[{"data":1,"prerenderedAt":157},["ShallowReactive",2],{"cheatsheet-gases-and-gas-laws":3},{"sheet":4},{"sheetSlug":5,"topicSlugs":6,"primaryTopic":7,"title":8,"subtitle":9,"sections":10},"gases-and-gas-laws",[5],17,"Gases & Gas Laws","Pressure units, the gas laws, PV=nRT, partial pressures, molecular speeds, and gas stoichiometry.",[11,23,32,75,84,92,115,123,131,139,148],{"heading":12,"kind":13,"items":14},"Pressure units","data",[15],{"ref":16,"mode":19,"provenance":20,"text":21,"source_hash":22},{"type":17,"topic":7,"id":18,"field":17},"rule","GL-R001","transform","owned_workbook","1 atm = 101,325 Pa = 760 mmHg = 760 torr ≈ 1.01325 bar ≈ 14.696 psi. torr ≡ mmHg; 1 bar = 100,000 Pa exactly. Chain conversions by dimensional analysis.","f4ccc8475ddb8c50c94abccf3e2b70422a82ddd3e8c00a387bf3c0397ec16ac5",{"heading":24,"kind":25,"items":26},"Always use Kelvin","pitfalls",[27],{"ref":28,"mode":19,"provenance":20,"text":30,"source_hash":31},{"type":17,"topic":7,"id":29,"field":17},"GL-R002","Every gas-law plug-in needs absolute T: T(K) = T(°C) + 273.15. Never put °C or °F into a gas-law equation. STP here = 0 °C (273.15 K) and 1 atm.","ac6f1b4f7f050c643ff4e064c4027149128a69562494b6d7862c34931f9410cc",{"heading":33,"kind":13,"columns":34,"items":38},"The simple gas laws",[35,36,37],"Law","Held constant","Relation",[39,48,57,66],{"ref":40,"mode":19,"provenance":20,"rows":42,"source_hash":47},{"type":17,"topic":7,"id":41,"field":17},"GL-R003",[43],[44,45,46],"Boyle","T, n","P₁V₁ = P₂V₂","3a5bac77852b3ba2b5ea1800630e92c9ebbb7e7a71e6e2f072223007e9cbf065",{"ref":49,"mode":19,"provenance":20,"rows":51,"source_hash":56},{"type":17,"topic":7,"id":50,"field":17},"GL-R004",[52],[53,54,55],"Charles","P, n","V₁/T₁ = V₂/T₂","7c163414748fd6081bd406f3b342bda798deb7c05519c97e2f30388f1946130f",{"ref":58,"mode":19,"provenance":20,"rows":60,"source_hash":65},{"type":17,"topic":7,"id":59,"field":17},"GL-R005",[61],[62,63,64],"Gay-Lussac","V, n","P₁/T₁ = P₂/T₂","5d3c585ecfd8b7da6c99c0bfa48874261f9a8936df64f8a82b5a69c285554aaa",{"ref":67,"mode":19,"provenance":20,"rows":69,"source_hash":74},{"type":17,"topic":7,"id":68,"field":17},"GL-R006",[70],[71,72,73],"Avogadro","T, P","V₁/n₁ = V₂/n₂","154a6fe4618abe2901127bf96c7962da1115dacc20167022872be27f5271f17a",{"heading":76,"kind":77,"items":78},"Combined gas law","rules",[79],{"ref":80,"mode":19,"provenance":20,"text":82,"source_hash":83},{"type":17,"topic":7,"id":81,"field":17},"GL-R007","P₁V₁/T₁ = P₂V₂/T₂ when P, V, and T all change (n fixed). T in Kelvin; P and V units just have to match between the two states.","3a8fabe0407998958dd97a68bde8d3ae343f952b4c098625d87387cc065f38f6",{"heading":85,"kind":77,"items":86},"Ideal gas law",[87],{"ref":88,"mode":19,"provenance":20,"text":90,"source_hash":91},{"type":17,"topic":7,"id":89,"field":17},"GL-R008","PV = nRT for a single state with 3 of 4 knowns. T in Kelvin. P = nRT/V, V = nRT/P, n = PV/RT, T = PV/nR. Pick the R whose units match P and V.","83b7da3ff1dcb1b8509b261530d3fd1c99d4e0f3f701023819e1acf2c4be9d20",{"heading":93,"kind":13,"columns":94,"items":97},"Choosing R",[95,96],"R value","Use when",[98],{"ref":99,"mode":19,"provenance":20,"rows":101,"source_hash":114},{"type":17,"topic":7,"id":100,"field":17},"GL-R009",[102,105,108,111],[103,104],"0.08206 L·atm/(mol·K)","P in atm, V in L",[106,107],"8.314 J/(mol·K)","SI; and all u_rms / KMT speeds",[109,110],"0.08314 L·bar/(mol·K)","P in bar, V in L",[112,113],"62.36 L·torr/(mol·K)","P in torr, V in L","80fea458a5265cdcbe8c39433ec76d0cf82a314ddaa70afc207cb6eccb1f7ee0",{"heading":116,"kind":77,"items":117},"Molar mass & density",[118],{"ref":119,"mode":19,"provenance":20,"text":121,"source_hash":122},{"type":17,"topic":7,"id":120,"field":17},"GL-R010","M = mRT/(VP); density ρ = PM/(RT). At STP one mole occupies 22.4 L, so ρ_STP = M / 22.4 (g/L). Match R to the pressure unit.","b3764f696226cea9efbb3fb92fca08b66ad90a7f9e9318a1a77644a34a821cea",{"heading":124,"kind":77,"items":125},"Partial pressures (Dalton)",[126],{"ref":127,"mode":19,"provenance":20,"text":129,"source_hash":130},{"type":17,"topic":7,"id":128,"field":17},"GL-R011","P_total = Σ P_partial. Mole fraction X_A = n_A/n_total = P_A/P_total, so P_A = X_A·P_total. Gas over water: P_gas = P_total − P_H₂O(T) (supplied).","7a57310019908eebb57721a043282d6de82862688f409cff54a31119a90e4792",{"heading":132,"kind":77,"items":133},"Molecular speeds",[134],{"ref":135,"mode":19,"provenance":20,"text":137,"source_hash":138},{"type":17,"topic":7,"id":136,"field":17},"GL-R012","u_rms = √(3RT/M), with M in kg/mol and R = 8.314 to get m/s. Ratio (same T): u_rms,A / u_rms,B = √(M_B/M_A). (Mean = √(8RT/πM); most probable = √(2RT/M).)","d42c9a6453de2b2d6bc38793350ef03731e9e0e5fcb68fa47da9880f084a003b",{"heading":140,"kind":77,"items":141},"Graham's law",[142],{"ref":143,"mode":19,"provenance":145,"text":146,"source_hash":147},{"type":17,"topic":7,"id":144,"field":17},"GL-R014","original","Effusion/diffusion: rate_A / rate_B = √(M_B/M_A): lighter gases move faster. Time scales the other way: time_A / time_B = √(M_A/M_B). Same temperature required.","8c24ac4b60c941b68e7b0b9cee79e21331b251905f4cc2201aa734e1938ec797",{"heading":149,"kind":150,"items":151},"Gas stoichiometry","steps",[152],{"ref":153,"mode":19,"provenance":20,"text":155,"source_hash":156},{"type":17,"topic":7,"id":154,"field":17},"GL-R013","mass → moles → mole ratio → moles of gas → V via PV=nRT (or 22.4 L/mol at STP). If reactants and products are all gases at the same T, P, mole ratios equal volume ratios directly.","3726a3c986987a2da4f73ba0eebdbc4392c371f948a613346342303ccfa4eed4",1787246033483]