Albite dissolution kinetics as a function of distance from equilibrium: Implications for natural feldspar weathering

Determining the kinetics of many geologic and engineering processes involving solid/fluid interactions requires a fundamental understanding of the Gibbs free energy dependency of the system. Currently, significant discrepancies seem to exist between kinetic datasets measured to determine the relationship between dissolution rate and Gibbs free energy. To identify the causes of these discrepancies, we have combined vertical scanning interferometry, atomic force microscopy, and scanning electron microscopy techniques to identify dissolution mechanisms and quantify dissolution rates of albite single crystals over a range of Gibbs free energy (−61.1 < ΔG < −10.2 kJ/mol). During our experiments, both a previously dissolved albite surface exhibiting etch pits and a pristine surface lacking dissolution features were dissolved simultaneously within a hydrothermal, flow-through reactor. Experimental results document an up to 2 orders of magnitude difference in dissolution rate between the differently pretreated surfaces, which are dominated by different dissolution mechanisms. The rate difference, which persists over a range of solution saturation state, indicates that the dissolution mechanisms obey different Gibbs free energy dependencies. We propose that this difference in rates is the direct consequence of a kinetic change in dissolution mechanism with deviation from equilibrium conditions. The existence of this kinetic “switch” indicates that a single, continuous function describing the relationship between dissolution rate and Gibbs free energy may be insufficient. Finally, we discuss some of the potential consequences of our findings on albite’s weathering rates with a particular focus on the sample’s history.     

Far from equilibrium enstatite dissolution rates in alkaline solutions at earth surface conditions

Far from equilibrium enstatite dissolution rates both open to atmospheric CO₂ and CO₂ purged were measured as a function of solution pH from 8 to 13 in batch reactors at room temperature. Congruent dissolution was observed after an initial period of incongruent dissolution with preferential Si release from the enstatite. Steady-state dissolution rates in open to atmospheric CO₂ conditions decrease with increase in solution pH from 8 to 12 similar to the behavior reported by other investigators. Judging from the pH 13 dissolution rate, rates increase with pH above pH 12. This is thought to occur because of the increase in overall negative surface charges on enstatite as Mg surface sites become negative above pH 12.4, the pH of zero surface charge of MgO.Steady-state dissolution rates of enstatite increase above pH 10 when CO₂ was purged by performing the experiments in a N₂ atmosphere. This suggests inhibition of dissolution rates above pH 10 when experiments were open to the atmosphere. The dissolved carbonate in these solutions becomes dominantly CO₃²⁻ above pH 10.33. It is argued that CO₃²⁻ forms a >Mg₂-CO₃ complex at positively charged Mg surface sites on enstatite, resulting in stabilization of the surface Si-O bonds. Therefore, removal of solution carbonate results in an increase in dissolution rates of enstatite above pH 10. The log rate of CO₂-purged enstatite dissolution in moles per cm² per s as a function of increasing pH above pH 10 is equal to 0.35. This is consistent with the model of silicate mineral dissolution in the absence of surface carbonation in alkaline solutions proposed earlier in the literature.     

Leaching of lead metallurgical slags and pollutant mobility far from equilibrium conditions

Lead metallurgical slags are partially vitrified materials containing residual amounts of Zn, Pb, Cr, Cd and As. These hazardous materials are generally buried on heaps exposed to weathering. In this study, leaching behavior of lead blast furnace slags has been tested using pure water and open flow experiments. It appears that in such far from equilibrium and slightly acidic conditions, the main phase to be altered is the vitreous phase. As for lunar, basaltic and nuclear glasses, alkalis/proton exchanges prevail and lead to the formation of a non-protective altered layer enriched in Si, Fe and Al. The composition of the altered layer is quite constant except for Si whose concentration decreases towards the leachate interface. Owing to their sizes, micrometric Pb droplets are not always totally dissolved at the slag surface. Nevertheless, nanometric Pb droplets are instantaneously dissolved while a surrounding altered layer is formed. This leads to high Pb releases in open flow systems. Leachate chemistry and dissolution rates of the vitreous phase are closely comparable to previous leaching tests with basaltic and nuclear glasses in conditions far from equilibrium. Moreover, this study confirms that Fe is a stable element in such conditions.     

