{"id":1427,"date":"2020-06-25T12:37:46","date_gmt":"2020-06-25T16:37:46","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/chbe220\/?post_type=chapter&p=1427"},"modified":"2020-08-20T13:43:52","modified_gmt":"2020-08-20T17:43:52","slug":"reaction-chemistry-chapter-review-v2","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/chbe220\/chapter\/reaction-chemistry-chapter-review-v2\/","title":{"raw":"Reaction Chemistry Chapter Review","rendered":"Reaction Chemistry Chapter Review"},"content":{"raw":"

Important Equations<\/h2>\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Reaction rate<\/td>\r\n[latex] r = \\frac{1}{\\nu}\\frac{d[J]}{dt} [\/latex]<\/td>\r\n<\/tr>\r\n
Extent of reaction<\/td>\r\n[latex] d n_{j} = \\nu_{j} d\\xi [\/latex]<\/td>\r\n<\/tr>\r\n
Relating extent of reaction with reaction rate<\/td>\r\n[latex]r = \\frac{1}{V} \\frac{d\\xi}{dt} = \\frac{1}{\\nu_{j}} \\frac{1}{V} \\frac{dn_{j}}{dt}[\/latex]<\/td>\r\n<\/tr>\r\n
Rate law (general form)<\/td>\r\n\r\n

[latex]r=k_{r}[A]^a[B]^b[\/latex]<\/p>\r\n

[latex]r=k_{r}p_{A}^a p_{B}^b[\/latex]<\/p>\r\n<\/td>\r\n<\/tr>\r\n

Zeroth-order rate law<\/td>\r\n[latex][A]-[A]_{0}=-k_{r}*t[\/latex]\r\n\r\n[latex][A]=[A]_{0}-k_{r}*t[\/latex]<\/td>\r\n<\/tr>\r\n
First-order rate law<\/td>\r\n\r\n

[latex]ln[A]-ln[A]_{0}=-k_{r}*t[\/latex]<\/p>\r\n

[latex][A]=[A]_{0}e^{-k_{r}*t}[\/latex]<\/p>\r\n<\/td>\r\n<\/tr>\r\n

Second-order rate law<\/td>\r\n\r\n

[latex]\\frac{1}{[A]}-\\frac{1}{[A]_{0}}=k_{r}*t[\/latex]<\/p>\r\n

[latex][A]=\\frac{[A]_{0}}{1+k_{r}*t*[A]_{0}}[\/latex]<\/p>\r\n<\/td>\r\n<\/tr>\r\n

Equilibrium constant<\/td>\r\n\r\n

[latex]K\\;\\; or\\;\\; K_{eq}=\\prod_{i} a_{i,eq}^{vi}[\/latex]<\/p>\r\n

[latex]K=\\frac{k_{r}}{k'_{r}} \\;\\;,c^\\theta\\text{is used for unit consistency}[\/latex]<\/p>\r\n

[latex]k'_{r}[product]_{eq}^{p}=k_{r}[reactant]_{eq}^{r}[\/latex]<\/p>\r\n<\/td>\r\n<\/tr>\r\n

Arrhenius equation<\/td>\r\n\r\n

[latex]ln(k_{r})=ln(A)-\\frac{E_{a}}{RT}[\/latex]<\/span><\/p>\r\n

[latex]k_{r}=Ae^{-\\frac{E_{a}}{RT}}[\/latex]<\/p>\r\nLinear form:\r\n

[latex] ln(k_{r}) = -\\frac{E_{a}}{R} * \\frac{1}{T} + ln(A) [\/latex]<\/p>\r\nSimplification for temperature dependency calculations: <\/span>\r\n

[latex]ln(\\frac{k_{r2}}{k_{r1}})=\\frac{E_{a}}{R}(\\frac{1}{T_{1}}-\\frac{1}{T_{2}})[\/latex]<\/span><\/p>\r\n<\/td>\r\n<\/tr>\r\n

Unimolecular rate law<\/td>\r\n[latex]A\u2192P:\\;\\;-\\frac{d[A]}{dt}=k_{r}*[A][\/latex]<\/td>\r\n<\/tr>\r\n
Biomolecular rate law<\/td>\r\n\r\n

[latex]A+B\u2192P:\\;\\;-\\frac{d[A]}{dt}=k_{r}*[A]*[B][\/latex]<\/p>\r\n

[latex]A+A\u2192P:\\;\\;-\\frac{d[A]}{dt}=k_{r}*[A]^2[\/latex]<\/p>\r\n<\/td>\r\n<\/tr>\r\n

Kinetic control<\/td>\r\nIf [latex]k_{e1},k_{e2}\\text{<<}k_{r1},k_{r2}[\/latex]:\r\n

[latex]\\frac{[P_{1}]}{[P_{2}]}=\\frac{k_{r1}}{k_{r2}}[\/latex]<\/p>\r\n<\/td>\r\n<\/tr>\r\n

