-uwaterloo_cact_2-0" class="reference"><a style="color: #008080;" href="https://en.wikipedia.org/wiki/Law_of_mass_action#cite_note-uwaterloo_cact-2">[2]</a></sup></span>  <span style="color: #008080;">Two aspects are involved in the initial formulation of the law: 1) the equilibrium aspect, concerning the composition of a <a style="color: #008080;" title="Chemical reaction" href="https://en.wikipedia.org/wiki/Chemical_reaction">reaction</a> mixture at <a style="color: #008080;" title="Chemical equilibrium" href="https://en.wikipedia.org/wiki/Chemical_equilibrium">equilibrium</a> and 2) the <a style="color: #008080;" title="Chemical kinetics" href="https://en.wikipedia.org/wiki/Chemical_kinetics">kinetic</a> aspect concerning the <a style="color: #008080;" title="Rate equation" href="https://en.wikipedia.org/wiki/Rate_equation">rate equations</a> for <a style="color: #008080;" title="Elementary reaction" href="https://en.wikipedia.org/wiki/Elementary_reaction">elementary reactions</a>. Both aspects stem from the research performed by <a style="color: #008080;" title="Cato Maximilian Guldberg" href="https://en.wikipedia.org/wiki/Cato_Maximilian_Guldberg">Cato M. Guldberg</a> and <a style="color: #008080;" title="Peter Waage" href="https://en.wikipedia.org/wiki/Peter_Waage">Peter Waage</a> between 1864 and 1879 in which equilibrium constants were derived by using kinetic data and the rate equation which they had proposed. Guldberg and Waage also recognized that chemical equilibrium is a dynamic process in which <a style="color: #008080;" title="Reaction rate" href="https://en.wikipedia.org/wiki/Reaction_rate">rates of reaction</a> for the forward and backward reactions must be equal at <a style="color: #008080;" title="Chemical equilibrium" href="https://en.wikipedia.org/wiki/Chemical_equilibrium">chemical equilibrium</a>. In order to derive the expression of the equilibrium constant appealing to kinetics, the expression of the rate equation must be used. The expression of the rate equations was rediscovered later independently by <a style="color: #008080;" title="Jacobus Henricus van 't Hoff" href="https://en.wikipedia.org/wiki/Jacobus_Henricus_van_%27t_Hoff">Jacobus Henricus van 't Hoff</a>.</span>  <span style="color: #008080;">The law is a statement about equilibrium and gives an expression for the <a style="color: #008080;" title="Equilibrium constant" href="https://en.wikipedia.org/wiki/Equilibrium_constant">equilibrium constant</a>, a quantity characterizing <a style="color: #008080;" title="Chemical equilibrium" href="https://en.wikipedia.org/wiki/Chemical_equilibrium">chemical equilibrium</a>. In modern chemistry this is derived using <a style="color: #008080;" title="Equilibrium thermodynamics" href="https://en.wikipedia.org/wiki/Equilibrium_thermodynamics">equilibrium thermodynamics</a>.</span> <h2><span id="History" class="mw-headline" style="color: #339966;">History</span></h2> <span style="color: #339966;">Two chemists generally expressed the composition of a mixture in terms of numerical values relating the amount of the product to describe the equilibrium state. <a style="color: #339966;" title="Cato Maximilian Guldberg" href="https://en.wikipedia.org/wiki/Cato_Maximilian_Guldberg">Cato Maximilian Guldberg</a> and <a style="color: #339966;" title="Peter Waage" href="https://en.wikipedia.org/wiki/Peter_Waage">Peter Waage</a>, building on <a class="mw-redirect" style="color: #339966;" title="Berthollet" href="https://en.wikipedia.org/wiki/Berthollet">Claude Louis Berthollet</a>'s ideas<sup id="cite_ref-3" class="reference"><a style="color: #339966;" href="https://en.wikipedia.org/wiki/Law_of_mass_action#cite_note-3">[3]</a></sup><sup id="cite_ref-Levere_4-0" class="reference"><a style="color: #339966;" href="https://en.wikipedia.org/wiki/Law_of_mass_action#cite_note-Levere-4">[4]</a></sup> about<a style="color: #339966;" title="Chemical equilibrium" href="https://en.wikipedia.org/wiki/Chemical_equilibrium">reversible chemical reactions</a>, proposed the law of mass action in 1864.