📚 Reactions 1.2.1 - Acids, Alkalis and pH | 酸、碱与pH的反应机理
Understanding how acids, alkalis and the pH scale interconnect is fundamental to mastering chemical reactivity. This article explores the reaction mechanisms that govern proton transfer, electron‑pair donation, and the dynamic equilibria in aqueous systems. We will examine the step‑by‑step processes behind neutralisation, hydrolysis, and the behaviour of strong versus weak species, providing a clear mechanistic picture suitable for advanced revision.
理解酸、碱与pH标度之间的相互联系是掌握化学反应性的基础。本文探讨了控制质子转移、电子对给予以及水相体系中动态平衡的反应机理。我们将逐步研究中和反应、水解过程以及强物种与弱物种行为背后的分步过程，为进阶复习提供清晰的机理图景。
1. Defining Acids and Alkalis in Terms of Reaction Mechanisms | 从反应机理角度定义酸与碱
Before diving into mechanisms, we must define the species involved. The earliest operational definition came from Arrhenius: an acid ionises in water to produce H⁺, while an alkali produces OH⁻. This view captures the outcome of many reactions but does not explain the electron‑level pathway. A more mechanistic perspective is offered by Brønsted and Lowry, who define an acid as a proton donor and a base as a proton acceptor, allowing us to trace the movement of a single hydrogen nucleus from one species to another.
在深入机理之前，我们必须定义涉及的物种。最早的操作性定义来自阿伦尼乌斯：酸在水中电离产生H⁺，而碱产生OH⁻。这一观点捕捉了许多反应的结果，但并未解释电子层面的反应途径。布朗斯特和劳里提供了更具机理性的视角，他们将酸定义为质子给体，碱定义为质子受体，使我们能够追踪单个氢核从一个物种转移到另一个物种的运动。
The Lewis theory extends this mechanistic vision to cover reactions where no proton is exchanged. A Lewis acid is an electron‑pair acceptor, capable of accepting a lone pair into an empty orbital, while a Lewis base is an electron‑pair donor. This framework is essential for understanding reactions like the formation of coordinate bonds in complex ions or the behaviour of compounds such as BF₃, which acts as an acid without possessing any hydrogen.
路易斯理论将这种机理视野扩展到没有质子交换的反应中。路易斯酸是电子对受体，能够将孤对电子接收到空轨道中，而路易斯碱是电子对给体。这一框架对于理解配合物中配位键的形成或像BF₃这类不含氢的化合物的行为至关重要，BF₃可作为酸发挥功能。
2. The Proton Transfer Mechanism in Water | 水中的质子转移机理
The key mechanistic step in any Brønsted acid–base reaction is the transfer of a proton from the acid to the base. In aqueous solution, this is rarely a simple leap of a bare H⁺ through the solvent; instead, water molecules participate actively. Proton transfer often proceeds through a Grotthuss‑type structural diffusion, where a hydronium ion H₃O⁺ passes a proton along a hydrogen‑bonded network without the bulk movement of the oxygen atoms. The excess proton “hops” from one water molecule to the next via consecutive breaking and forming of O–H bonds, a process with a remarkably low activation energy.
任何布朗斯特酸碱反应的关键机理步骤都是质子从酸向碱的转移。在水溶液中，这极少表现为一个裸露的H⁺在溶剂中的简单跳跃；相反，水分子积极参与其中。质子转移通常通过格罗特胡斯型结构扩散进行，在此过程中，水合氢离子H₃O⁺沿着氢键网络传递质子，而氧原子本身并不发生整体移动。多余的质子通过O–H键的连续断裂和形成从一个水分子“跳跃”到下一个水分子，该过程的活化能显著偏低。
This mechanism explains why reactions like HCl dissolving in water are extremely fast. The HCl molecule first transfers its proton to a neighbouring H₂O molecule, forming H₃O⁺ and Cl⁻. The newly formed hydronium immediately becomes part of the hydrogen‑bonded chain, and the excess positive charge is rapidly delocalised through the Grotthuss pathway. Consequently, neutralisation reactions between strong acids and strong bases appear instantaneous at the macroscopic scale because the proton transfer network operates on a picosecond timescale.
