[{"data":1,"prerenderedAt":153},["ShallowReactive",2],{"cheatsheet-chemical-kinetics":3},{"sheet":4},{"sheetSlug":5,"topicSlugs":6,"primaryTopic":7,"title":8,"subtitle":9,"sections":10},"chemical-kinetics",[5],20,"Chemical Kinetics","Rate laws, integrated rate laws, half-lives, Arrhenius, mechanisms, and energy diagrams.",[11,23,31,56,75,83,92,100,121,129,137,145],{"heading":12,"kind":13,"items":14},"Rate of reaction","rules",[15],{"ref":16,"mode":19,"provenance":20,"text":21,"source_hash":22},{"type":17,"topic":7,"id":18,"field":17},"rule","KN-R001","transform","owned_workbook","For aA + bB → cC + dD: rate = −(1/a)d[A]/dt = −(1/b)d[B]/dt = +(1/c)d[C]/dt = +(1/d)d[D]/dt. The 1/coefficient prefactor makes the single rate value independent of which species you track.","56c6580cd05c2a100a1380e9025d2b6776c6efadebfb176f9b5503fccfa23e07",{"heading":24,"kind":13,"items":25},"Rate law",[26],{"ref":27,"mode":19,"provenance":20,"text":29,"source_hash":30},{"type":17,"topic":7,"id":28,"field":17},"KN-R002","rate = k[A]ᵐ[B]ⁿ. Orders m, n are found by EXPERIMENT, not from coefficients (except for an elementary step). k depends only on temperature. Overall order = m + n.","10b33d03fe8f749b76eac78281f4b9db71856f1cc08bfacda892f8a9821090e5",{"heading":32,"kind":33,"columns":34,"items":38},"Integrated rate laws","data",[35,36,37],"Order","Integrated law","Linear plot",[39],{"ref":40,"mode":19,"provenance":20,"rows":42,"source_hash":55},{"type":17,"topic":7,"id":41,"field":17},"KN-R004",[43,47,51],[44,45,46],"0","[A]ₜ = [A]₀ − kt","[A] vs t (slope −k)",[48,49,50],"1","ln[A]ₜ = ln[A]₀ − kt","ln[A] vs t (slope −k)",[52,53,54],"2","1/[A]ₜ = 1/[A]₀ + kt","1/[A] vs t (slope +k)","8f17173c19a534c18ee1053d2f84553815ab7918f082f80bd5ce49f217995c2b",{"heading":57,"kind":33,"columns":58,"items":61},"Half-life by order",[35,59,60],"t₁/₂","Depends on [A]₀?",[62],{"ref":63,"mode":19,"provenance":20,"rows":65,"source_hash":74},{"type":17,"topic":7,"id":64,"field":17},"KN-R003",[66,69,72],[44,67,68],"[A]₀ / (2k)","yes",[48,70,71],"ln2 / k ≈ 0.693/k","no",[52,73,68],"1 / (k·[A]₀)","a560357f5d4478dcfbfa7de00d97878f693faa7bb18b90629cb10e21e5cac02e",{"heading":76,"kind":13,"items":77},"Fraction remaining (first order)",[78],{"ref":79,"mode":19,"provenance":20,"text":81,"source_hash":82},{"type":17,"topic":7,"id":80,"field":17},"KN-R005","After N half-lives, fraction left = (1/2)ᴺ (50%, 25%, 12.5%, …), with N = t/t₁/₂. For any time: [A]ₜ/[A]₀ = e^(−kt). If X% decomposes, (100−X)% remains.","c7abddf594c05fa7c3f020bcecb00cbe4054e716f166e39b16d23b94d50cf6ac",{"heading":84,"kind":85,"items":86},"Method of initial rates","steps",[87],{"ref":88,"mode":19,"provenance":20,"text":90,"source_hash":91},{"type":17,"topic":7,"id":89,"field":17},"KN-R006","Pick two trials where only ONE concentration changes: rate₂/rate₁ = ([X]₂/[X]₁)^order, so order = log(rate ratio) / log(conc ratio). Repeat per reactant, then get k by plugging one trial into rate = k[A]ᵐ[B]ⁿ.","fbf5c0eadd7b7f966051c43db0b0831f985a9a4463a545eb3c93cfdc4131b1a3",{"heading":93,"kind":13,"items":94},"Arrhenius equation",[95],{"ref":96,"mode":19,"provenance":20,"text":98,"source_hash":99},{"type":17,"topic":7,"id":97,"field":17},"KN-R007","k = A·e^(−Ea/RT). Two-temperature: ln(k₂/k₁) = (Ea/R)(1/T₁ − 1/T₂). Plot ln k vs 1/T: slope = −Ea/R. T in Kelvin; R = 8.314 J/(mol·K) for Ea in J/mol.","feae22858e38fac529d536c2f5ef5b50fa32dea117483be4a84e2e916de31a30",{"heading":101,"kind":33,"columns":102,"items":105},"Units of k",[103,104],"Overall order","k units",[106],{"ref":107,"mode":19,"provenance":109,"rows":110,"source_hash":120},{"type":17,"topic":7,"id":108,"field":17},"KN-R010","original",[111,113,115,117],[44,112],"M/s",[48,114],"s⁻¹",[52,116],"M⁻¹·s⁻¹",[118,119],"3","M⁻²·s⁻¹","16f14af91ccba6d0b9aab0dc14894128c0c650353b12213817441e20a5218797",{"heading":122,"kind":13,"items":123},"Rate-determining step",[124],{"ref":125,"mode":19,"provenance":20,"text":127,"source_hash":128},{"type":17,"topic":7,"id":126,"field":17},"KN-R008","The slowest (RDS) step sets the overall rate. For an ELEMENTARY step the orders DO equal its coefficients: A + 2B → products gives rate = k[A][B]². If the RDS contains an intermediate, substitute it out via the pre-equilibrium.","7a50656ba6c4be1969c741eb3f376b89a3f688ab08077c8242c6c7abb40a8d2c",{"heading":130,"kind":13,"items":131},"Intermediate vs catalyst",[132],{"ref":133,"mode":19,"provenance":20,"text":135,"source_hash":136},{"type":17,"topic":7,"id":134,"field":17},"KN-R009","Both have net-zero stoichiometry (not in the overall equation). Intermediate: produced first, then consumed. Catalyst: consumed first, then regenerated (it lowers Ea).","f28908ff68eddc980b8800363c546d37540db75c922b23c904394db304232d1e",{"heading":138,"kind":13,"items":139},"Energy diagram",[140],{"ref":141,"mode":19,"provenance":109,"text":143,"source_hash":144},{"type":17,"topic":7,"id":142,"field":17},"KN-R011","Peak = transition state; valley between peaks = intermediate. Forward Ea = peak − reactants; ΔH = products − reactants. A catalyst gives a lower-Ea path with the SAME ΔH. RDS = the highest peak.","b84c81db95b243a6840340e01be8e6c670afd1898cc8da3d42af00503bc16656",{"heading":146,"kind":85,"items":147},"Pre-equilibrium",[148],{"ref":149,"mode":19,"provenance":109,"text":151,"source_hash":152},{"type":17,"topic":7,"id":150,"field":17},"KN-R012","If a fast equilibrium precedes the RDS, solve the intermediate from that step: [int] = K_eq·[reactants], then substitute into the RDS rate. E.g. 2NO + Cl₂: rate = k₂K_eq[NO]²[Cl₂].","3c0fc6bdbf24e2114cf5a4e58e5041ed3edfbab4bc09c572a448769a8fbf45d9",1787246033420]