The dissolution kinetics of a granite and its minerals—Implications for comparison between laboratory and field dissolution rates

The present study compares the dissolution rates of plagioclase, microcline and biotite/chlorite from a bulk granite to the dissolution rates of the same minerals in mineral-rich fractions that were separated from the granite sample. The dissolution rate of plagioclase is enhanced with time as a result of exposure of its surface sites due to the removal of an iron oxide coating. Removal of the iron coating was slower in the experiment with the bulk granite than in the mineral-rich fractions due to a higher Fe concentration from biotite dissolution. As a result, the increase in plagioclase dissolution rate was initially slower in the experiment with the bulk granite. The measured steady state dissolution rates of both plagioclase (6.2 ± 1.2 × 10⁻¹¹ mol g⁻¹ s⁻¹) and microcline (1.6 ± 0.3 × 10⁻¹¹ mol g⁻¹ s⁻¹) were the same in experiments conducted with the plagioclase-rich fraction, the alkali feldspar-rich fraction and the bulk granite.Based on the observed release rates of the major elements, we suggest that the biotite/chlorite-rich fraction dissolved non-congruently under near-equilibrium conditions. In contrast, the biotite and chlorite within the bulk granite sample dissolved congruently under far from equilibrium conditions. These differences result from variations in the degree of saturation of the solutions with respect to both the dissolving biotite/chlorite and to nontronite, which probably was precipitating during dissolution of the biotite and chlorite-rich fraction. Following drying of the bulk granite, the dissolution rate of biotite was significantly enhanced, whereas the dissolution rate of plagioclase decreased.The presence of coatings, wetting and drying cycles and near equilibrium conditions all significantly affect mineral dissolution rates in the field in comparison to the dissolution rate of fully wetted clean minerals under far from equilibrium laboratory conditions. To bridge the gap between the field and the laboratory mineral dissolution rates, these effects on dissolution rate should be further studied.     

Experimentally determined compositions of diopside-jadeite pyroxene in equilibrium with albite and quartz at 1200–1350°C and 15–34 kbar

Equilibrium compositions of diopside-jadeite pyroxene coexisting with albite and quartz were experimentally determined at 25 different P-T conditions, using an electron microprobe for analysis. The new data and the 600°C data of Holland (1983) provided the following mixing properties of the diopside (Di)-jadeite (Jd) solid solution (J, K): G^xs = X_JdX_Di[12600 ? 9.45T + (12600 ? 7.6T)(X_Jd ? X_Di) ? (21400 ? 16.2T)(X_Jd ? X_Di)²]. The Di-Jd solution is close to ideal above 1000°C but immiscible below 565°C. The Di-Jd solvus is slightly asymmetric with the crest at composition Di_42.4Jd_57.6. Excess enthalpy is positive but smaller than indicated by the enthalpy of solution measurements of Woodet al. (1980). Disorder in the Di-Jd solution is significantly smaller than complete disorder implied by the ionic two-site model.     

Natural gas at thermodynamic equilibrium Implications for the origin of natural gas

It is broadly accepted that so-called 'thermal' gas is the product of thermal cracking, 'primary' thermal gas from kerogen cracking, and 'secondary' thermal gas from oil cracking. Since thermal cracking of hydrocarbons does not generate products at equilibrium and thermal stress should not bring them to equilibrium over geologic time, we would not expect methane, ethane, and propane to be at equilibrium in subsurface deposits. Here we report compelling evidence of natural gas at thermodynamic equilibrium. Molecular compositions are constrained to equilibrium,

