[{"data":1,"prerenderedAt":97},["ShallowReactive",2],{"cheatsheet-buffers-and-titration-curves":3},{"sheet":4},{"sheetSlug":5,"topicSlugs":6,"primaryTopic":7,"title":8,"subtitle":9,"sections":10},"buffers-and-titration-curves",[5],23,"Buffers & Titration Curves","Buffer action, Henderson-Hasselbalch, effective range, the four titration regions, and indicators.",[11,23,31,39,47,55,64,73,81,89],{"heading":12,"kind":13,"items":14},"What makes a buffer","rules",[15],{"ref":16,"mode":19,"provenance":20,"text":21,"source_hash":22},{"type":17,"topic":7,"id":18,"field":17},"rule","BF-R001","transform","owned_workbook","A buffer needs appreciable amounts of BOTH a weak acid and its conjugate base (or a weak base and its conjugate acid), with a non-hydrolyzing spectator counter-ion. Strong-acid- or strong-base-only solutions cannot buffer.","bde96f81dd747fadf9b188000909e25e2966ac1da8db16ae259ae629f8aa6343",{"heading":24,"kind":13,"items":25},"How it resists",[26],{"ref":27,"mode":19,"provenance":20,"text":29,"source_hash":30},{"type":17,"topic":7,"id":28,"field":17},"BF-R002","Added base is neutralized by the weak acid: HA + OH⁻ → A⁻ + H₂O. Added acid by the conjugate base: A⁻ + H₃O⁺ → HA + H₂O. Each added strong species becomes a weak conjugate-pair member.","b3cea0b44f24c6466af0d147deaaa846108f49a6c10cf1dc5a7aec55d0eaa29c",{"heading":32,"kind":13,"items":33},"Henderson-Hasselbalch",[34],{"ref":35,"mode":19,"provenance":20,"text":37,"source_hash":38},{"type":17,"topic":7,"id":36,"field":17},"BF-R003","pH = pKa + log([A⁻]/[HA]). Basic buffer: pOH = pKb + log([BH⁺]/[B]), pH = 14 − pOH. Volume cancels in the ratio, so moles can be used directly.","548d5a0a408d939a617298eb3398da67b9e6f01ea780626ef791ae3b0286b587",{"heading":40,"kind":13,"items":41},"Polyprotic buffer pKa",[42],{"ref":43,"mode":19,"provenance":20,"text":45,"source_hash":46},{"type":17,"topic":7,"id":44,"field":17},"BF-R004","Use the pKa of the step whose two species ARE the buffer pair. H₃PO₄/H₂PO₄⁻ → pKa1 (2.12); H₂PO₄⁻/HPO₄²⁻ → pKa2 (7.21); HPO₄²⁻/PO₄³⁻ → pKa3 (12.32).","16a62e7231a72f2ec0c97c9183bd4705835ada5ceaa823af7f516f2e52e4ad03",{"heading":48,"kind":13,"items":49},"Ratio for a target pH",[50],{"ref":51,"mode":19,"provenance":20,"text":53,"source_hash":54},{"type":17,"topic":7,"id":52,"field":17},"BF-R005","Inverse H-H: [A⁻]/[HA] = 10^(pH − pKa). Used for buffer prep and post-perturbation pH. Give the ratio in the direction the problem asks; the reciprocal is a different quantity.","d5d92bf5da09ed1cd42256ac474469b3a40ad9ef89a67c37a318ce2f463c81a9",{"heading":56,"kind":13,"items":57},"Effective range & capacity",[58],{"ref":59,"mode":19,"provenance":61,"text":62,"source_hash":63},{"type":17,"topic":7,"id":60,"field":17},"BF-R007","original","A buffer works over pKa ± 1 (ratio 0.1 to 10). For a target pH, pick a weak acid with pKa ≈ pH. Capacity scales with absolute concentrations: 1.0 M/1.0 M holds ~10× more than 0.1 M/0.1 M at the same pH.","f3e1327348eaeed45092e03112f0878f965c756a61594dc2cadab78f62581202",{"heading":65,"kind":66,"items":67},"Four titration regions","steps",[68],{"ref":69,"mode":19,"provenance":20,"text":71,"source_hash":72},{"type":17,"topic":7,"id":70,"field":17},"BF-R006","(1) Initial: analyte alone. (2) Buffer region (weak analyte only): both analyte + formed conjugate, use H-H. (3) Equivalence: only the salt (strong-strong pH 7; weak acid + strong base pH > 7; weak base + strong acid pH \u003C 7). (4) Post-equivalence: excess titrant.","ffe7d8d1bc9b1114d633b8b965da21f13056fd1c6222b02238985eb82a96f6f2",{"heading":74,"kind":13,"items":75},"Half-equivalence = pKa",[76],{"ref":77,"mode":19,"provenance":61,"text":79,"source_hash":80},{"type":17,"topic":7,"id":78,"field":17},"BF-R009","At V = V_equiv/2, half the weak acid is neutralized so [HA] = [A⁻] and pH = pKa. (Weak base + strong acid: pOH = pKb there.) Read pKa straight off the curve.","029e84abec72c27b97f6cce91be46b31ecc24074a859be106f14ebcea4ce4887",{"heading":82,"kind":13,"items":83},"Curve features",[84],{"ref":85,"mode":19,"provenance":61,"text":87,"source_hash":88},{"type":17,"topic":7,"id":86,"field":17},"BF-R008","Equivalence point = the volume where pH rises most steeply; half-equivalence = half that volume; the buffer region is the slow-changing pre-equivalence span. A weak-acid curve starts higher and has a smaller equivalence jump than strong-strong.","2ea03050adcfc4a24b912de58183cb86cb4f8914b9c72b4b20a61557caba0c09",{"heading":90,"kind":13,"items":91},"Indicator selection",[92],{"ref":93,"mode":19,"provenance":61,"text":95,"source_hash":96},{"type":17,"topic":7,"id":94,"field":17},"BF-R010","An indicator changes colour over pKa(ind) ± 1. Pick one with pKa ≈ equivalence pH. Weak acid + strong base (equiv > 7): phenolphthalein (9.4). Weak base + strong acid (equiv \u003C 7): methyl red (5.1).","f095208f627af0ca0ef32c81f57e29ce7562f3fb8cd28129cb0813f0534e855d",1787246033393]