<sup id="cite_ref-GW1_5-0" class="reference"><a style="color: #339966;" href="https://en.wikipedia.org/wiki/Law_of_mass_action#cite_note-GW1-5">[5]</a></sup><sup id="cite_ref-GW2_6-0" class="reference"><a style="color: #339966;" href="https://en.wikipedia.org/wiki/Law_of_mass_action#cite_note-GW2-6">[6]</a></sup><sup id="cite_ref-GW3_7-0" class="reference"><a style="color: #339966;" href="https://en.wikipedia.org/wiki/Law_of_mass_action#cite_note-GW3-7">[7]</a></sup> These papers, in Danish, went largely unnoticed, as did the later publication (in French) of 1867 which contained a modified law and the experimental data on which that law was based.<sup id="cite_ref-8" class="reference"><a style="color: #339966;" href="https://en.wikipedia.org/wiki/Law_of_mass_action#cite_note-8">[8]</a></sup><sup id="cite_ref-GW4_9-0" class="reference"><a style="color: #339966;" href="https://en.wikipedia.org/wiki/Law_of_mass_action#cite_note-GW4-9">[9]</a></sup></span>  <span style="color: #339966;">In 1877 <a style="color: #339966;" title="Jacobus Henricus van 't Hoff" href="https://en.wikipedia.org/wiki/Jacobus_Henricus_van_%27t_Hoff">van 't Hoff</a> independently came to similar conclusions,<sup id="cite_ref-10" class="reference"><a style="color: #339966;" href="https://en.wikipedia.org/wiki/Law_of_mass_action#cite_note-10">[10]</a></sup> but was unaware of the earlier work, which prompted Guldberg and Waage to give a fuller and further developed account of their work, in German, in 1879.<sup id="cite_ref-GW5_11-0" class="reference"><a style="color: #339966;" href="https://en.wikipedia.org/wiki/Law_of_mass_action#cite_note-GW5-11">[11]</a></sup> Van 't Hoff then accepted their priority.</span> <h3><span id="1864" class="mw-headline" style="color: #339966;">1864</span></h3> <h4><span style="color: #339966;"><span id="The_equilibrium_state_.28composition.29"></span><span id="The_equilibrium_state_(composition)" class="mw-headline">The equilibrium state (composition)</span></span></h4> <span style="color: #339966;">In their first paper,<sup id="cite_ref-GW1_5-1" class="reference"><a style="color: #339966;" href="https://en.wikipedia.org/wiki/Law_of_mass_action#cite_note-GW1-5">[5]</a></sup> Guldberg and Waage suggested that in a reaction such as</span> <dl>  	<dd><span class="mwe-math-element" style="color: #339966;"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y">\displaystyle {\ce {{A}+ B <=> {A'}+ B'}}</span></span></dd> </dl> <span style="color: #339966;">the "chemical affinity" or "reaction force" between A and B did not just depend on the chemical nature of the reactants, as had previously been supposed, but also depended on the amount of each reactant in a reaction mixture. Thus the Law of Mass Action was first stated as follows:</span> <dl>  	<dd><span style="color: #339966;">When two reactants, A and B, react together at a given temperature in a "substitution reaction," the affinity, or chemical force between them, is proportional to the active masses, [A] and [B], each raised to a particular power</span> <dl>  	<dd><span style="color: #339966;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y">\displaystyle {\text{affinity}}=\alpha [{{\ce {A}}}]^{a}[{{\ce {B}}}]^{b} </span></span>.</span></dd> </dl> </dd> </dl> <span style="color: #339966;">In this context a substitution reaction was one such as\displaystyle {\ce {{alcohol}+ acid <=> {ester}+ water}} . Active mass was defined in the 1879 paper as "the amount of substance in the sphere of action".<sup id="cite_ref-12" class="reference"><a style="color: #339966;" href="https://en.wikipedia.org/wiki/Law_of_mass_action#cite_note-12">[12]</a></sup> For species in solution active mass is equal to concentration. For solids, active mass is taken as a constant.\displaystyle \alpha , a and b were regarded as empirical constants, to be determined by experiment.