Ionic (Saline) Hydrides of the s-Block

Saline hydrides remain genuinely important reagents rather than historical curiosities. Sodium hydride, NaH, is a workhorse strong, non-nucleophilic base in organic and organometallic synthesis, used to deprotonate alcohols, amides, and active-methylene compounds cleanly, generating H₂ gas as the only byproduct — a direct, everyday consequence of H⁻'s extreme Brønsted basicity discussed above, and a preview of the reducing/hydridic reactivity explored further in Reducing and Hydridic Reactivity of s-Block Hydrides. Calcium hydride, CaH₂, is one of the most common laboratory desiccants for drying organic solvents (particularly hydrocarbons and ethers) because it reacts quantitatively and irreversibly with trace water, releasing measurable, stoichiometric H₂ that also serves as a built-in indicator of solvent dryness. Beyond the bench, saline and related complex hydrides are studied intensively as solid-state hydrogen-storage materials, since the volumetric hydrogen density of a compact ionic hydride lattice can exceed that of compressed or even liquid H₂ gas; LiH and related complex hydrides (LiAlH₄, NaBH₄ — themselves built partly on the hydridic character established here) are central to ongoing work in Industrial Uses of s-Block Hydrides and Metals, including battery and fuel-cell adjacent chemistry. Lithium hydride specifically has found application as a lightweight neutron shielding and moderating material in nuclear technology, exploiting hydrogen's exceptional efficiency at slowing fast neutrons through elastic collisions, while also serving historically as a component in thermonuclear weapons research (lithium-6 deuteride). In metallurgy, calcium hydride is used as a reducing agent to extract certain reactive and refractory metals from their oxides, exploiting H⁻'s powerful reducing character — a theme that generalizes across the entire family of saline hydrides and connects directly to their industrial value as clean, byproduct-friendly (H₂-releasing) reducing and desiccating agents across the chemical industry.

Ask the tutor: Why does the Kapustinskii equation give a reasonable lattice-enthalpy estimate for CaH₂ even without knowing its true (non-cubic) crystal structure?

Hydrogen is peculiar among elements because it can appear in three fundamentally different bonding environments with metals, and the saline hydrides represent only one extreme. In covalent/molecular hydrides (CH₄, NH₃, B₂H₆) hydrogen shares electrons roughly symmetrically or is bound in electron-deficient multicenter bonds. In metallic/interstitial hydrides (PdH_x, the transition-metal and rare-earth hydrides) hydrogen atoms occupy interstices in a metallic lattice, and the material remains a conductor. In saline hydrides, hydrogen is reduced outright: it accepts an electron from an electropositive metal to become H⁻, a closed-shell 1s² anion isoelectronic with helium, and the compound is best described as a normal ionic solid, M⁺H⁻ or M²⁺(H⁻)₂. The chemical identity of H⁻ is worth dwelling on because it is counter-intuitive. In water, hydrogen is overwhelmingly found as H⁺ (really H₃O⁺), because water's oxygen lone pairs stabilize the proton and because H⁻ would instantaneously protonate from any O–H bond, releasing H₂ gas:

This reaction is essentially irreversible and enormously exothermic, which is precisely why saline hydrides must be handled and characterized under strictly anhydrous, often inert-atmosphere conditions, and why H⁻ never survives in aqueous solution. The existence of a stable solid salt of H⁻ is a lattice-energy phenomenon: in the solid state, H⁻ is locked into a low-energy electrostatic environment from which it cannot escape without disrupting the whole crystal, whereas in solution it is a free, wildly basic ion with no such protection. Only metals from Groups 1 and 2 that are sufficiently electropositive form these true ionic hydrides. Down Group 1, all of Li, Na, K, Rb, Cs form MH with the rock-salt (NaCl-type) structure: each M⁺ is octahedrally coordinated by six H⁻ and vice versa, exactly like Na⁺ and Cl⁻ in table salt. Down Group 2, Be and Mg do not form saline hydrides — BeH₂ is a covalent polymeric solid with three-center two-electron Be–H–Be bridges (structurally analogous to (BeH₂)ₙ chains, echoing the electron-deficient bonding seen in boranes), and MgH₂, while ionic in character, adopts the rutile structure with only moderate ionic character and significant covalent contribution. It is only Ca, Sr, and Ba — the larger, more electropositive alkaline earths — that form clearly ionic dihydrides, CaH₂, SrH₂, BaH₂, and these adopt a distorted PbCl₂-type (cotunnite-related) structure rather than a simple fluorite lattice, because H⁻ is not quite the right size/shape for a perfect CaF₂-type arrangement. The size of H⁻ itself deserves comment because it is genuinely unusual among anions. Unlike halide ions, whose radii are set by a nucleus of substantial charge holding a compact electron cloud, H⁻ has only one proton holding onto two electrons. The electron cloud is diffuse, highly polarizable, and its effective radius depends strongly on the surrounding cation — it swells in the field of a weak, large cation and compresses next to a small, polarizing cation. Crystallographic estimates place r(H⁻) anywhere from about 130 pm (in LiH, where the small Li⁺ compresses it) to 150 pm or more (in CsH, where the large, weakly polarizing Cs⁺ lets it expand). This anion "softness" is itself diagnostic of the ionic-but-not-perfectly-ionic character of these solids, and it is the reason simple hard-sphere ionic radius tables give only approximate lattice-energy predictions for hydrides compared to halides.