The dissolution of olivine added to soil: Implications for enhanced weathering

Chemical weathering of silicate minerals consumes atmospheric CO₂ and is a fundamental component of geochemical cycles and of the climate system on long timescales. Artificial acceleration of such weathering (“enhanced weathering”) has recently been proposed as a method of mitigating anthropogenic climate change, by adding fine-grained silicate materials to continental surfaces. The efficacy of such intervention in the carbon cycle strongly depends on the mineral dissolution rates that occur, but these rates remain uncertain. Dissolution rates determined from catchment scale investigations are generally several orders of magnitude slower than those predicted from kinetic information derived from laboratory studies. Here we present results from laboratory flow-through dissolution experiments which seek to bridge this observational discrepancy by using columns of soil returned to the laboratory from a field site. We constrain the dissolution rate of olivine added to the top of one of these columns, while maintaining much of the complexity inherent in the soil environment. Continual addition of water to the top of the soil columns, and analysis of elemental composition of waters exiting at the base was conducted for a period of five months, and the solid and leachable composition of the soils was also assessed before and after the experiments. Chemical results indicate clear release of Mg²⁺ from the dissolution of olivine and, by comparison with a control case, allow the rate of olivine dissolution to be estimated between 10^−16.4 and 10^−15.5 moles(Mg) cm⁻² s⁻¹. Measurements also allow secondary mineral formation in the soil to be assessed, and suggest that no significant secondary uptake of Mg²⁺ has occurred. The olivine dissolution rates are intermediate between those of pure laboratory and field studies and provide a useful constraint on weathering processes in natural environments, such as during soil profile deepening or the addition of mineral dust or volcanic ash to soils surfaces. The dissolution rates also provide critical information for the assessment of enhanced weathering including the expected surface-area and energy requirements.     

Sapphirine-bearing Granulites from Abu-Balaram Area, Gujarat State: Implications for India-Madagascar Connection

P-T conditions of sapphirine bearing granulites from a new locality from the north eastern part of Gujarat range from 8.2–8.8 kbars at T of 950°C. The discovery of this UHT assemblage in the north western part of the Indian shield bordering the Aravalli-Delhi fold belt provides additional evidences for India-Madagascar connection, linking the Aravalli- Malani sequences to similar lithologies in northern Madagascar.     

南海北部ODP 1144站中更新世气候转型期有孔虫稳定同位素古气候意义

中更新世气候转型期是第四纪古气候研究的一个特殊时期。利用大洋钻探ODP 184航次在南海北部钻取的1144站时间分辨率高达约290年的沉积物样品，开展中更新世气候转型期古气候变化的研究。在中更新世距今80~100万年前，浮游和底栖有孔虫壳体的稳定氧碳同位素变化揭示出，中更新世气候转型中心，即中更新世革命0.9 Ma左右，南海北部表层海水温度的降低和降水量的增加指示东亚冬、夏季风增强。以中更新世革命为界，水体垂向结构上温跃层和营养跃层的深度从之前的间冰期较浅转变为之后的间冰期较深，底层水与表层水的垂直温度梯度从冰期时较大转变为冰期时较小。轨道尺度上，冰消期时南海北部的表层水、次表层水和底层水的变化几乎是同时发生的，不存在超前或滞后的相位差。千年尺度上，有孔虫的氧碳同位素变化都呈现出非常明显的约0.8 ka和约1.4 ka的气候波动周期。氧同位素0.8 ka滤波显示出：在中更新世气候转型期，较强的信号主要出现在间冰期，有时也出现在冰期，与晚第四纪千年尺度气候波动主要出现在冰期不同，说明中更新世的气候转型不仅表现在轨道尺度的气候周期变化上，同时也体现在千年尺度气候波动的特征变化中。      

A Study on the Dissolution Kinetics of Basalt—Water Interaction under Different pH Conditions I：Release of Elements and pH Neutralization Effect

Experimental research on the chemical weathering of alkaline-olivine basalt from Huangyi Mountain,Kuandain County,Liaoning.Province and olivine basalt from Dayangke,Mingxi County,Fujian Province has shown that the acidity of the solution tends to become neutral regardless of what the acidity of the starting solution would be during basalt0-water interaction.We call this phenome-non“pH neutralized Effect”.The dissolved species in the solution were determined and unreacted and reacted sample-surface chemical components involved or uninvolved in reaction were analyzed using X-ray photoelectron spectroscopy(XPS).The results revealed two different mechanisms of dissolution of basalt in acidic and basic solutions.     

