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ATP is a nucleotide consisting of adenosine, itself adenine joined to ribose, carrying three phosphate groups. From the ribose outward, these groups are labelled $\alpha$, $\beta$, and $\gamma$. ATP connects energy-supplying processes to energy coupling for synthesis and active transport; the same carrier can be regenerated and reused. ^[ref].

The net hydrolysis commonly used in energy coupling isHere ${\mathrm{P}}_i$ denotes inorganic phosphate. At buffered pH $7$, this biochemical shorthand groups the appropriate protonation states into pools and leaves proton exchange with the buffer solution implicit. An explicit, charge-balanced choice is ${\mathrm{ATP}}^{4-}+{\mathrm{H}}_2\mathrm{O}⟶{\mathrm{ADP}}^{3-}+{\mathrm{HP}{\mathrm{O}}_4}^{2-}+{\mathrm{H}}^{+}$, without implying these are the only chemical species present. See the IUBMB recommendations for biochemical thermodynamics.

The quoted textbook biochemical standard state value is approximatelyThis convention uses fixed pH $7$, temperature $298.15\mathrm{K}$ ($25{}^{\circ }\mathrm{C}$), reference pressure $100\mathrm{kPa}$ ($1\mathrm{bar}$), unit reference thermodynamic activities for dissolved reactants and reaction products, and water thermodynamic activity approximated by one. The prime indicates the fixed-pH biochemical convention. See OpenStax Biology 2e, 6.4: standard ATP hydrolysis value and Biology 2e, 6.2: biochemical standard conditions. This is a reference value, rather than a universal value inside a biological cell; precise tables must also specify chemical solution conditions and any magnesium ion binding convention. Different reference conventions and data treatments give different tabulated values, as discussed in Li et al., 2010: a database of thermodynamic quantities for biochemical reactions.

An exergonic reaction has a negative change in Gibbs free energy, so the overall ATP hydrolysis is favourable under those reference conditions. Breaking a chemical bond by itself costs energy; forming new chemical bonds can release energy. The net change compares all reactants with all reaction products, including their interactions with water and the entropy contribution. Calling the phosphate connection a "high-energy bond" describes a large favourable change in Gibbs free energy on hydrolysis, rather than energy released by bond breaking alone. See 7.5 Strengths of Ionic and Covalent Bonds and Cooper, The Cell: ATP and metabolic energy.

Composition changes the driving force. At the same fixed pH, temperature, pressure, and binding convention, write the molar reaction change asHere $R$ is the molar gas constant, $T$ the absolute temperature, and $a$ a dimensionless thermodynamic activity for a biochemical pool. Constant water thermodynamic activity is absorbed into the reference term; fixed pH accounts for buffered protons. The shorthand $\Delta G$ means transformed molar reaction Gibbs free energy change, ${\Delta }_r{G}^{\prime }$, rather than a finite sample's total change. The natural logarithm acts on a dimensionless reaction quotient, never on concentrations with units. See the IUBMB biochemical thermodynamics recommendations and the general equilibrium constant relation.

For a stipulated ideal dilute chemical solution, let $a_i=[i]/c^{\circ }$, with $c^{\circ }=1\mathrm{mol}{\mathrm{L}}^{-1}$. Choose $[\mathrm{ATP}]=5\mathrm{mmol}{\mathrm{L}}^{-1}$, $[\mathrm{ADP}]=0.5\mathrm{mmol}{\mathrm{L}}^{-1}$, and $[{\mathrm{P}}_i]=1\mathrm{mmol}{\mathrm{L}}^{-1}$, ignoring activity coefficient corrections and magnesium binding. These are illustrative inputs, not a claim about a particular biological cell. ThenandIncreasing $Q$ tenfold raises $\Delta G$ by $RT\ln 10\approx 5.708\mathrm{kJ}\mathrm{mo}{\mathrm{l}}^{-1}$ at this temperature. Thus the ATP to ADP ratio and available inorganic phosphate matter, even with the same standard state value. These are local molar predictions at the stipulated composition, rather than a constant total yield as an isolated sample reacts.

