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øê5.•½t‚â‹t”½‰ž‚Æ‚ÌŠÖŒW
5.1.ŠÈ’P‚È—á
ˆÈ‰º‚̂悤‚ɤ2‚‚̉»ŠwŽí‚ÌŠÔ‚É•½t‚ª¬—§‚µ‚Ä‚¢‚é‚Æ‚·‚é¡

A B {\displaystyle {\ce {A <=> B}}} ”½‰ž‚Ít=0‚ÅA‚̏‰Šú”Z“x‚ª¤B‚̏‰Šú”Z“x‚ª0‚̏ó‘Ô‚©‚çŽn‚Ü‚é¡

‚±‚Ì‚Æ‚«¤•½t’萔K‚͈ȉº‚̂悤‚ɏ‘‚¯‚é¡

K   = d e f   k f k b = [ B ] e [ A ] e {\displaystyle K\ {\stackrel {\mathrm {def} }{=}}\ {\frac {k_{f}}{k_{b}}}={\frac {\left[{\ce {B}}\right]_{e}}{\left[{\ce {A}}\right]_{e}}}} ‚±‚±‚Ť‚Æ‚Í•½tó‘Ô‚Å‚ÌA‚ÆB‚Ì”Z“x‚Å‚ ‚é¡

Žžt‚É‚¨‚¯‚éA‚Ì”Z“x‚ð¤B‚Ì”Z“x‚ð‚Æ‚·‚é‚Ƥ—¼ŽÐ‚ÍŽŸ‚Ì•½t”½‰ž‚Ì“™Ž®‚ð–ž‚½‚·¡

[ A ] t = [ A ] 0 [ B ] t {\displaystyle {\ce {[A]_{\mathit {t}}=[A]_{0}-[B]_{\mathit {t}}}}} ‚±‚±‚Ť‚Í0‚Å‚ ‚邱‚Æ‚É’ˆÓ‚·‚é¡

‚±‚ê‚ͤŽž‚ª–³ŒÀ‘å‚ƂȂ褕½t‚É’B‚µ‚½ó‘Ô‚Å‚à¬—§‚·‚é¡

[ A ] e = [ A ] 0 [ B ] e {\displaystyle {\ce {[A]_{\mathit {e}}=[A]_{0}-[B]_{\mathit {e}}}}} ‚±‚ê‚Í•½t’萔K‚Ì’è‹`‚æ‚è¤

[ B ] e = x = k f k f + k b [ A ] 0 {\displaystyle [{{\ce {B}}}]_{e}=x={\frac {k_{f}}{k_{f}+k_{b}}}[{{\ce {A}}}]_{0}} ‚䂦‚ɤ

  [ A ] e = [ A ] 0 x = k b k f + k b [ A ] 0 {\displaystyle \ [{{\ce {A}}}]_{e}=[{{\ce {A}}}]_{0}-x={\frac {k_{b}}{k_{f}+k_{b}}}[{{\ce {A}}}]_{0}} ‚±‚ê‚ç‚Ì“™Ž®‚É‚æ‚褔÷•ª•û’öŽ®‚ð‰ð‚©‚¸‚Æ‚àA‚Ì”Z“x‚ð‹‚ß‚é‚±‚Æ‚ª‚Å‚«‚é¡

”½‰ž‘¬“xŽ®‚͈ȉº‚̂悤‚É—^‚¦‚ç‚ê‚é¡

r = k 1 [ A ] s [ B ] t k 2 [ X ] u [ Y ] v {\displaystyle r={k_{1}[{\ce {A}}]^{s}[{\ce {B}}]^{t}}-{k_{2}[{\ce {X}}]^{u}[{\ce {Y}}]^{v}}\,} ”÷•ªŒW”‚ª•‰‚Ȃ̂͐³”½‰ž‚ªA‚©‚çB‚É•Ï‚í‚锽‰ž‚Ȃ̂ŤA‚Ì”Z“x‚ÍŒ¸­‚µ‚Ä‚¢‚é‚©‚ç‚Å‚ ‚é¡ŠÈ—ª‰»‚·‚邽‚ߤŽžt‚Å‚ÌA‚Ì”Z“x‚ðx‚Æ‚¨‚­¡‚Ü‚½•½tŽž‚ÌA‚Ì”Z“x‚ð‚Æ‚·‚é¡‚±‚Ì‚Æ‚«¤

d [ A ] d t = k f [ A ] t k b [ B ] t d x d t = k f x k b [ B ] t = k f x k b ( [ A ] 0 x ) = ( k f + k b ) x k b [ A ] 0 {\displaystyle {\begin{aligned}-{\frac {d[{{\ce {A}}}]}{dt}}&={k_{f}[{{\ce {A}}}]_{t}}-{k_{b}[{{\ce {B}}}]_{t}}\\-{\frac {dx}{dt}}&={k_{f}x}-{k_{b}[{{\ce {B}}}]_{t}}\\&={k_{f}x}-{k_{b}([{{\ce {A}}}]_{0}-x)}\\&={(k_{f}+k_{b})x}-{k_{b}[{{\ce {A}}}]_{0}}\end{aligned}}} ‚¾‚©‚ç

k f + k b = k b [ A ] 0 x e {\displaystyle k_{f}+k_{b}={k_{b}{\frac {{\ce {[A]_0}}}{x_{e}}}}} ‚æ‚Á‚Ä”½‰ž‘¬“x‚Í

  d x d t = k b [ A ] 0 x e ( x e x ) {\displaystyle \ {\frac {dx}{dt}}={\frac {k_{b}[{{\ce {A}}}]_{0}}{x_{e}}}(x_{e}-x)} ‚‚܂è¤

ln ( [ A ] 0 [ A ] e [ A ] t [ A ] e ) = ( k f + k b ) t {\displaystyle \ln \left({\frac {[{{\ce {A}}}]_{0}-[{{\ce {A}}}]_{e}}{[{{\ce {A}}}]_{t}-[{{\ce {A}}}]_{e}}}\right)=(k_{f}+k_{b})t} ‚Æ‚¢‚¤Œ‹‰Ê‚É‚È‚é[7]¡

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(5.•½t‚â‹t”½‰ž‚Æ‚ÌŠÖŒW)
[6]ŽŸÍß°¼Þ
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o“T:Wikipedia
2018/10/15 16:00
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