The central quantitative relationship governing whether a saline hydride can form is the Born–Haber cycle, which decomposes the overall formation enthalpy into atomization, ionization, electron-affinity, and lattice terms:

where:

• $\Delta_{sub}H(\mathrm{M})$ = enthalpy to atomize/sublime the solid metal to gaseous atoms (endothermic, +);
• $\tfrac12 D(\mathrm{H-H})$ = half the H–H bond dissociation enthalpy, to make one mole of H atoms from H₂(g) (endothermic, +);
• $IE_1(\mathrm{M})$ = first ionization energy of the metal atom, M(g) → M⁺(g) + e⁻ (endothermic, +);
• $\Delta_{EA}H(\mathrm{H})$ = enthalpy change for H(g) + e⁻ → H⁻(g) (this is endothermic, small positive value, unlike halogens);
• $\Delta_L H(\mathrm{MH})$ = lattice enthalpy of formation, M⁺(g) + H⁻(g) → MH(s) (strongly exothermic, large negative).

Reading this equation: every step before the last is either endothermic or only mildly exothermic, and critically the electron-affinity step for hydrogen is endothermic — adding a second electron to the compact hydrogen 1s orbital costs energy because of strong electron-electron repulsion in such a small orbital, unlike a halogen atom where the incoming electron fills a larger p-shell more comfortably and net EA is exothermic. The entire viability of saline hydride formation is therefore carried by the last term: the lattice enthalpy must be large and negative enough to make the sum favorable. This is why the reaction only proceeds for the most electropositive metals (low IE₁, or in Group 2 a favorable combination of IE₁+IE₂ and small Δ_sub H) combined with small enough cation radius to make Δ_L H very large. The lattice enthalpy itself is captured, to reasonable accuracy for a rock-salt structure, by the Born–Landé / Born–Mayer type expression:

where:

• $N_A$ = Avogadro's number;
• $M$ = Madelung constant (1.7476 for the NaCl-type structure);
• $z_+, z_-$ = ionic charges (+1 and −1 for MH, or effectively +2 for MH₂ built from M²⁺ and two H⁻);
• $e^2/4\pi\varepsilon_0$ = the Coulomb energy prefactor;
• $r_+ + r_-$ = the sum of ionic radii (the interionic distance);
• $n$ = the Born exponent, reflecting short-range electron-cloud repulsion (typically 7–10 for these ions).

Reading this equation: lattice enthalpy scales as $1/(r_+ + r_-)$ and as $z_+z_-$, so it is most negative (strongest binding) for the smallest cations and for the doubly-charged alkaline-earth hydrides. This single dependence is the quantitative backbone of every trend discussed below: LiH has the largest lattice enthalpy magnitude of the alkali hydrides and CsH the smallest; CaH₂ has a substantially larger lattice enthalpy magnitude (per mole of "MH unit," and certainly per formula unit given the doubled charge) than the alkali hydrides, which correlates with the higher thermal stability of the alkaline-earth dihydrides.

Example 1 (Foundational): Complete Born–Haber cycle for NaH and confirm the sign logic. Given data (all in kJ mol⁻¹, standard literature values): $\Delta_{sub}H(\mathrm{Na}) = +108$; $D(\mathrm{H-H}) = +436$ so $\tfrac12 D = +218$; $IE_1(\mathrm{Na}) = +496$; the "electron affinity" step for hydrogen, H(g) + e⁻ → H⁻(g), taken as $\Delta_{EA}H = -73$ kJ mol⁻¹ using the convention that this is slightly exothermic overall in some compilations (values in the literature range from mildly exothermic, ≈ −73 kJ mol⁻¹, to mildly endothermic depending on source and definition; here we use the commonly tabulated Born–Haber value of −73 kJ mol⁻¹ for internal consistency with the experimental ΔfH); lattice enthalpy $\Delta_L H(\mathrm{NaH}) = -809$ kJ mol⁻�1 (calculated/experimental composite for the rock-salt lattice). Find $\Delta_f H^\circ(\mathrm{NaH})$ and compare to the experimental value of −56 kJ mol⁻¹. Sum the cycle:

This is close to the experimental value of −56 kJ mol⁻¹ (the 4 kJ mol⁻¹ discrepancy reflects the approximate nature of the tabulated lattice enthalpy and the sensitivity of the H⁻ electron-affinity value to the source used). The important qualitative check: without the lattice term, the sum of the first four terms is

strongly endothermic — confirming that it is the lattice enthalpy alone that converts an otherwise wildly unfavorable process into a stable, isolable ionic solid. As a limiting-case sanity check: if the lattice enthalpy magnitude were only, say, −400 kJ mol⁻¹ (roughly what a much larger, singly-charged cation with r₊ ≈ 300 pm might give), $\Delta_f H^\circ$ would be +349 kJ mol⁻¹ and NaH-like compound would simply not exist as a stable solid — precisely the situation for metals too large or too weakly charged to generate sufficient lattice stabilization.