</span>  <span style="color: #339966;">At <a style="color: #339966;" title="Chemical equilibrium" href="https://en.wikipedia.org/wiki/Chemical_equilibrium">equilibrium</a>, the chemical force driving the forward reaction must be equal to the chemical force driving the reverse reaction. Writing the initial active masses of A,B, A' and B' as p, q, p' and q' and the dissociated active mass at equilibrium as\displaystyle \xi  , this equality is represented by</span> <dl>  	<dd><span class="mwe-math-element" style="color: #339966;"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y">\displaystyle \alpha (p-\xi )^{a}(q-\xi )^{b}=\alpha '(p'+\xi )^{a'}(q'+\xi )^{b'}</span></span></dd> </dl> <span style="color: #339966;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y">\displaystyle \xi  </span></span>represents the amount of reagents A and B that has been converted into A' and B'. Calculations based on this equation are reported in the second paper.<sup id="cite_ref-GW2_6-1" class="reference"><a style="color: #339966;" href="https://en.wikipedia.org/wiki/Law_of_mass_action#cite_note-GW2-6">[6]</a></sup></span> <h4><span id="Dynamic_approach_to_the_equilibrium_state" class="mw-headline" style="color: #339966;">Dynamic approach to the equilibrium state</span></h4> <span style="color: #339966;">The third paper of 1864<sup id="cite_ref-GW3_7-1" class="reference"><a style="color: #339966;" href="https://en.wikipedia.org/wiki/Law_of_mass_action#cite_note-GW3-7">[7]</a></sup> was concerned with the kinetics of the same equilibrium system. Writing the dissociated active mass at some point in time as x, the rate of reaction was given as</span> <dl>  	<dd><span class="mwe-math-element" style="color: #339966;"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y">\displaystyle \left({\frac {dx}{dt}}\right)_{forward}=k(p-x)^{a}(q-x)^{b}</span></span></dd> </dl> <span style="color: #339966;">Likewise the reverse reaction of A' with B' proceeded at a rate given by</span> <dl>  	<dd><span class="mwe-math-element" style="color: #339966;"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y">\displaystyle \left({\frac {dx}{dt}}\right)_{reverse}=k'(p'+x)^{a'}(q'+x)^{b'}</span></span></dd> </dl> <span style="color: #339966;">The overall rate of conversion is the difference between these rates, so at equilibrium (when the composition stops changing) the two rates of reaction must be equal. Hence</span> <dl>  	<dd><span style="color: #339966;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y">\displaystyle (p-x)^{a}(q-x)^{b}={\frac {k'}{k}}(p'+x)^{a'}(q'+x)^{b'} </span></span>...</span></dd> </dl> <h3><span id="1867" class="mw-headline" style="color: #339966;">1867</span></h3> <span style="color: #339966;">The rate expressions given in the 1864 paper could not be differentiated, so they were simplified as follows.<sup id="cite_ref-GW4_9-1" class="reference"><a style="color: #339966;" href="https://en.wikipedia.org/wiki/Law_of_mass_action#cite_note-GW4-9">[9]</a></sup> The chemical force was assumed to be directly proportional to the product of the active masses of the reactants.</span> <dl>  	<dd><span class="mwe-math-element" style="color: #339966;"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y">\displaystyle {\mbox{affinity}}=\alpha [A][B]</span></span></dd> </dl> <span style="color: #339966;">This is equivalent to setting the exponents a and b of the earlier theory to one. The proportionality constant was called an affinity constant, k. The equilibrium condition for an "ideal" reaction was thus given the simplified form</span> <dl>  	<dd><span class="mwe-math-element" style="color: #339966;"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y">\displaystyle k[A]_{\text{eq}}[B]_{\text{eq}}=k'[A']_{\text{eq}}[B']_{\text{eq}}</span></span></dd> </dl> <span style="color: #339966;">[A]<sub>eq</sub>, [B]<sub>eq</sub> etc. are the active masses at equilibrium. In terms of the initial amounts reagents p,q etc. this becomes</span> <dl>  	<dd><span class="mwe-math-element" style="color: #339966;"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y">\displaystyle (p-\xi )(q-\xi )={\frac {k'}{k}}(p'+\xi )(q'+\xi )</span></span></dd> </dl> <span style="color: #339966;">The ratio of the affinity coefficients, k'/k, can be recognized as an equilibrium constant. Turning to the kinetic aspect, it was suggested that the velocity of reaction, v, is proportional to the sum of chemical affinities (forces). In its simplest form this results in the