这一机理解释了为何HCl溶解于水的反应极其迅速。HCl分子首先将其质子转移给邻近的H₂O分子，形成H₃O⁺和Cl⁻。新生成的水合氢离子立即成为氢键网络的一部分，多余的正电荷通过格特罗胡斯途径迅速离域。因此，强酸与强碱之间的中和反应在宏观尺度上看起来是瞬时的，因为质子传递网络在皮秒时间尺度上运行。
3. Autoionisation of Water and the Ionic Product Mechanism | 水的自电离与离子积机理
Mechanistically, two water molecules undergo a proton transfer: one molecule acts as a Brø reaction is reversible, and both forward and reverse processes involve the same Grotthuss‑ quilibrium constant Kₑq gives the ionic product Kₑq = [H₃O⁺][OH⁻] = 1.0 × 10⁻¹⁴ mol² dm⁻⁶.
纯水表现出自电离，这是一个为pH标度建立基线的根本性平衡。从机理上讲，两个水分子发生质子转移：一个分子充当布朗斯特酸，给出质子，而另一个分子充当碱，接受质子。这产生一个水合氢离子H₃O⁺和一个氢氧根离子OH⁻。该反应是可逆的，正向和逆向过程都涉及相同的格罗特胡斯辅助跳跃。在298 K时，平衡常数Kₑq给出离子积Kₑq = [H₃O⁺][OH⁻] = 1.0 × 10⁻¹⁴ mol² dm⁻⁶。
ium concentration reflects a dynamic steady state. Whenever an acid is added, it donates protons, momentarily increasing [H₃O⁺]; the system shifts left, consuming OH⁻ via recombination. This mechanistic coupling between hydronium and hydroxide concentrations is what gives every aqueous solution a strict inter‑dependence of [H⁺] and [OH⁻], ultimately expressed in the pH definition: pH = –log₁₀[H⁺].
必须理解的是，由于持续的质子交换，任何单个H₃O⁺或OH⁻离子的寿命都极其短暂。平衡浓度反映的是一种动态稳态。每当加入酸时，它会给出质子，瞬间提高[H₃O⁺]；体系向左移动，通过复合消耗OH⁻。水合氢离子浓度与氢氧根离子浓度之间的这种机理耦合，赋予了每一种水溶液[H⁺]与[OH⁻]之间严格的相互依赖关系，并最终体现在pH的定义中：pH = –log₁₀[H⁺]。
4. Mechanism of Strong Acid and Strong Base Dissociation | 强酸与强碱的解离机理
A strong acid such as HCl, HNO₃, or H₂SO₄ (first dissociation) undergoes complete proton transfer to water. The mechanism begins when the polar H–A bond interacts with the lone pair on a water oxygen. The proton is transferred in a concerted or near‑concerted fashion, with the breaking of the H–A bond and the formation of the H–O bond occurring simultaneously. The resulting conjugate base (Cl⁻, NO₃⁻, HSO₄⁻) is a very weak base, meaning it has negligible tendency to recapture a proton. Because the reverse reaction is essentially absent, the forward proton transfer goes to completion; this is why the acid is classified as “strong” in mechanistic terms.
像HCl、HNO₃或H₂SO₄（第一步解离）这样的强酸会向水发生完全的质子转移。反应机理始于极性的H–A键与水分子的氧上孤对电子相互作用。质子的转移以协同或近乎协同的方式进行，H–A键的断裂与H–O键的形成同时发生。所产生的共轭碱（Cl⁻、NO₃⁻、HSO₄⁻）是非常弱的碱，这意味着它重新捕获质子的倾向可以忽略不计。由于逆反应基本不存在，正向质子转移得以进行到底；这就是从机理角度将这类酸归类为“强”的原因。
For strong alkalis such as NaOH or KOH, the mechanism involves an existing ionic lattice that dissolves with the release of solvated OH⁻ ions. The solid’s ionic bonds are overcome by hydration energy, and the separated hydroxide ion is free to act as a potent proton acceptor. In water, OH⁻ also participates in the Grotthuss network, but as a proton‑abstracting species. The anionic oxygen readily forms a bond with a hydrogen from a neighbouring water or hydronium ion, completing any neutralisation via the same hopping‑and‑transfer mechanism.
