van’t Hoff plot (ln P vs. 1000/T) for the hydrogen storage on Ca/Al(OH)5 nanoparticles

The pressure–temperature (P–T) data were obtained from hydrogen adsorption measurements conducted at four distinct equilibrium temperatures (77, 173, 223, and 273 K). At each temperature, the equilibrium hydrogen pressure was recorded after allowing sufficient time for adsorption equilibrium to be established. These measurements reflect the reversible interaction between molecular hydrogen and the Ca/Al(OH)₅ nanoparticle matrix.The thermodynamic parameters were derived using the classical van’t Hoff equation:ln⁡(P)=−ΔHR(1T)+ΔSR\ln(P) = -\frac{\Delta H}{R}\left(\frac{1}{T}\right) + \frac{\Delta S}{R}ln(P)=−RΔH​(T1​)+RΔS​where P is the equilibrium pressure (bar), T is the absolute temperature (K), R is the universal gas constant, ΔH is the enthalpy change (kJ·mol⁻¹ H₂), and ΔS is the entropy change (J·mol⁻¹ H₂·K⁻¹).A minimum of four P–T data points was used to ensure a unique and statistically reliable linear fit, enabling accurate determination of both ΔH and ΔS.Description of Data Content and File StructureThe dataset consists of a single table (Table 2) containing five primary data columns, each defined as follows:T (K): Absolute temperature at which hydrogen adsorption equilibrium was measured.1/T (K⁻¹): Inverse temperature, calculated directly from T, used for van’t Hoff linearization.P (bar): Equilibrium hydrogen pressure corresponding to each temperature.ln(P): Natural logarithm of the equilibrium pressure, used as the dependent variable in the van’t Hoff plot.ΔH (kJ·mol⁻¹ H₂): Enthalpy change of hydrogen adsorption, obtained from the slope of the van’t Hoff plot.ΔS (J·mol⁻¹ H₂·K⁻¹): Entropy change of hydrogen adsorption, obtained from the intercept of the van’t Hoff plot.Empty cells for ΔH and ΔS at individual temperatures indicate that these parameters were extracted from the overall linear regression, not from single data points.Data Interpretation and ValueThe negative values of ΔS observed in this dataset are consistent with hydrogen absorption in solid-state materials, reflecting the loss of translational entropy as gaseous hydrogen becomes confined within the nanoparticle structure.

The magnitude of ΔS falls within the typical range reported for metal hydrides and hydroxide-based storage systems (approximately −100 to −150 J·mol⁻¹ H₂·K⁻¹), supporting the physical validity of the measurements.The relatively low absolute ΔH value indicates moderate binding strength between hydrogen and the Ca/Al(OH)₅ matrix, which is advantageous for reversible hydrogen storage under mild conditions.