Example 2 (Applied): Rank the thermal stability of LiH, NaH, and KH using lattice enthalpy and ionic radius data, and predict relative decomposition temperatures. Using cation radii (6-coordinate, Shannon): Li⁺ = 76 pm, Na⁺ = 102 pm, K⁺ = 138 pm, and a fixed effective H⁻ radius of ≈ 137 pm (an intermediate compromise value, acknowledging H⁻'s compressibility), estimate the relative lattice enthalpies using the simple Coulombic scaling $\Delta_L H \propto -1/(r_++r_-)$, normalized so LiH's calculated value matches its accepted lattice enthalpy of −909 kJ mol⁻¹ (a slightly different literature value from Example 1's rock-salt composite, since different compilations use different H⁻ radii; we use −909 kJ mol⁻¹ here for LiH specifically to illustrate the scaling method). Interionic distances:

Scaling lattice enthalpy inversely with distance (holding Madelung constant and Born exponent fixed, a reasonable first approximation since all three share the NaCl structure type):

These estimates (−909, −810, −704 kJ mol⁻¹ for Li, Na, K respectively) track the experimentally observed order of thermal stability: LiH is stable to the highest temperature (decomposing only above ~720 °C, close to its melting point), NaH decomposes noticeably around 425 °C, and KH is thermally the least robust of the three, consistent with the monotonic fall in lattice enthalpy magnitude. As a check on the scaling assumption, note that the ratio of lattice enthalpies (810/909 = 0.891) is close to the inverse ratio of distances (213/239 = 0.891) by construction — confirming the arithmetic — while the physically meaningful result is that this ordering matches the experimentally measured decomposition temperature order, validating the simple $1/(r_++r_-)$ model as a good first approximation even though it neglects small differences in Born exponent and Madelung geometry distortion.

Example 3 (Exam-level): Estimate the lattice enthalpy of CaH₂ using the Kapustinskii equation and use it to rationalize CaH₂'s superior thermal stability relative to NaH. The Kapustinskii equation estimates lattice enthalpy without needing a known crystal structure, useful for MH₂ where the true structure (distorted PbCl₂-type, coordination number 7–9) is more complex than simple rock-salt:

where $\nu$ is the number of ions per formula unit (3 for CaH₂: one Ca²⁺ + two H⁻), $z_+z_- = (+2)(-1) = -2$ (we take $|z_+ z_-| = 2$ for the magnitude calculation), and $r_+ + r_-$ is in picometers, with $r_+(\mathrm{Ca}^{2+}) = 100$ pm (6-coordinate Shannon value, used as an approximation despite CaH₂'s higher coordination number) and $r_-(\mathrm{H}^-) = 130$ pm (compressed value appropriate to a small, doubly-charged, polarizing cation). Compute the interionic distance:

Compute the bracket correction term:

Assemble the full expression:

This value (≈ −2666 kJ mol⁻¹) is roughly 3.3 times larger in magnitude than NaH's lattice enthalpy (−809 kJ mol⁻¹ from Example 1), driven by the $z_+z_- = 2$ factor (doubling the numerator relative to a hypothetical 1:1 charge) compounded by the smaller cation radius and the extra ion per formula unit ($\nu=3$ rather than 2). Physically: even though Ca must pay a much larger ionization cost (IE₁+IE₂ ≈ 1735 kJ mol⁻¹ versus Na's 496 kJ mol⁻¹), the roughly 1850 kJ mol⁻¹ extra lattice stabilization more than compensates, explaining why CaH₂ is a stable, thermally robust solid used industrially as a drying agent and portable hydrogen source, decomposing only well above 600 °C, in clear contrast to the more modest thermal ceiling of the alkali hydrides. As a limiting-case check: if instead $z_+z_-$ were only 1 (hypothetically, as if Ca⁺H⁻ existed with singly-ionized calcium), the numerator would halve to give roughly −1333 kJ mol⁻¹, comparable in magnitude to the alkali hydrides — confirming that it is specifically the doubled charge, not merely the smaller radius, that drives CaH₂'s markedly larger lattice enthalpy.

The conceptual foundation for classifying hydrides by bonding type — ionic/saline, covalent/molecular, and metallic/interstitial — is generally credited to the systematic structural and thermodynamic work carried out in the early-to-mid twentieth century, building on the broader ionic-crystal framework established by Max Born and Alfred Landé, whose lattice-energy theory (the Born–Landé equation) provided the first quantitative tool for testing whether a proposed ionic formula for a solid was energetically self-consistent. Applying that machinery specifically to metal hydrides — recognizing that H⁻ could be treated as a genuine anion with a crystallographic radius, and that its "abnormal," strongly cation-dependent size reflected weak nuclear control over a two-electron cloud — was a natural and important extension of ionic-crystal theory into a new and initially counter-intuitive chemical territory.