Occupying an antibonding molecular orbital opposes a chemical bond. For equivalent $1s$ atomic orbitals of the hydrogen atom, the difference ${\sigma }_u^{\ast }={\sigma }_{-}$ vanishes on the plane halfway between the protons: every point there is equally far from both centres, so the amplitudes cancel. This nodal plane removes the contribution of this molecular orbital to Electron density on that plane; it does not make an entire finite region empty. The $1s$-derived antibonding molecular orbital lies above its bonding molecular orbital partner in energy. See Field, MIT 5.61, lecture 25, pp. 1–2.

In the ${\mathrm{He}}_2$ minimal model, $({\sigma }_u^{\ast }{)}^2$ adds $N_a=2$ and cancels the bond order contribution of $({\sigma }_g{)}^2$. Opposite signs on the two lobes describe probability amplitudes, while both lobes have nonnegative probability density after squaring. The star is an orbital label, not an extra Electron or an electric charge.

A bond angle is the angle between two chemical bonds sharing a central chemical atom. In H–O–H, the middle symbol identifies the vertex: the angle is at oxygen. Let $u$ and $v$ be the nonzero displacement vectors from that atomic nucleus to the two neighbours. The actual three-dimensional bond angle satisfiesusing the dot product and Euclidean norm. Rotating the whole molecule preserves this expression; projecting it onto a page generally does not.

There is another useful way to find a bond angle. If the two bond lengths are $a,b$ and the distance between the outer atomic nuclei is $d$, the law of cosines givesFor equal bond lengths $a=b$, this becomes $d=2b\sin (\theta /2)$. Thus a measured outer-atom separation contains information about a bond angle even though those outer chemical atoms are not directly joined by a chemical bond.

For a stipulated rigid, equal-bond length model using water's $104.4776^{\circ }$ equilibrium bond angle, $d/b\approx 1.5811$, whereas a straight H–O–H arrangement would give $d/b=2$. These are calculated geometric ratios, not new measured distances. Gas electron diffraction illustrates how pair-distance information can constrain molecular geometry. Substituting independently averaged distances into the rigid triangle formula does not automatically recover an equilibrium bond angle, because averaging and this nonlinear calculation need not commute.

A bond dipole represents the separation of positive and negative electric charge associated with a chemical bond. In a neutral two-point charge model put $+q$ at ${\mathbf{r}}_A$ and $-q$ at ${\mathbf{r}}_B$, with $q>0$. Its physical electric dipole moment isIf $B$ is the negative end, the physical electric dipole moment points from $B$ to $A$. The customary crossed-tail chemical arrow points towards the negative, more electronegative end, from $A$ to $B$. It therefore has the opposite direction. State the convention before doing vector addition; use physical electric dipole moments in the interaction potential energy $U=-\mathbf{p}\cdot \mathbf{E}$, where $\mathbf{E}$ is the electric field.^[ref]

For a fixed neutral molecule, its complete electric dipole moment follows from all atomic nuclei and the electron density, not just point charges assigned to sites. If $n(\mathbf{r})$ is the expected number of Electrons per unit volume, the corresponding charge density is ${\rho }_e(\mathbf{r})=-en(\mathbf{r})$; the nuclear terms contribute separately. Partitioning that distribution into bond dipoles is a model. Lone pairs and electric polarization within a chemical atom can contribute as well. A measured molecular electric dipole moment cannot uniquely recover every individual bond dipole or partial atomic charge.

A bond-dissociation energy specifies the energy needed for a stated dissociation into separated fragments. An energy from the lowest vibrational state, an energy from the bottom of a potential energy well, and a finite-temperature molar dissociation enthalpy require different conventions; do not silently mix them in an electronegativity formula.