对于NaOH或KOH等强碱，反应机理涉及原有的离子晶格溶解，并释放出溶剂化的OH⁻离子。固体的离子键被水合能所克服，分离出来的氢氧根离子能够自由地充当强效的质子受体。在水中，OH⁻同样参与格罗特胡斯网络，但作为一个攫取质子的物种。带负电的氧原子极易与邻近的水分子或水合氢离子中的氢形成键，通过相同的跳跃转移机理完成任何中和过程。
5. Weak Acids and the Equilibrium Protonation Mechanism | 弱酸与平衡质子化机理
Weak acids such as ethanoic acid CH₃COOH do not fully transfer their proton to water; instead, a dynamic equilibrium is established. The mechanistic difference lies in the stability of the conjugate base. When CH₃COOH donates a proton to H₂O, the resulting acetate ion CH₃COO⁻ is relatively stable and possesses sufficient basicity to recapture a proton from H₃O⁺. Thus, the forward proton transfer and the reverse protonation occur at comparable rates, leading to an equilibrium mixture that contains appreciable concentrations of both the molecular acid and its dissociated ions.
像乙酸CH₃COOH这样的弱酸并不会将质子完全转移给水，而是建立起一个动态平衡。机理上的差异在于共轭碱的稳定性。当CH₃COOH将质子提供给H₂O时，生成的乙酸根离子CH₃COO⁻相对稳定，并具有足够的碱性，能够从H₃O⁺处重新捕获质子。因此，正向质子转移和逆向质子化以可比拟的速率进行，导致平衡混合物中含有可观浓度的分子态酸及其解离离子。
A]. On a molecular scale, individual CH₃COOH molecules undergo a continuous cycle of deprotonation and reprotonation. The mechanistic hallmark of a weak acid is the presence of a significant activation barrier for the reverse protonation step – molecular orbital capability to host the proton again. This also explains why dilution shifts the equilibrium to the right: with a larger volume, the probability of a hydronium ion encountering an acetate ion decreases, favouring dissociation.
平衡常数Kₐ量化了这一平衡：Kₐ = [H₃O⁺][A⁻]/[HA]。在分子尺度上，单个CH₃COOH分子经历着去质子化与再质子化的连续循环。弱酸的机理标志在于逆向质子化步骤存在一个显著的概率屏障——并非能量上的屏障，而是因为共轭碱确实具有接受质子的分子轨道能力，从而使质子化容易发生。这也解释了为什么稀释会使平衡向右移动：随着体积增大，水合氢离子遇到乙酸根离子的概率降低，从而有利于解离。
6. Weak Bases and the Hydrolysis Mechanism | 弱碱与水解机理
Weak bases, such as ammonia NH₃ or amines, accept protons only partially from water. The mechanistic step involves the lone pair on the nitrogen atom attacking a hydrogen atom of a water molecule. This leads to a transition state where the O–H bond is lengthening as the N–H bond forms. The resulting products are the ammonium ion NH₄⁺ and OH⁻. Because the reverse reaction – deprotonation of NH₄⁺ by OH⁻ – is also feasible, an equilibrium arises, described by the base dissociation constant Kₑ.
如氨NH₃或胺一类的弱碱只能部分地接受来自水的质子。其反应机理步骤包括氮原子上的孤对电子进攻水分子中的一个氢原子。这导致一个过渡态的形成，其中O–H键正在伸长，而N–H键正在形成。结果是生成铵离子NH₄⁺和OH⁻。由于逆向反应——NH₄⁺被OH⁻去质子化——同样可行，因此会产生一个平衡，该平衡用碱解离常数Kₑ来描述。
The same mechanistic logic applies to the conjugate bases of weak acids, such as the acetate ion. When sodium acetate dissolves in water, the acetate ion acts as a Brønsted base, accepting a proton from water to form CH₃COOH and OH⁻. This is often called hydrolysis, but it is fundamentally a proton transfer from the water molecule to the base. The pH of such a salt solution rises above 7 because the equilibrium produces excess hydroxide ions. Understanding this mechanism is critical for predicting the acidity or basicity of salt solutions.