expression</span> <dl>  	<dd><span class="mwe-math-element" style="color: #339966;"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y">\displaystyle v=\psi (k(p-x)(q-x)-k'(p'+x)(q'+x))</span></span></dd> </dl> <span style="color: #339966;">where\displaystyle \psi  is the proportionality constant. Actually, Guldberg and Waage used a more complicated expression which allowed for interaction between A and A', etc. By making certain simplifying approximations to those more complicated expressions, the rate equation could be integrated and hence the equilibrium quantity\displaystyle \xi  could be calculated. The extensive calculations in the 1867 paper gave support to the simplified concept, namely,</span> <dl>  	<dd><span style="color: #339966;">The rate of a reaction is proportional to the product of the active masses of the reagents involved.</span></dd> </dl> <span style="color: #339966;">This is an alternative statement of the Law of Mass Action.</span> <h3><span id="1879" class="mw-headline" style="color: #339966;">1879</span></h3> <span style="color: #339966;">In the 1879 paper<sup id="cite_ref-GW5_11-1" class="reference"><a style="color: #339966;" href="https://en.wikipedia.org/wiki/Law_of_mass_action#cite_note-GW5-11">[11]</a></sup> the assumption that reaction rate was proportional to the product of concentrations was justified microscopically in terms of <a style="color: #339966;" title="Collision theory" href="https://en.wikipedia.org/wiki/Collision_theory">collision theory</a>, as had been developed for gas reactions. It was also proposed that the original theory of the equilibrium condition could be generalised to apply to any arbitrary chemical equilibrium.</span> <dl>  	<dd><span class="mwe-math-element" style="color: #339966;"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y">\displaystyle {\text{affinity}}=k[{{\ce {A}}}]^{\alpha }[{{\ce {B}}}]^{\beta }\dots</span></span></dd> </dl> <span style="color: #339966;">The exponents α, β etc. are explicitly identified for the first time as the <a style="color: #339966;" title="Stoichiometry" href="https://en.wikipedia.org/wiki/Stoichiometry">stoichiometric coefficients</a> for the reaction.</span> <h2><span id="Modern_statement_of_the_law" class="mw-headline" style="color: #339966;">Modern statement of the law</span></h2> <span style="color: #339966;">The affinity constants, k<sub>+</sub> and k<sub>−</sub>, of the 1879 paper can now be recognised as <a class="mw-redirect" style="color: #339966;" title="Rate constant" href="https://en.wikipedia.org/wiki/Rate_constant">rate constants</a>. The equilibrium constant, K, was derived by setting the rates of forward and backward reactions to be equal. This also meant that the chemical affinities for the forward and backward reactions are equal. The resultant expression</span> <dl>  	<dd><span class="mwe-math-element" style="color: #339966;"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y">\displaystyle K={\frac {[S]^{\sigma }[T]^{\tau }\dots }{[A]^{\alpha }[B]^{\beta }\dots }}</span></span></dd> </dl> <span style="color: #339966;">is correct<sup id="cite_ref-uwaterloo_cact_2-1" class="reference"><a style="color: #339966;" href="https://en.wikipedia.org/wiki/Law_of_mass_action#cite_note-uwaterloo_cact-2">[2]</a></sup> even from the modern perspective, apart from the use of concentrations instead of activities (the concept of chemical activity was developed by <a style="color: #339966;" title="Josiah Willard Gibbs" href="https://en.wikipedia.org/wiki/Josiah_Willard_Gibbs">Josiah Willard Gibbs</a>, in the 1870s, but was not <a style="color: #339966;" title="Josiah Willard Gibbs" href="https://en.wikipedia.org/wiki/Josiah_Willard_Gibbs#Scientific_recognition">widely known</a> in Europe until the 1890s). The derivation from the reaction rate expressions is no longer considered to be valid. Nevertheless, Guldberg and Waage were on the right track when they suggested that the driving force for both forward and backward reactions is equal when the mixture is at equilibrium. The term they used for this force was chemical affinity. Today the expression for the equilibrium constant is derived by setting the <a style="color: #339966;" title="Chemical potential" href="https://en.wikipedia.org/wiki/Chemical_potential">chemical potential</a> of forward and backward reactions to be equal. The generalisation of the Law of Mass Action, in terms of affinity, to equilibria of arbitrary stoichiometry was a bold and correct conjecture.