Which fragments, in which quantum states, and at which temperature? For a neutral gaseous molecule with a specified two-electron covalent bond, the usual thermochemical convention is homolysis,Each fragment receives one of the two bonding Electrons; the dots denote unpaired Electrons. The final fragments are isolated from each other, with their own relaxed molecular geometry and specified electronic quantum states. The energy cost includes this relaxation, rather than merely stretching the initial chemical bond while freezing everything else. For a neutral parent, heterolysis instead produces ${\mathrm{A}}^{+}(g)+{\mathrm{B}}^{-}(g)$, or the opposite assignment of electric charges; those are different final states and different energies. A value for gaseous neutral fragments cannot be transferred to ions, a chemical solution, or a solid without accounting for those changed conditions.^[ref]

The distinction is useful beyond terminology. Pauling electronegativity compares consistently defined bond-dissociation energies; photodissociation can reveal a specified ground-state threshold; a thermal chemical reaction balance requires compatible enthalpies. A threshold is also different from an activation energy: it compares initial and final quantum states, whereas a barrier can obstruct the path between them.

Occupying a bonding molecular orbital favours a chemical bond. For the two equivalent $1s$ atomic orbitals of the hydrogen atom, the sum ${\sigma }_g={\sigma }_{+}$ has constructive interference between the protons. The resulting Electron density in that region helps stabilize the combined system. Its lower energy in this model follows from the Quantum Hamiltonian, not from the plus sign alone; see Field, MIT 5.61, lecture 25, pp. 1–2.

For example, $({\sigma }_g{)}^2$ in molecular hydrogen supplies $N_b=2$, hence bond order one when $N_a=0$. The sum in the molecular orbital theory toy has midpoint probability density $0.303468$, whereas the difference has zero there. The normalization factors must be included in this comparison.

Bond polarization is unequal sharing of electron density across a chemical bond. An electronegativity difference is a heuristic for its direction and tendency, not a unique partial atomic charge.

A simple two-site model makes the notation explicit. Represent each site by effective positive electric charge $+e$, and allocate expected Electron populations $1-s$ to $A$ and $1+s$ to $B$, with $0\le s<1$. Here $e$ is the elementary charge; these effective sites omit the internal structure of real chemical atoms. Subtraction givesFor the stipulated illustration $s=0.35$, the populations are $0.65$ and $1.35$, and the effective partial atomic charges are $+0.35e$ and $-0.35e$. Fractional expected populations do not split an individual Electron into pieces. The total population remains two, and the pair remains neutral. No formula connecting $s$ to $\Delta \chi$ has been assumed; many electron density distributions and partitioning conventions can share one qualitative electronegativity ordering.

A catalytic cycle follows the changing forms of a catalyst through a reaction mechanism until its starting form is regenerated. The schematic binding cycle in catalyst illustrates the bookkeeping: C is consumed and recovered, whereas AC is a reaction intermediate formed and consumed. Cancelling both gives the net A-to-B chemical equation. Regeneration concerns the completed cycle; it does not imply that C avoids forming chemical bonds or exchanging Electrons. An alternative reaction mechanism may have more elementary reactions than the uncatalysed route and still be faster.^[ref]

For that reversible binding cycle, ideal thermodynamic activities give step equilibrium constants $K_1=a_{\mathrm{AC}}/(a_{\mathrm{A}}{a}_{\mathrm{C}})$ and $K_2=a_{\mathrm{B}}{a}_{\mathrm{C}}/a_{\mathrm{AC}}$. Their product is $K_1{K}_2=a_{\mathrm{B}}/a_{\mathrm{A}}=K$: the same cancellations occur in the equilibrium bookkeeping. Choose consistent standard states for the species. A proposed cycle with $K_1{K}_2\ne K$ for the same net conversion at the same temperature would contradict its specified thermodynamics. This statement concerns free-species thermodynamic activities. Appreciable binding in AC can change how the conserved total amount is partitioned among free A, free B and bound AC. An assay counting bound and free material together therefore needs that additional balance; unchanged $a_{\mathrm{B}}/a_{\mathrm{A}}$ does not by itself guarantee identical analytical totals when the amount of C changes.

Real chemical bonds can stretch as molecular rotation increases. The resulting larger moment of inertia lowers the energy eigenvalues relative to a rigid rotor. Within one vibrational quantum state, a leading effective correction isBoth $B_v$ and $D_v$ are in frequency units here; $v$ labels the vibrational quantum state. For positive $D_v$, the adjacent-line spacing becomesso the departures grow with $J$. Molecular vibration also changes the effective rotational constant: even the lowest vibrational quantum state does not have motionless atomic nuclei.^[ref]

The quartic correction is a limited expansion, not a model to extrapolate to arbitrary $J$. It is small relative to the rigid contribution only while $(D_v/B_v)J(J+1)\ll 1$; eventually higher terms, changed internal motion, or chemical bond breaking matter. In the synthetic plot, the largest upper-state label is $J=5$, giving a stipulated correction ratio of $0.03$. No universal maximum valid $J$ follows without a particular molecule and precision target.