相同的机理逻辑也适用于弱酸的共轭碱，例如乙酸根离子。当乙酸钠溶于水时，乙酸根离子充当布朗斯特碱，接受水分子中的质子，形成CH₃COOH和OH⁻。这通常被称为水解，但本质上是从水分子到碱的质子转移。这种盐溶液的pH会升至7以上，因为该平衡产生了过量的氢氧根离子。理解这一机理对于预测盐溶液的酸碱性至关重要。
7. The Mechanism of Neutralisation: More than Mixing | 中和反应机理：远不止于混合
e mechanistic reality, however, is a concerted proton transfer between a hydrated proton (often represented as H₉O₄⁺ or an Eigen cation) and a hydroxide ion that also carries its own solvation shell. When the two approach within a critical distance, a hydrogen‑ed structure forms in which a central H is positioned between two oxygen atoms. The double‑ o transfer very rapidly, releasing a substantial amount of energy as the strong covalent O–H bond is formed.
水溶液中酸与碱的中和反应通常被写作H⁺ + OH⁻ → H₂O。然而，机理现实是水合质子（通常表示为H₉O₄⁺或特征阳离子）与同样携带着自身溶剂化层的氢氧根离子之间的协同质子转移。当两者接近到临界距离时，会形成一个氢键结构，其中一个中心氢位于两个氧原子之间。双阱势能使质子能够非常迅速地转移，并随着强共价O–H键的形成释放出大量能量。
This explains the characteristic exothermic nature of neutralisation: the enthalpy of neutralisation for strong acids with strong bases is approximately –57 kJ mol⁻¹, almost independent of the specific acid or base. This constant value arises because the only net chemical change is the formation of water molecules from hydronium and hydroxide ions. The spectator ions (Na⁺, Cl⁻, etc.) do not participate in the proton transfer and merely balance the charge, so the mechanism and its energy profile remain unchanged.
这解释了中和反应特征性的放热性质：强酸与强碱的中和焓约为–57 kJ mol⁻¹，几乎与具体的酸或碱无关。这一恒定值的出现是因为唯一的净化学变化是水分子由水合氢离子和氢氧根离子形成。旁观离子（Na⁺、Cl⁻等）不参与质子转移，仅起到平衡电荷的作用，因此反应机理及其能量分布保持不变。
8. Reaction of Acids with Metals and Carbonates: Electron‑Transfer Link | 金属与酸及碳酸盐的反应：电子转移的关联
When an acid reacts with a reactive metal such as zinc or magnesium, the overall process involves both acid–base and redox mechanisms. The first step is a Brønsted acid–base interaction: the metal surface acts as a Brønsted base, abstracting protons from hydronium ions. However, simultaneous electron transfer from the metal atom to the proton is required to form hydrogen gas. A zinc atom donates two electrons to two H₃O⁺ ions, generating Zn²⁺ and H₂. The mechanism therefore proceeds via a combined proton–electron transfer, a concept central to modern electrochemistry.
当酸与活泼金属如锌或镁反应时，整个过程同时涉及酸碱和氧化还原机理。第一步是布朗斯特酸碱相互作用：金属表面充当布朗斯特碱，从水合氢离子中攫取质子。然而，同时还需要从金属原子向质子传输电子，才能形成氢气。一个锌原子向两个H₃O⁺离子提供两个电子，生成Zn²⁺和H₂。因此，该机理通过一个联合的质子-电子转移过程进行，这是现代电化学的核心概念。
The reaction of acids with carbonates has a different mechanistic pathway. The carbonate ion CO₃²⁻ first accepts a proton to become hydrogen carbonate HCO₃⁻, a fast Brønsted acid–base step. Then, a second protonation on the HCO₃⁻ leads to the formation of carbonic acid H₂CO₃, which is unstable and decomposes into CO₂ and H₂O. The decomposition step is a unimolecular reaction with a distinct activation barrier. This is why effervescence is observed: the slowest step is often the collapse of H₂CO₃ into the gas and water, rather than the initial proton transfers.
酸与碳酸盐的反应遵循不同的反应机理路径。碳酸根离子CO₃²⁻首先接受一个质子变成碳酸氢根HCO₃⁻，这是一个快速的布朗斯特酸碱步骤。然后，第二个质子加到HCO₃⁻上，导致形成碳酸H₂CO₃，该分子不稳定，会分解为CO₂和H₂O。分解步骤是一个具有明显活化势垒的单分子反应。这就是为何能观察到冒泡现象：最慢的步骤通常是H₂CO₃分解为气体和水，而非最初的质子转移过程。
9. pH Curves and the Mechanical Meaning of Buffer Regions | pH曲线与缓冲区的机理意义
Plotting pH against the volume of added alkali during a titration reveals distinct mechanistic regions. Before any titrant is added, the pH is determined by the dissociation equilibrium of the weak acid (or the free H⁺ concentration of a strong acid). As strong base is added, the OH⁻ consumes free H₃O⁺, shifting the HA dissociation equilibrium rapidly to the right. The pH rises slowly in the buffer region because the solution contains a mixture of HA and A⁻. Here, any added OH⁻ is neutralised by HA, while added H⁺ is absorbed by A⁻, with minimal overall change in pH.