Thermodynamic control<\/td>\r\nIf [latex]k_{e1},k_{e2}>>k_{r1},k_{r2}[\/latex]:\r\n

[latex]\\frac{[P_{1}]}{[P_{2}]}=\\frac{k_{e1}}{k_{e2}}[\/latex]<\/p>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

Terms to Know:<\/h2>\r\n[h5p id=\"7\"]","rendered":"

Important Equations<\/h2>\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
Reaction rate<\/td>\n[latex]r = \\frac{1}{\\nu}\\frac{d[J]}{dt}[\/latex]<\/td>\n<\/tr>\n
Extent of reaction<\/td>\n[latex]d n_{j} = \\nu_{j} d\\xi[\/latex]<\/td>\n<\/tr>\n
Relating extent of reaction with reaction rate<\/td>\n[latex]r = \\frac{1}{V} \\frac{d\\xi}{dt} = \\frac{1}{\\nu_{j}} \\frac{1}{V} \\frac{dn_{j}}{dt}[\/latex]<\/td>\n<\/tr>\n
Rate law (general form)<\/td>\n\n

[latex]r=k_{r}[A]^a[B]^b[\/latex]<\/p>\n

[latex]r=k_{r}p_{A}^a p_{B}^b[\/latex]<\/p>\n<\/td>\n<\/tr>\n

Zeroth-order rate law<\/td>\n[latex][A]-[A]_{0}=-k_{r}*t[\/latex]<\/p>\n

[latex][A]=[A]_{0}-k_{r}*t[\/latex]<\/td>\n<\/tr>\n

First-order rate law<\/td>\n\n

[latex]ln[A]-ln[A]_{0}=-k_{r}*t[\/latex]<\/p>\n

[latex][A]=[A]_{0}e^{-k_{r}*t}[\/latex]<\/p>\n<\/td>\n<\/tr>\n

Second-order rate law<\/td>\n\n

[latex]\\frac{1}{[A]}-\\frac{1}{[A]_{0}}=k_{r}*t[\/latex]<\/p>\n

[latex][A]=\\frac{[A]_{0}}{1+k_{r}*t*[A]_{0}}[\/latex]<\/p>\n<\/td>\n<\/tr>\n

Equilibrium constant<\/td>\n\n

[latex]K\\;\\; or\\;\\; K_{eq}=\\prod_{i} a_{i,eq}^{vi}[\/latex]<\/p>\n

[latex]K=\\frac{k_{r}}{k'_{r}} \\;\\;,c^\\theta\\text{is used for unit consistency}[\/latex]<\/p>\n

[latex]k'_{r}[product]_{eq}^{p}=k_{r}[reactant]_{eq}^{r}[\/latex]<\/p>\n<\/td>\n<\/tr>\n

Arrhenius equation<\/td>\n\n

[latex]ln(k_{r})=ln(A)-\\frac{E_{a}}{RT}[\/latex]<\/span><\/p>\n

[latex]k_{r}=Ae^{-\\frac{E_{a}}{RT}}[\/latex]<\/p>\n

Linear form:<\/p>\n

[latex]ln(k_{r}) = -\\frac{E_{a}}{R} * \\frac{1}{T} + ln(A)[\/latex]<\/p>\n

Simplification for temperature dependency calculations: <\/span><\/p>\n

[latex]ln(\\frac{k_{r2}}{k_{r1}})=\\frac{E_{a}}{R}(\\frac{1}{T_{1}}-\\frac{1}{T_{2}})[\/latex]<\/span><\/p>\n<\/td>\n<\/tr>\n

Unimolecular rate law<\/td>\n[latex]A\u2192P:\\;\\;-\\frac{d[A]}{dt}=k_{r}*[A][\/latex]<\/td>\n<\/tr>\n
Biomolecular rate law<\/td>\n\n

[latex]A+B\u2192P:\\;\\;-\\frac{d[A]}{dt}=k_{r}*[A]*[B][\/latex]<\/p>\n

[latex]A+A\u2192P:\\;\\;-\\frac{d[A]}{dt}=k_{r}*[A]^2[\/latex]<\/p>\n<\/td>\n<\/tr>\n

Kinetic control<\/td>\nIf [latex]k_{e1},k_{e2}\\text{<<}k_{r1},k_{r2}[\/latex]:\n\n\n

[latex]\\frac{[P_{1}]}{[P_{2}]}=\\frac{k_{r1}}{k_{r2}}[\/latex]<\/p>\n<\/td>\n<\/tr>\n

Thermodynamic control<\/td>\nIf [latex]k_{e1},k_{e2}>>k_{r1},k_{r2}[\/latex]:<\/p>\n

[latex]\\frac{[P_{1}]}{[P_{2}]}=\\frac{k_{e1}}{k_{e2}}[\/latex]<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Terms to Know:<\/h2>\n
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