</span>  <span style="color: #339966;">The hypothesis that reaction rate is proportional to reactant concentrations is, strictly speaking, only true for <a style="color: #339966;" title="Elementary reaction" href="https://en.wikipedia.org/wiki/Elementary_reaction">elementary reactions</a> (reactions with a single mechanistic step), but the empirical rate expression</span> <dl>  	<dd><span class="mwe-math-element" style="color: #339966;"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y">\displaystyle r_{f}=k_{f}[A][B]</span></span></dd> </dl> <span style="color: #339966;">is also applicable to <a style="color: #339966;" title="Rate equation" href="https://en.wikipedia.org/wiki/Rate_equation">second order</a> reactions that may not be concerted reactions. Guldberg and Waage were fortunate in that reactions such as ester formation and hydrolysis, on which they originally based their theory, do indeed follow this rate expression.</span>  <span style="color: #339966;">In general many reactions occur with the formation of reactive intermediates, and/or through parallel reaction pathways. However, all reactions can be represented as a series of elementary reactions and, if the mechanism is known in detail, the rate equation for each individual step is given by the\displaystyle r_{f} expression so that the overall rate equation can be derived from the individual steps. When this is done the equilibrium constant is obtained correctly from the rate equations for forward and backward reaction rates.</span>  <span style="color: #339966;">In biochemistry, there has been significant interest in the appropriate mathematical model for chemical reactions occurring in the intracellular medium. This is in contrast to the initial work done on chemical kinetics, which was in simplified systems where reactants were in a relatively dilute, pH-buffered, aqueous solution. In more complex environments, where bound particles may be prevented from disassociation by their surroundings, or diffusion is slow or anomalous, the model of mass action does not always describe the behavior of the reaction kinetics accurately. Several attempts have been made to modify the mass action model, but consensus has yet to be reached. Popular modifications replace the rate constants with functions of time and concentration. As an alternative to these mathematical constructs, one school of thought is that the mass action model can be valid in intracellular environments under certain conditions, but with different rates than would be found in a dilute, simple environment<sup class="noprint Inline-Template Template-Fact">[<i><a style="color: #339966;" title="Wikipedia:Citation needed" href="https://en.wikipedia.org/wiki/Wikipedia:Citation_needed"><span title="This claim needs references to reliable sources. (July 2007)">citation needed</span></a></i>]</sup>.</span>  <span style="color: #339966;">The fact that Guldberg and Waage developed their concepts in steps from 1864 to 1867 and 1879 has resulted in much confusion in the literature as to which equation the Law of Mass Action refers. It has been a source of some textbook errors.<sup id="cite_ref-13" class="reference"><a style="color: #339966;" href="https://en.wikipedia.org/wiki/Law_of_mass_action#cite_note-13">[13]</a></sup> Thus, today the "law of mass action" sometimes refers to the (correct) equilibrium constant formula, <sup id="cite_ref-14" class="reference"><a style="color: #339966;" href="https://en.wikipedia.org/wiki/Law_of_mass_action#cite_note-14">[14]</a></sup> <sup id="cite_ref-15" class="reference"><a style="color: #339966;" href="https://en.wikipedia.org/wiki/Law_of_mass_action#cite_note-15">[15]</a></sup> <sup id="cite_ref-16" class="reference"><a style="color: #339966;" href="https://en.wikipedia.org/wiki/Law_of_mass_action#cite_note-16">[16]</a></sup> <sup id="cite_ref-17" class="reference"><a style="color: #339966;" href="https://en.wikipedia.org/wiki/Law_of_mass_action#cite_note-17">[17]</a></sup> <sup id="cite_ref-18" class="reference"><a style="color: #339966;" href="https://en.wikipedia.org/wiki/Law_of_mass_action#cite_note-18">[18]</a></sup> <sup id="cite_ref-19" class="reference"><a style="color: #339966;" href="https://en.wikipedia.org/wiki/Law_of_mass_action#cite_note-19">[19]</a></sup> <sup id="cite_ref-20" class="reference"><a style="color: #339966;" href="https://en.wikipedia.org/wiki/Law_of_mass_action#cite_note-20">[20]</a></sup> <sup id="cite_ref-21" class="reference"><a style="color: #339966;" href="https://en.wikipedia.org/wiki/Law_of_mass_action#cite_note-21">[21]</a></sup> <sup id="cite_ref-22" class="reference"><a style="color: #339966;" href="https://en.wikipedia.org/wiki/Law_of_mass_action#cite_note-22">[22]</a></sup> <sup id="cite_ref-23" class="reference"><a style="color: #339966;" href="https://en.wikipedia.org/wiki/Law_of_mass_action#cite_note-23">[23]</a></sup> and at other times to the (usually incorrect)\displaystyle r_{f} rate formula. <sup id="cite_ref-24" class="reference"><a style="color: #339966;" href="https://en.wikipedia.org/wiki/Law_of_mass_action#cite_note-24">[24]</a></sup> <sup id="cite_ref-25" class="reference"><a style="color: #339966;" href="https://en.wikipedia.org/wiki/Law_of_mass_action#cite_note-25">[25]</a></sup></span>     <span style="color: #666699;">可以觀『鹽』自得︰</span>  <span style="font-size: 18pt;"><strong><a style="color: #ff9900;" href="https://zh.wikipedia.org/zh-tw/%E6%BA%B6%E8%A7%A3%E5%B9%B3%E8%A1%A1">溶解平衡</a></strong></span>  <span style="color: #ff9900;"><b>溶解平衡</b>是一種關於<a style="color: #ff9900;" title="化合物" href="https://zh.wikipedia.org/wiki/%E5%8C%96%E5%90%88%E7%89%A9">化合物</a><a style="color: #ff9900;" title="溶解" href="https://zh.wikipedia.org/wiki/%E6%BA%B6%E8%A7%A3">溶解</a>的<a style="color: #ff9900;" title="化學平衡" href="https://zh.wikipedia.org/wiki/%E5%8C%96%E5%AD%A6%E5%B9%B3%E8%A1%A1">化學平衡</a>。溶解平衡能作用於化合物的應用,並且可以用於預測特定情況下化合物的<a style="color: #ff9900;" title="溶解性" href="https://zh.wikipedia.org/wiki/%E6%BA%B6%E8%A7%A3%E6%80%A7">溶解度</a>。</span>  <span style="color: #ff9900;">溶解的固體可以是<a class="mw-redirect" style="color: #ff9900;" title="共價化合物" href="https://zh.wikipedia.org/wiki/%E5%85%B1%E4%BB%B7%E5%8C%96%E5%90%88%E7%89%A9">共價化合物</a>(<a style="color: #ff9900;" title="有機化合物" href="https://zh.wikipedia.org/wiki/%E6%9C%89%E6%9C%BA%E5%8C%96%E5%90%88%E7%89%A9">有機化合物</a>:<a style="color: #ff9900;" title="糖類" href="https://zh.wikipedia.org/wiki/%E7%B3%96%E7%B1%BB">糖</a>和<a style="color: #ff9900;" title="無機化合物" href="https://zh.wikipedia.org/wiki/%E6%97%A0%E6%9C%BA%E5%8C%96%E5%90%88%E7%89%A9">無機化合物</a>:<a style="color: #ff9900;" title="氯化氫" href="https://zh.wikipedia.org/wiki/%E6%B0%AF%E5%8C%96%E6%B0%A2">氯化氫</a>)或<a style="color: #ff9900;" title="離子化合物" href="https://zh.wikipedia.org/wiki/%E7%A6%BB%E5%AD%90%E5%8C%96%E5%90%88%E7%89%A9">離子化合物</a>(如<a style="color: #ff9900;" title="食鹽" href="https://zh.wikipedia.org/wiki/%E9%A3%9F%E7%9B%90">食鹽</a>,即<a style="color: #ff9900;" title="氯化鈉" href="https://zh.wikipedia.org/wiki/%E6%B0%AF%E5%8C%96%E9%92%A0">氯化鈉</a>),它們溶解時的主要區別是離子化合物會在溶於<a style="color: #ff9900;" title="水" href="https://zh.wikipedia.org/wiki/%E6%B0%B4">水</a>時<a style="color: #ff9900;" title="電離" href="https://zh.wikipedia.org/wiki/%E7%94%B5%E7%A6%BB">電離</a>為<a style="color: #ff9900;" title="離子" href="https://zh.wikipedia.org/wiki/%E7%A6%BB%E5%AD%90">離子</a>(部分共價化合物亦可,如<a class="mw-redirect" style="color: #ff9900;" title="醋酸" href="https://zh.wikipedia.org/wiki/%E9%86%8B%E9%85%B8">醋酸</a>、<a style="color: #ff9900;" title="氯化氫" href="https://zh.wikipedia.org/wiki/%E6%B0%AF%E5%8C%96%E6%B0%A2">氯化氫</a>、<a style="color: #ff9900;" title="硝酸" href="https://zh.wikipedia.org/wiki/%E7%A1%9D%E9%85%B8">硝酸</a>、<a class="mw-redirect" style="color: #ff9900;" title="醋酸鉛" href="https://zh.wikipedia.org/wiki/%E9%86%8B%E9%85%B8%E9%93%85">醋酸鉛</a>等)。水是最常用的<a style="color: #ff9900;" title="溶劑" href="https://zh.wikipedia.org/wiki/%E6%BA%B6%E5%89%82">溶劑</a>,但同樣的原則適用於任何溶劑。