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化学
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化学方程式配平
Balancing a chemical equation
原子矩阵的精确整数零空间 · 每种元素守恒
Exact integer nullspace of the atom matrix · every element conserved
三维分子模型 · 球棍模型
3D molecular model · ball-and-stick
原子位置来自理想 VSEPR 构型 —— 拖动可旋转
Atom positions from ideal VSEPR geometry — drag to rotate
Lewis 电子式 · 路易斯结构
Lewis structures · electron dot diagrams
成键对 + 孤对必须覆盖全部价电子
Bonds + lone pairs must account for every valence electron
分子轨道能级图 · 双原子分子
Molecular-orbital diagram · diatomics
填充分子轨道 → 键级与磁性随之确定
Fill the MO ladder → bond order & magnetism follow
键型与极性 · 电负性
Bond type & polarity · electronegativity
电负性差决定键型;几何构型决定分子净偶极
ΔEN sets the bond; geometry sets the molecule's net dipole
晶体点阵 · 晶胞
Crystal lattices · unit cells
由各结构的分数坐标生成 —— 拖动可旋转
Generated from each structure's fractional coordinates — drag to rotate
原子轨道形状 · s / p / d
Atomic orbital shapes · s / p / d
每个形状都是角向波函数的精确极坐标图
Each shape is the exact polar plot of the angular wavefunction
查理定律 · V = kT(恒压)
Charles' law · V = kT (constant pressure)
恒压下体积与热力学温度成正比(T 为开尔文温度)
At constant P, volume ∝ absolute temperature (T in kelvin)
指数衰减 N(t) = N₀·e^(−kt)
Exponential decay N(t) = N₀·e^(−kt)
放射性衰变 / 一级反应 · 半衰期 = ln2/k
Radioactive decay / first-order reaction · half-life = ln2/k
玻意耳定律 · P = k/V(等温线)
Boyle's law · P = k/V (isotherm)
恒温下压强与体积成反比 · PV = k
At constant T, pressure ∝ 1/volume · PV = k
滴定曲线 · pH–体积
Titration curve · pH vs volume
强酸 + 强碱 · 在等当点(pH 7)附近陡然突跃
Strong acid + strong base · sharp jump at the equivalence point (pH 7)
麦克斯韦–玻尔兹曼速率分布
Maxwell–Boltzmann speed distribution
各速率上的分子数占比 · 温度越高,峰越靠右且越矮
Fraction of molecules at each speed · higher T shifts the peak right and flattens it
化学平衡 · 勒夏特列原理
Chemical equilibrium · Le Chatelier's principle
A ⇌ B · 改变条件,平衡向削弱这一改变的方向移动
A ⇌ B · a stress on the system is opposed by a shift in the equilibrium
反应能量图(活化能与反应热)
Reaction energy profile
反应物越过活化能 Ea 的势垒到达生成物;ΔH = 生成物 − 反应物
Reactants climb the activation barrier Ea, then fall to products; ΔH = products − reactants
pH 值 · 酸碱度
pH scale · acidity
pH = −log[H⁺] · 每变化 1 个单位,[H⁺] 相差 10 倍
pH = −log[H⁺] · each unit is a 10× change in [H⁺]
溶液稀释 · C₁V₁ = C₂V₂
Dilution · C₁V₁ = C₂V₂
加入溶剂只降低浓度,溶质的物质的量不变
Adding solvent lowers the concentration but not the amount of solute
玻尔模型 · 氢原子能级
Bohr model · hydrogen energy levels
Eₙ = −13.6/n² eV · 跃迁向下发射光子 λ = 1240/ΔE nm
Eₙ = −13.6/n² eV · a jump down emits a photon λ = 1240/ΔE nm
原电池 · 电化学
Galvanic cell · electrochemistry
较活泼的金属被氧化;E°cell = E°(正极) − E°(负极)
The more reactive metal is oxidised; E°cell = E°cathode − E°anode
ICE 表 · 平衡浓度计算
ICE table · equilibrium concentrations
A ⇌ B + C · 由 K = x²/(A₀−x) 解出反应进度 x
A ⇌ B + C · solve K = x²/(A₀−x) for the extent of reaction x
周期表趋势
Periodic trends
元素性质随周期重复出现 —— 这正是元素周期律的本质
Properties repeat period by period — the essence of the periodic law
缓冲溶液 · 亨德森方程
Buffer solution · Henderson–Hasselbalch
pH = pKa + log([A⁻]/[HA]) · 缓冲溶液抵抗 pH 变化
pH = pKa + log([A⁻]/[HA]) · a buffer resists pH change
价层电子对互斥(VSEPR)· 分子构型
VSEPR · molecular geometry
价层电子对相互排斥而尽量分开;孤对电子使构型弯折
Electron pairs repel to spread out; lone pairs bend the shape
摩尔质量计算器
Molar mass calculator
化学式解析 · 摩尔质量 / 相对分子质量 · 质量分数
Parse the formula → sum count × atomic mass → per-element mass %
限量试剂与产率
Limiting reagent & yield
限量试剂 / 过量 · 理论产量 · 产率
moles ÷ coefficient → smallest wins → theoretical mass, excess, % yield
吉布斯自由能与自发性
Gibbs free energy & spontaneity
ΔG=ΔH−TΔS · 自发性判据 · 转折温度
ΔG = ΔH − TΔS · sign of ΔG decides · crossover at T = ΔH/ΔS
理想气体与组合气体定律
Ideal & combined gas law
PV=nRT · 组合气体定律 P₁V₁/T₁=P₂V₂/T₂
PV = nRT (R = 0.0821 L·atm/mol·K) · and P₁V₁/T₁ = P₂V₂/T₂
能斯特方程
Nernst equation
E=E°−(0.0592/n)logQ · 非标准电势 · 由 E° 求 K
E = E° − (0.0592/n)·log Q at 298 K · general RT/nF otherwise
阿伦尼乌斯方程 · k = A·e^(−Ea/RT)
Arrhenius equation · k = A·e^(−Ea/RT)
