An Analytical Model Based on Experimental Data for the Self-Hydrolysis Kinetics of Aqueous Sodium Borohydride

The objective of this work is to determine the self-hydrolysis kinetics of sodium borohydride (NaBH₄) in a solution with liquid water (H₂O) for hydrogen (H₂) generation and storage purposes. In order to be able to derive two semi-global rate expressions, an extensive series of batch process experiments was performed in a glass flask where the following parameters were systematically varied: solution temperature varied from 298 K (25°C) to 348 K (75°C), NaBH₄ concentration ranged from 0.5 wt% to 25.0 wt%, and the concentration of the hydrolysis stabilizer sodium hydroxide (NaOH) varied from 0.0 wt% to 4.0 wt%, which corresponds to initial solution pH values ranging from 9.5 to 12.95. Transient hydrogen generation rates and transient solution pH were measured during hydrolysis. Based on the data collected, the decomposition rate for NaBH₄ when the effect of the transition period diminishes is found to be:

-d[NaBH₄]/dt=A₁e^{(-49860 J/mol/R/T)}[NaBH₄][H⁺]^0.788

Where

A₁=1.72x10⁹(1/s)(L/mol)^0.788

[NaBH₄] represents the NaBH₄ concentration in units of moles per kilogram of solution, [H⁺] represents the concentration of the hydrogen ion, H⁺, in units of moles per liter of water, R in the Arrhenius term is the universal gas constant and T is temperature in Kelvin. The expression for the rate of change of [H⁺] (or equivalently pH level) is:

-d[H⁺]/dt=A₂f([NaBH₄]_O)e^{(-7930 J/mol/R/T)}e^{(-4.529(1-[NaBH₄]/ [NaBH₄]_O))}[H⁺]^{B₂f([NaBH₄]_O)}

Where

A₂f([NaBH₄]_O)=(-2.236[NaBH₄]_O+36.608)(1/s)(L/mol)^B₂

B₂f([NaBH₄]_O)=0.0973[NaBH₄]_O -2.763

The quantity [NaBH₄]_O represents the initial concentration of sodium borohydride and f is symbolic for a function. In principle, given initial conditions (temperature, NaBH₄ concentration and H⁺ concentration), the two quasi-global coupled equations can be integrated to obtain the transient time history of H₂ (or NaBH₄) and solution pH (or H⁺). The model transient hydrogen generation rate and transient pH trends were compared with experimental data. Good agreement between analytical and experimental data was reached for many conditions, especially for elevated solution pH values, levels at which NaBH₄ solutions are used practically.