The quantum numbers also have limits of meaning. Here $J$ describes spin-free rotation. In a molecule with electronic spin, rotation alone is commonly labelled $N$, while $J$ includes electronic angular momentum; including nuclear spin introduces additional total-angular momentum labels and resolved splittings. An applied electric field can mix different field-free $J$ states through the Stark effect. For identical atomic nuclei, the Pauli exclusion principle can restrict combinations of rotational and nuclear-spin states. The simple $2J+1$ degeneracy and every-integer-$J$ ladder therefore describe the stated idealization, not all observed sublevels.^[ref]

A chemical bond associates chemical atoms or groups of chemical atoms into a sufficiently stable structure to treat it as a distinct entity. The concept covers connections within molecules and in extended solids; see the IUPAC Gold Book, chemical bond. It is useful because composition alone does not specify how the chemical atoms are connected, and those connections help determine a chemical substance's properties and possible chemical reactions.

In a covalent bond, Electrons are shared between chemical atoms. Two hydrogen chemical atoms can form a molecular hydrogen molecule, with its Electrons interacting with both atomic nuclei. In the usual description of this diatomic molecule, the potential energy as a function of nuclear separation has a minimum: moving the nuclei too close or too far raises the energy. See 7.2 Covalent Bonding.

Separating bonded chemical atoms requires energy; forming the corresponding chemical bonds releases energy. Whether an overall chemical reaction releases energy depends on both the chemical bonds broken and those formed. The lines in the stoichiometry diagram indicate connections schematically, rather than literal rods or a sequence of microscopic events.

A chemical element is an identity shared by all chemical atoms whose atomic nuclei contain the same number of protons. That number is its atomic number, $Z$: six means carbon, eleven means sodium. The identity survives differences in neutron count, which distinguish isotopes, and differences in Electron count, which distinguish neutral chemical atoms from ions. See the IUPAC Gold Book, chemical element.

The same name can also denote a pure chemical substance containing only that chemical element. These two uses answer different questions. Molecular oxygen, ${\mathrm{O}}_2$, is a chemical substance made entirely of oxygen; water, ${\mathrm{H}}_2\mathrm{O}$, is a chemical compound containing both hydrogen and oxygen. A water molecule contains three chemical atoms but only two chemical elements. Joining chemical atoms through chemical bonds changes their arrangement without changing their atomic numbers.

This distinction makes stoichiometry possible: ordinary chemical reactions rearrange chemical atoms, so one can count each chemical element before and after a transformation. Changing the proton count instead changes the chemical element and requires a nuclear reaction. The periodic table organizes these identities into a useful map, while atomic number bookkeeping keeps identity, isotope, and electric charge separate.

A chemical equation represents a chemical reaction using chemical formulas, with reactants on the left and reaction products on the right. A balanced chemical equation has the same number of chemical atoms of each chemical element on both sides. For molecular hydrogen and molecular oxygen forming water,The coefficients $2,1,2$ give the relative numbers of molecules; the coefficient $1$ is normally omitted. Count hydrogen as $2\times 2=4$ on the left and $2\times 2=4$ on the right, and oxygen as $1\times 2=2$ on the left and $2\times 1=2$ on the right. See Flowers et al., Chemistry 2e, §4.1: writing and balancing chemical equations.

To balance the initial expression ${\mathrm{H}}_2+{\mathrm{O}}_2⟶{\mathrm{H}}_2\mathrm{O}$, first put $2$ before water to match the two oxygen chemical atoms. This creates four hydrogen chemical atoms on the right, so put $2$ before molecular hydrogen. Changing a coefficient multiplies the entire chemical formula. Changing a subscript changes composition and usually the chemical substance: $2{\mathrm{H}}_2\mathrm{O}$ is two water molecules, whereas ${\mathrm{H}}_2{\mathrm{O}}_2$ is one hydrogen peroxide molecule. Never balance a chemical equation by changing its subscripts.