在滴定过程中绘制pH随加入碱体积变化的曲线，可以揭示出不同的机理区域。在加入任何滴定剂之前，pH由弱酸的解离平衡（或强酸中游离H⁺的浓度）决定。当加入强碱时，OH⁻消耗游离的H₃O⁺，使HA的解离平衡迅速向右移动。在缓冲区中，pH缓慢上升，因为溶液中含有HA与A⁻的混合物。在此区域中，任何加入的OH⁻会被HA中和，而加入的H⁺则被A⁻吸收，从而使pH的整体变化极小。
At the equivalence point, the predominant species is the conjugate base A⁻, and the pH is governed by the hydrolysis mechanism described earlier. The steep rise in pH near equivalence reflects the exhaustion of the buffer: once all HA has been converted to A⁻, even a drop of excess base causes a dramatic increase in pH. Mechanistically, this is the transition from a proton‑buffered environment to one where free OH⁻ dominates. Understanding these zones is essential for selecting appropriate indicators whose colour‑change intervals match the steep part of the curve.
在等当点时，主要物种是共轭碱A⁻，pH由此前描述的水解机理所决定。接近等当点时pH的急剧上升反映了缓冲体系的耗尽：一旦所有HA都转化为A⁻，即使是一滴过量的碱也会导致pH的剧烈升高。从机理上讲，这是从质子缓冲环境向游离OH⁻主导环境的过渡。理解这些区域对于选择合适的指示剂至关重要，指示剂的变色区间必须与曲线陡峭部分相匹配。
10. Buffer Solutions: A Dynamic Molecular‑Level Mechanism | 缓冲溶液：动态分子水平机理
A buffer works on the principle of a conjugate acid–base pair that can mop up both added H⁺ and OH⁻. In an ethanoic acid / sodium ethanoate buffer, the two key molecular events are: (i) when a strong acid is added, the hydronium ions react with acetate ions to form ethanoic acid molecules, effectively removing the extra H⁺ from solution; (ii) when a base is added, the hydroxide ions react with ethanoic acid molecules to produce acetate ions and water. The rates of these proton transfers are extremely fast, so the system adjusts almost instantly.
缓冲溶液的工作原理基于一对共轭酸碱对能够清扫加入的H⁺和OH⁻。在乙酸/乙酸钠缓冲溶液中，两个关键的分子事件是：(i) 当加强酸时，水合氢离子与乙酸根离子反应生成乙酸分子，从而有效地从溶液中移除多余的H⁺；(ii) 当加碱时，氢氧根离子与乙酸分子反应生成乙酸根离子和水。这些质子转移的速率极快，因此体系几乎是即时作出调整。
The ratio of [HA] to [A⁻] determines the pH according to the Henderson–Hasselbalch equation. Mechanistically, this means the probability of a hydronium ion encountering an acetate ion versus an ethanoic acid molecule is set by their relative concentrations. The buffer’s capacity is exhausted when one component is completely consumed; after that, the solution behaves as a simple solution of a weak acid or a weak base, and the pH changes more dramatically upon further addition.
[HA]与[A⁻]的比值根据亨德森-哈塞尔巴尔赫方程决定pH。从机理上讲，这意味着水合氢离子遇到乙酸根离子的概率与遇到乙酸分子的概率由它们的相对浓度所决定。当某一组分被完全消耗时，缓冲容量便耗尽；此后，溶液表现为单纯的弱酸或弱碱溶液，继续加入试剂时pH的变化会更为剧烈。
11. Lewis Acid–Base Mechanisms Beyond the Proton | 超越质子的路易斯酸碱机理
Many important reaction mechanisms in inorganic and organic chemistry do not involve protons at all. For instance, the formation of the tetraamminecopper(II) ion [Cu(NH₃)₄]²⁺ from Cu²⁺ and ammonia is a Lewis acid–base reaction. The Cu²⁺ ion, with empty 4s and 4p orbitals, acts as an electron‑pair acceptor. Each ammonia molecule donates its lone pair into the metal’s vacant orbitals, forming a coordinate or dative covalent bond. The mechanism proceeds stepwise, with each successive ligand association replacing water molecules in the copper’s inner hydration sphere.
