Total Dynamics of Quartz–Water System at Ambient Conditions

Abstract

New data on the dissolution and growth of quartz in acid, nearly neutral and slightly alkaline solutions at ambient conditions are presented. During batch dissolutions, aqueous Si-concentrations increased nonlinearly towards limit values. During parallel growth experiments, however, the high Si-concentrations corresponding to 13-fold supersaturation with respect to quartz did not decreased. To interpret these results, two dynamic models (1) a reaction model and (2) a surface-complexation model, were derived. Both models were focused on (a) reversible dissolution/growth of “bulk quartz” and b) irreversible dissolution of “disturbed quartz” (weakly bounded Si-atoms) on “new surface”. Based on the reaction model, the differential rate law,

$${{dn_{{\rm Si(aq)}}}\over{dt}}=\left(p+{{r}\over {a_{{\rm H}^+}}}\right)+\left(u-p- {{r}\over {a_{{\rm H}^+}}}\right){{n_{{\rm Q_D}}}\over {\sum\limits_i{n_{{\rm Qi}}}}}-{{1}\over {V}}\left(q+ {{s}\over {a_{{\rm H}^+}}}\right)n_{{\rm Si(aq)}},$$

was derived, where dn ^Si(aq)/dt is the overall Si-flux into solution [mol s⁻¹], $a_{{\rm H}^+}$ is H⁺ ion activity, n ^QD is the instantaneous content of disturbed quartz (weakly bounded Si-atoms onto quartz surface) [mol], $\sum\limits_ in_{{\rm Qi}}$ is the total content of Si-atoms on quartz surface [mol], V is the volume of solution [L], and n ^Si(aq) is the content of silicic acid in solution. The rate law parameters are $p=k_1\{A\}a_{\rm w}^2$, q=−k ₂ {A}γ_Si, r=k ₃  K _{w{A}a_w}, s=−k ₄  K _{Si{A} γSi}, and $u = k_5\{A\}a_{\rm w}^2$, where k ¹ and k ² are the rate constants for the dissolution and growth of bulk quartz in pure water, and k³ and k⁴ are the rate constants for the reaction of bulk quartz with hydroxyls. k ⁵ is the rate constant for the dissolution of disturbed quartz. K ^Si and K ^w are the dissociation constants of silicic acid and water, respectively. A is surface area [m²], a ^w is water activity, and γ ^Si is activity coefficient of silicic acid. The values of the rate constant were determined as follows: k ¹=(3.0 ±1.0) × 10⁻¹⁴, k ² < 1.62 × 10⁻¹¹, k ³=(1.41 ± 0.09) × 10⁻⁷, k ⁴=(5.26 ± 0.62) × 10⁻⁹, and k ⁵=(1.71 ± 0.38) × 10⁻¹², all in the units of mol m⁻² s⁻¹. In the acid, neutral, and alkaline solutions, respectively, the initial contents of disturbed quartz, n ⁰ _QD, were found to be (3.42 ± 0.53) × 10⁻⁵, (2.63 ± 0.53) × 10⁻⁵, and (3.94 ± 0.50) × 10⁻⁵ mol per 1.66 mol (i.e., 100 g) of quartz samples (grain fraction of 71–150 μm in diameter). It relates to 23, 18, and 27 of total surface area (11 m²)

Based on the surface-complexation model, the alternative differential rate law,

$$\eqalign{{{dn_{\rm Si(aq)}}\over {dt}} =\{A\}(k_{\rm d(s)} a_{\rm w}{{n_{\rm s}}\over {n}}+k_{{\rm d}(0)}a_{\rm w}^\nu\theta_{(0)}+k_{{\rm d}(-)} a_{\rm w}^\nu \theta _{(-)}+ \cr \quad+k_{\rm d(Na)}a_{\rm w}^\nu\theta_{({\rm Na})}+ k_{{\rm d}(+)}a_{\rm w}^\nu \theta _{(+)}-\sum_i{k_{{\rm g(i)}}}\gamma _{\rm Si}{{n_{\rm Si(aq)}} \over V}),}$$

was derived, where A is total surface area [m²], a ^w is water activity, n ^s is the content of single bounded surface complex, –Si(OH)³ [mol], n is the total Si on quartz surface [mol], ν is a stoichiometric coefficient (2 or 3), γ ^Si is activity coefficient of silicic acid, and V is the volume of solution [L]. k ^d(i) is dissolution rate constants and θ ⁽ⁱ⁾ is molar fraction of ith surface complex. The indexes ^{(s), (0), (}-), (Na), and ⁽⁺⁾ denote single bounded complex, –Si–(OH)³, uncharged complex, >Si–OH, negatively charged complex, >Si–O⁻, sodium complex, >Si–ONa, and positively charged complex, >Si–OH ⁺₂ , respectively. $\sum\limits_{i} { k}_{{\rm g(i)}}$ is the sum of the rate constants for growth, k ^g(0) + k ^g(-) + k ^g(Na) + k ^g(s). The values of the rate constants were determined as follow: k ^d(s)=(1.79 ± 0.17) × 10⁻¹², k ^d(0) < 5.8 × 10⁻¹⁵, k ^d(+)=(1.74 ± 0.06) × 10⁻¹², k ^d(-)= (2.45 ± 0.09) × 10⁻¹², k ^d(Na)=(7.23 ± 0.87) × 10⁻¹² , and $\sum\limits_{i} k_{{\rm g(i)}}$< 2.3 × 10⁻¹¹, all in the unit of mol m⁻² s⁻¹. The initial contents of disturbed quartz (as a single bounded complex –Si(OH)³, n ⁰ _S), were found to be (3.20 ± 0.20) × 10⁻⁵, (2.30 ± 0.20) × 10⁻⁵, and (3.65 ± 0.15) × 10⁻⁵ mol on 1.66 mol of quartz samples in the acid, neutral, and alkaline solutions, respectively.