</span>  <span style="color: #ff9900;">在<a style="color: #ff9900;" title="環境科學" href="https://zh.wikipedia.org/wiki/%E7%8E%AF%E5%A2%83%E7%A7%91%E5%AD%A6">環境科學</a>中,溶解在水中的全部固體物質(無論是否達到<a class="mw-redirect" style="color: #ff9900;" title="飽和溶液" href="https://zh.wikipedia.org/wiki/%E9%A5%B1%E5%92%8C%E6%BA%B6%E6%B6%B2">飽和</a>)的<a style="color: #ff9900;" title="濃度" href="https://zh.wikipedia.org/wiki/%E6%B5%93%E5%BA%A6">濃度</a>被稱為<a style="color: #ff9900;" title="總溶解固體" href="https://zh.wikipedia.org/wiki/%E6%80%BB%E6%BA%B6%E8%A7%A3%E5%9B%BA%E4%BD%93">總溶解固體</a>(<a class="mw-redirect" style="color: #ff9900;" title="TDS" href="https://zh.wikipedia.org/wiki/TDS">TDS</a>)。</span>  <img class="alignnone size-full wp-image-89729" src="http://www.freesandal.org/wp-content/uploads/220px-SaltInWaterSolutionLiquid.jpg" alt="" width="220" height="417" />  <span style="color: #cc99ff;">食鹽(氯化鈉)易溶於水</span> <h2><span id="非离子化合物" class="mw-headline" style="color: #808080;">非離子化合物</span></h2> <span style="color: #808080;">有機固體的溶解平衡是其固態部分與溶解部分之間的平衡:</span> <dl>  	<dd><span class="mwe-math-element" style="color: #808080;"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y">\displaystyle \mathrm {{C}_{12}{H}_{22}{O}_{11}(s)} \rightleftharpoons \mathrm {{C}_{12}{H}_{22}{O}_{11}(aq)}</span></span></dd> </dl> <span style="color: #808080;">而<a class="new" style="color: #808080;" title="平衡表達式(頁面不存在)" href="https://zh.wikipedia.org/w/index.php?title=%E5%B9%B3%E8%A1%A1%E8%A1%A8%E8%BE%BE%E5%BC%8F&action=edit&redlink=1">平衡表達式</a>可以如下所寫(這適用於任何此類反應):</span> <dl>  	<dd><span style="color: #808080;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y">\displaystyle K={\frac {\left\{\mathrm {{C}_{12}{H}_{22}{O}_{11}} (aq)\right\}}{\left\{\mathrm {{C}_{12}{H}_{22}{O}_{11}} (s)\right\}}}</span></span><sup id="cite_ref-Atkins_1-0" class="reference"><a style="color: #808080;" href="https://zh.wikipedia.org/zh-tw/%E6%BA%B6%E8%A7%A3%E5%B9%B3%E8%A1%A1#cite_note-Atkins-1">[1]</a></sup></span></dd> </dl> <span style="color: #808080;">K 是<a style="color: #808080;" title="平衡常數" href="https://zh.wikipedia.org/wiki/%E5%B9%B3%E8%A1%A1%E5%B8%B8%E6%95%B0">平衡常數</a>,花括號代表相應物質的<a class="mw-redirect" style="color: #808080;" title="活度" href="https://zh.wikipedia.org/wiki/%E6%B4%BB%E5%BA%A6">活度</a>,而根據定義,固體物質的活度是1。如果<a class="new" style="color: #808080;" title="離子氛(頁面不存在)" href="https://zh.wikipedia.org/w/index.php?title=%E7%A6%BB%E5%AD%90%E6%B0%9B&action=edit&redlink=1">離子氛</a>之間的作用可以忽略(一種常見的情形是溶液的濃度極低時),則活度也可用<a style="color: #808080;" title="濃度" href="https://zh.wikipedia.org/wiki/%E6%B5%93%E5%BA%A6">濃度</a>代替:</span> <dl>  	<dd><span class="mwe-math-element" style="color: #808080;"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y">\displaystyle K_{s}=\left[\mathrm {{C}_{12}{H}_{22}{O}_{11}} (aq)\right]</span></span></dd> </dl> <span style="color: #808080;">方括號代表<a class="mw-redirect" style="color: #808080;" title="摩爾濃度" href="https://zh.wikipedia.org/wiki/%E6%91%A9%E5%B0%94%E6%B5%93%E5%BA%A6">摩爾濃度</a>(通常用M表示)。</span>  <span style="color: #808080;">這個表達式是說在達到溶解平衡時,水中含有的已溶解的糖的濃度等於K。在 25℃時,當標準濃度為1mol/L時,蔗糖的K=1.971,這是在 25℃時能溶解的蔗糖的最大量,這時的溶液被稱為「飽和的」 。如果當前溶液濃度低於<a class="new" style="color: #808080;" title="飽和濃度(頁面不存在)" href="https://zh.wikipedia.org/w/index.php?title=%E9%A5%B1%E5%92%8C%E6%B5%93%E5%BA%A6&action=edit&redlink=1">飽和濃度</a>,固體會繼續溶解直到兩者相等或所有固體均已經溶解;如果當前溶液濃度高於飽和濃度,這時的溶液是「過飽和的」,溶液中的蔗糖將會以固體形式析出,直到兩者相等。這個過程可能是緩慢的,但是平衡常數描述的是體系平衡時的狀態,不是體系達到平衡的速度。</span> <h2><span style="color: #808080;"><span id=".E7.A6.BB.E5.AD.90.E5.8C.96.E5.90.88.E7.89.A9"></span><span id="离子化合物" class="mw-headline">離子化合物</span></span></h2> <span style="color: #808080;"><a style="color: #808080;" title="離子化合物" href="https://zh.wikipedia.org/wiki/%E7%A6%BB%E5%AD%90%E5%8C%96%E5%90%88%E7%89%A9">離子化合物</a>在<a style="color: #808080;" title="溶解" href="https://zh.wikipedia.org/wiki/%E6%BA%B6%E8%A7%A3">溶解</a>時通常會發生<a style="color: #808080;" title="電離" href="https://zh.wikipedia.org/wiki/%E7%94%B5%E7%A6%BB">電離</a>,即在<a style="color: #808080;" title="水" href="https://zh.wikipedia.org/wiki/%E6%B0%B4">水</a>的作用下<a class="mw-redirect" style="color: #808080;" title="解離" href="https://zh.wikipedia.org/wiki/%E8%A7%A3%E9%9B%A2">解離</a>為<a style="color: #808080;" title="離子" href="https://zh.wikipedia.org/wiki/%E7%A6%BB%E5%AD%90">離子</a> 。