无机与有机化学中许多重要的反应机理完全不涉及质子。例如，由Cu²⁺与氨形成四氨合铜(II)离子[Cu(NH₃)₄]²⁺就是一个路易斯酸碱反应。Cu²⁺离子具有空的4s和4p轨道，充当电子对受体。每个氨分子将其孤对电子提供到金属的空轨道中，形成配位键或配位共价键。该反应机理分步进行，每个后续配体的结合都会置换铜内层水合球中的水分子。
classic example is the reaction between boron trifluoride BF₃ and ammonia. BF₃ is electron‑ the empty p orbital of boron, forming a N→B dative bond. This mechanism is purely orbital‑ c understanding of catalysis, complexation, and many organic functional group transformations.
另一个经典例子是三氟化硼BF₃与氨的反应。BF₃在硼原子处是缺电子的，其价层只有六个电子。NH₃将其孤对电子提供给硼的空p轨道，形成一个N→B配位键。这一机理纯粹由轨道驱动，并说明了酸性和碱性是比质子交换更为广泛的概念。因此，路易斯定义为理解催化作用、配合作用以及许多有机官能团转化提供了机理性的视角。
12. Summary of Key Mechanistic Principles for Revision | 复习用关键机理原则总结
Across all the systems discussed, three underlying mechanistic themes emerge. First, proton transfer is rarely a simple jump but involves organised solvent networks, leading to the rapid equilibration of hydronium and hydroxide ions. Second, the strength of an acid or base is a direct reflection of the position of the proton‑transfer equilibrium; complete dissociation occurs when the conjugate partner is extremely stable and unreactive. Third, buffer action and pH control are dynamic, probability‑based phenomena that depend on the relative populations of conjugate species.
在讨论的所有体系中，浮现出三个根本性的机理主题。首先，质子转移很少是简单的跳跃，而是涉及有组织的溶剂网络，导致水合氢离子和氢氧根离子的快速平衡。其次，酸或碱的强度直接反映了质子转移平衡的位置；当共轭伙伴极其稳定且不活泼时，便发生完全解离。第三，缓冲作用与pH控制是动态的、基于概率的现象，取决于共轭物种的相对种群数量。
When revising, it is helpful to visualise the molecular scenario: picture the acid HA approaching a water molecule, the hydrogen atom in transit, the momentary negative charge developing on A⁻, and the subsequent competition for the proton. This dynamic picture unifies the Arrhenius, Brønsted, and Lewis views into a single coherent reaction‑mechanism framework. Mastering these ideas will equip you to predict the outcome of countless reactions, interpret titration curves accurately, and understand the chemical basis of pH regulation in biological and industrial systems.
复习时，在脑海中勾画出分子场景会很有帮助：想象酸HA靠近一个水分子，氢原子正在转移中，A⁻上出现瞬时的负电荷，以及随后对质子的竞争。这一动态图景将阿伦尼乌斯、布朗斯特和路易斯的观点统一为一个连贯的反应机理框架。掌握这些思想将使你能够预测无数反应的结果、准确解释滴定曲线，并理解生物和工业体系中pH调节的化学基础。
| Theory | Key Mechanistic Focus | Example |
|---|---|---|
| Arrhenius | Ionisation yielding H⁺ or OH⁻ | HCl → H⁺ + Cl⁻ |
| Brønsted–Lowry | Proton transfer step | HA + H₂O ⇌ A⁻ + H₃O⁺ |
| Lewis | Electron‑pair acceptance / donation | BF₃ + NH₃ → F₃B–NH₃ |
pH = –log₁₀[H₃O⁺] Kₐ = [H₃O⁺][A⁻]/[HA] Kₑq = [H₃O⁺][OH⁻] = 1.0 × 10⁻¹⁴
Published by TutorHao | Chemistry Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
或截图后用「扫一扫 → 相册」选择本图