k=A·e^(−Ea/RT) · ln k–1/T 直线 · 活化能/催化
How temperature and activation energy set the rate constant
比尔-朗伯定律 · A = ε·b·c
Beer-Lambert law · A = ε·b·c
A=εbc · %T=100·10^−A · 标准曲线/比色皿
Absorbance, transmittance and the spectrophotometric calibration
晶体场理论 · d 轨道分裂
Crystal field splitting
Δo/Δt 分裂 · 高/低自旋 · CFSE
Ligand field splits the d orbitals · high-spin vs low-spin from Δ vs P · CFSE
法拉第电解定律
Faraday's laws of electrolysis
m=I·t·M/(nF) · 电荷 Q · 析出质量/气体
Charge Q = I·t → moles of electrons → deposited mass and gas volume
依数性(colligative properties)
Colligative properties
ΔTb=i·Kb·m · ΔTf=i·Kf·m · 渗透压 Π
Boiling-point elevation, freezing-point depression & osmotic pressure
溶度积 Ksp 与同离子效应
Solubility product Ksp & common-ion effect
Ksp=xˣ·yʸ·sⁿ · 同离子效应 · Q vs Ksp
Molar solubility from Ksp · common-ion suppression · Q-vs-Ksp precipitation test
氧化还原配平 · 半反应法
Redox balancing by half-reactions
氧化/还原半反应 · 电子平衡 · 酸/碱介质
Split into oxidation & reduction halves · balance atoms, H₂O/H⁺ (or OH⁻), charge · combine
玻恩-哈伯循环 · 晶格能
Born-Haber cycle · lattice energy
升华/电离/EA/晶格能 · 盖斯求 U
Hess's law on an ionic solid: solve any term (usually lattice energy U)
反应级数与积分速率方程
Reaction order & integrated rate laws
0/1/2 级 · 积分速率方程 · 半衰期/线性化
How order shapes the decay curve and which plot goes straight
电子排布 · 构造原理
Electron configuration
Aufbau/洪特/泡利 · 轨道图 · Cr/Cu 例外
Aufbau order · Pauli exclusion · Hund's rule of maximum multiplicity
拉乌尔定律 · 理想溶液
Raoult's law · ideal solution
P=xA·P°A+xB·P°B · 分压 · 气相组成 yA
Total & partial vapour pressures · vapour composition differs from the liquid
盖斯定律 · 反应焓的加和
Hess's law · enthalpy summation
反应焓加和 · 能量循环 · 多步求 ΔH
Combine step reactions to reach a target; ΔH is path-independent
Organic functional groups
Organic functional groups
−OH/C=O/−COOH/−NH2/酯/醚/卤代 · 族名+后缀
The reactive atom-cluster fixes the family, the reactions and the IUPAC naming suffix.
Structural isomers
Structural isomers
同分子式不同连接 · C4H10正/异丁烷 · 计数
Same molecular formula, different connectivity → different compounds.
Naming a hydrocarbon (IUPAC)
Naming a hydrocarbon (IUPAC)
IUPAC · 最长链母体+取代基+最低编号 · 组装
Find the longest chain → number for lowest locants → name substituents → assemble.
Chirality & enantiomers
Chirality & enantiomers
手性碳=四不同基团 · 镜像不可重叠 · R/S · CIP
A carbon with four different groups is a chiral centre — its mirror image cannot be superimposed.
Optical activity of enantiomers
Optical activity of enantiomers
对映体等量反向旋光± · 外消旋净=0 · 旋光仪
α = [α] · (f₊ − f₋) — enantiomers rotate polarised light by equal, opposite angles; racemic → 0.
E / Z isomerism at C=C
E / Z isomerism at C=C
C=C受限旋转 · 高优先基同侧Z反侧E · CIP
Compare CIP priority on each carbon: higher-priority groups on the same side = Z, opposite sides = E.
SN1 vs SN2 · nucleophilic substitution
SN1 vs SN2 · nucleophilic substitution
SN1两步碳正外消旋 vs SN2一步背面进攻翻转
Nu⁻ replaces the leaving group X — one concerted step (SN2) or via a carbocation (SN1)
Markovnikov's rule · HX addition to alkenes
Markovnikov's rule · HX addition to alkenes
HX加烯烃 · H加多H碳 · 更稳定碳正离子决定
H adds to the double-bond carbon with MORE hydrogens; X ends up on the more substituted carbon
Fischer esterification · acid + alcohol ⇌ ester + water
Fischer esterification · acid + alcohol ⇌ ester + water
Fischer · 羧酸+醇⇌酯+水 · 酸催化 · 可逆
The acid's –OH and the alcohol's –H leave as water, joining acyl to alkoxy through the ester bond
Benzene resonance & aromaticity
Benzene resonance & aromaticity
6π离域 · 两Kekulé↔杂化 · 等键长 · 芳香稳定
Six delocalized π electrons · one hybrid, equal C−C bonds
Addition polymerization
Addition polymerization
单体C=C打开连链 · 乙烯→聚乙烯 · 聚合度n
n · CH₂=CHX → −(CH₂−CHX)−ₙ · the C=C opens and links into a chain
Alkane conformations (Newman projection)
Alkane conformations (Newman projection)
Newman投影 · 交叉式低能vs重叠式高能 · 二面角能量
Rotate about a C−C bond · staggered (low energy) vs. eclipsed (high energy)