The bookkeeping follows from conservation of the atomic nuclei in ordinary, non-nuclear chemical reactions; chemical bonds and the distribution of Electrons can change. For a chemical equation involving ions, total electric charge must also match. For example, the existing self-ionization of water equation has zero total electric charge on each side, since the $+1$ of hydronium cancels the $-1$ of hydroxide. See 2.6 Ionic and Molecular Compounds (§2.6: nuclei and ions).

The same $2:1:2$ ratio relates changes in amount of substance: two moles of molecular hydrogen consumed per mole of molecular oxygen correspond to two moles of water formed. A mole is a defined unit, not one molecule; the little whole-number picture is an abstract counting model, not a claim that a macroscopic sample contains just five molecules. See molecular count and amount of substance for the exact conversion and SI base unit: mole by Bureau International des Poids et Mesures for the definition.

This is why a balanced chemical equation is useful: stoichiometry turns the same atom accounting into relations between measurable quantities. It does not determine reaction rate, the final conversion set by chemical equilibrium, or the actual yield of recovered reaction products. The limiting reagent gives an upper bound under the specified chemical reaction.

A chemical formula uses symbols of chemical elements and numerical subscripts to record composition. In the molecular formula ${\mathrm{H}}_2\mathrm{O}$ of water, the subscript $2$ counts two hydrogen chemical atoms, and the omitted subscript after $\mathrm{O}$ means one oxygen chemical atom. A molecular formula describes one molecule; a chemical formula need not describe a discrete molecule.

Read a preceding coefficient separately from the subscripts. One ${\mathrm{H}}_2\mathrm{O}$ contains two hydrogen and one oxygen chemical atom; $2{\mathrm{H}}_2\mathrm{O}$ contains four hydrogen and two oxygen chemical atoms distributed between two water molecules. In ${\mathrm{H}}_2{\mathrm{O}}_2$, the second subscript instead puts two oxygen chemical atoms into each hydrogen peroxide molecule. Thus $2{\mathrm{H}}_2\mathrm{O}\ne {\mathrm{H}}_2{\mathrm{O}}_2$: the coefficient scales the whole chemical formula, while a subscript specifies its composition. See Flowers et al., Chemistry 2e, §2.4: chemical formulas.

For crystalline $\mathrm{NaCl}$, the chemical formula specifies a $1:1$ ratio of sodium ions ${\mathrm{Na}}^{+}$ to chlorine ions ${\mathrm{Cl}}^{-}$. Its formula unit is the accounting entity; the ordinary crystal is an extended arrangement of ions, rather than a collection of discrete $\mathrm{NaCl}$ molecules. Specifying the entity matters when assigning an amount of substance. See formula unit and 2.6 Ionic and Molecular Compounds (§2.6: ionic and molecular compounds).

A molecular formula gives an atom inventory, not the full arrangement of chemical bonds or the molecular geometry. For example, ${\mathrm{C}}_6{\mathrm{H}}_{12}{\mathrm{O}}_6$ counts six carbon, twelve hydrogen, and six oxygen chemical atoms in a glucose molecule, but does not specify the pattern shown by its Fischer projection. Different structures can share a molecular formula. This compact inventory is useful for chemical equation accounting precisely because it leaves the structural detail to other representations.

The choice of letters has an early explanation in Jöns Jacob Berzelius, Essay on the Cause of Chemical Proportions (1813–1814), §III, transcribed by Carmen Giunta: letters made chemical signs easier to write and print, and formulas compressed information about composition. His numerical notation differed from modern subscripts; the lasting idea was to make proportions readable in ordinary text.

Chemical polarity concerns unequal distribution of electron density in a chemical bond or molecule. A polar molecule has a permanent electric dipole moment; the effects of individual bonds must be combined with their spatial arrangement. In a symmetric linear carbon dioxide molecule, opposing bond-dipole contributions cancel. In water, its bent molecular geometry prevents that cancellation, giving a permanent electric dipole moment.^[ref]