例如<a style="color: #808080;" title="硫酸鈣" href="https://zh.wikipedia.org/wiki/%E7%A1%AB%E9%85%B8%E9%92%99">硫酸鈣</a>:</span> <dl>  	<dd><span class="mwe-math-element" style="color: #808080;"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y">\displaystyle \mathrm {CaSO} _{4}(s)\rightleftharpoons {\mbox{Ca}}^{2+}(aq)+{\mbox{SO}}_{4}^{2-}(aq)</span></span></dd> </dl> <span style="color: #808080;">對上例而言,<a class="new" style="color: #808080;" title="平衡表達式(頁面不存在)" href="https://zh.wikipedia.org/w/index.php?title=%E5%B9%B3%E8%A1%A1%E8%A1%A8%E8%BE%BE%E5%BC%8F&action=edit&redlink=1">平衡表達式</a>為:</span> <dl>  	<dd><span style="color: #808080;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y">\displaystyle K={\frac {\left\{{\mbox{Ca}}^{2+}(aq)\right\}\left\{{\mbox{SO}}_{4}^{2-}(aq)\right\}}{\left\{{\mbox{CaSO}}_{4}(s)\right\}}}</span></span><sup id="cite_ref-Atkins_1-1" class="reference"><a style="color: #808080;" href="https://zh.wikipedia.org/zh-tw/%E6%BA%B6%E8%A7%A3%E5%B9%B3%E8%A1%A1#cite_note-Atkins-1">[1]</a></sup></span></dd> </dl> <span style="color: #808080;">K 被稱作<a style="color: #808080;" title="平衡常數" href="https://zh.wikipedia.org/wiki/%E5%B9%B3%E8%A1%A1%E5%B8%B8%E6%95%B0">平衡常數</a>,而花括號代表<a class="mw-redirect" style="color: #808080;" title="活度" href="https://zh.wikipedia.org/wiki/%E6%B4%BB%E5%BA%A6">活度</a>。固態物質的活度,根據定義,等於 1。當<a style="color: #808080;" title="溶液" href="https://zh.wikipedia.org/wiki/%E6%BA%B6%E6%B6%B2">溶液</a>的<a style="color: #808080;" title="濃度" href="https://zh.wikipedia.org/wiki/%E6%B5%93%E5%BA%A6">濃度</a>極低,即離子的活度可以看做 1時,這個表達式可以改寫為以下的「<a style="color: #808080;" title="溶度積" href="https://zh.wikipedia.org/wiki/%E6%BA%B6%E5%BA%A6%E7%A7%AF">溶度積</a>」表達式:</span> <dl>  	<dd><span class="mwe-math-element" style="color: #808080;"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y">\displaystyle K_{\mathrm {sp} }=\left[{\mbox{Ca}}^{2+}(aq)\right]\left[{\mbox{SO}}_{4}^{2-}(aq)\right].</span></span></dd> </dl> <span style="color: #808080;">這個表達式說明了硫酸鈣的水溶液達平衡時,由硫酸鈣電離出的兩種<a class="new" style="color: #808080;" title="離子濃度(頁面不存在)" href="https://zh.wikipedia.org/w/index.php?title=%E7%A6%BB%E5%AD%90%E6%B5%93%E5%BA%A6&action=edit&redlink=1">離子濃度</a>的乘積等於 K<sub>sp</sub>,即溶度積。硫酸鈣的溶度積為4.93×10<sup>−5</sup>。如果溶液中只含硫酸鈣,即只含由其電離出的 Ca<sup>2+</sup>和 SO<sub>4</sub><sup>2−</sup>,那麼每種離子的濃度為:</span> <dl>  	<dd><span class="mwe-math-element" style="color: #808080;"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y">\displaystyle {\sqrt {K_{\mathrm {sp} }}}={\sqrt {4.93\times 10^{-5}}}=7.02\times 10^{-3}=\left[{\mbox{Ca}}^{2+}\right]=\left[{\mbox{SO}}_{4}^{2-}\right].</span></span></dd> </dl> <span style="color: #808080;">當一種溶質電離為<a class="new" style="color: #808080;" title="計量數(頁面不存在)" href="https://zh.wikipedia.org/w/index.php?title=%E8%AE%A1%E9%87%8F%E6%95%B0&action=edit&redlink=1">計量數</a>不相等的幾部分時:</span> <dl>  	<dd><span style="color: #808080;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y">\displaystyle \mathrm {Ca(OH)_{2}} (s)\rightleftharpoons {\mbox{Ca}}^{2+}(aq)+{\mbox{2OH}}^{-}(aq) </span></span>,</span></dd> </dl> <span style="color: #808080;">K<sub>sp</sub>的確定會稍有複雜。對於如下電離過程:</span> <dl>  	<dd><span class="mwe-math-element" style="color: #808080;"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y">\displaystyle \mathrm {A} (s)\rightleftharpoons {\mbox{xB}}^{p+}(aq)+{\mbox{yC}}^{q-}(aq)</span></span></dd> </dl> <span style="color: #808080;">溶度積和溶解度的關係由以下方程確定:</span> <dl>  	<dd><span class="mwe-math-element" style="color: #808080;"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y">\displaystyle {\sqrt[{n}]{K_{\mathrm {sp} } \over {x^{x}\cdot y^{y}}}}={C \over M_{M}}$

其中:

  • n是電離方程右邊的總計量數(對上例,x+y),無量綱
  • x是所有陽離子的總計量數,無量綱;
  • y是所有陰離子的總計量數,無量綱;
  • Ksp是溶度積,(mol/kg)n
  • C是化合物 A的溶解度(A的質量比溶液的質量),無量綱;
  • MM是化合物 A的摩爾質量,kg/mol。

上述方程假設電離過程發生在純溶劑(無同離子效應發生),亦不存在絡合水解(即溶液中只存在Bp+和Cq-),且濃度小到離子活度可被認為等於1。

 

 

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