Near hydrothermal alteration of obsidian glass: Implications for long term performance assessments

Obsidian glass alteration experiments under near hydrothermal conditions were performed to study mechanism and conditions of formation of altered minerals. X-ray diffraction patterns and cell dimensions of the specimens treated at 150, 200 and 300°C (pH = 8.03) revealed appearance of three main minerals — illite (9.5–10 Å), chlorite (7.04 Å) and halloysite (10.25Å). Further increase in the pH favours matrix dissolution with the formation of secondary altered layers. SEM-EDS study show that the alteration causes smoothing of the grain surfaces. These surfaces exhibits etch pits and series of depressions, formed by the process of dissolution. SEM — Back Scattered Electron images of obsidian specimens show thin laminae of smectite, with foliated bulky rims and cellular honeycomb texture, formed by precipitation from the solution as well as by direct transformation of glass during alteration. This mechanism is resulting from the alteration of alkalis by ionic inter-diffusion with H₃O⁺ and H⁺ and inward diffusion of H₂O, leading to free diffusion of silica into solution and then to a local rearrangement of the glass framework. Thus, a direct transformation of glass into clay minerals is the major reaction mechanism as evidenced by the mechanism of glass dissolution and subsequent mineral precipitation.     

Thermodynamics and behavior of γ-Mg2SiO4 at high pressure: Implications for Mg2SiO4 phase equilibrium

Raman spectra of γ-Mg₂SiO₄ taken to 200 kbar were used to calculate entropy and heat capacity at various P-T conditions. These new thermodynamic data on γ-MgSiO₄, similar data on MgSiO₃ perovskite (pv), previous data on β-MgSiO₄ and MgO (mw), and previous volumetric data of all phases were used to calculate the phase boundaries in the Mg₂SiO₄ phase diagram. Our resulting slope for the β→γ transition (50±4 bar K^-1) is in excellent agreement with recent multi-anvil studies. The slopes for the β→pv+MgO and γ→pv+MgO are-7±3 and -25±4 bar K^-1, respectively, and are consistent with our CO₂ laser heated diamond anvil studies. These slopes result in a β-γ-MgO+pv triple point at approximately 229 kbar and 2260 K for the iron free system.     

Kurnakovite deposits on the Qinghai-Tibet Plateau (II): an investigation from chemical kinetics of chloropinnoite dissolution

Lakes on the Qinghai-Tibet Plateau (QTP) are of particular interest to researchers because of their unusual high concentrations of lithium (Li), boron (B), and potassium (K). Kurnakovite, a member of the inderite group, is well-distributed on the QTP, however, the geochemical mechanisms of kurnakovite transformation requires further identification and clarification. This study aims to elucidate the geochemical mechanisms of kurnakovite deposits on the QTP from chloropinnoite dissolution using chemical kinetic and spectroscopic techniques. The new borate, chloropinnoite 2MgO · 2B₂O₃ · MgCl₂ · 14H₂O, was obtained from the natural concentrated salt lake brine on the QTP. The kinetics of chloropinnoite dissolved in 4.5 % (wt%) boric acid solution at 303, 313, and 323 K were investigated. The characterization of the phase transitions and the kinetics were carried out by chemical titration analysis, X-ray powder diffraction spectrometry, Fourier Transform Infrared (FT-IR), and Raman spectrometry. The results demonstrate that similar kinetic processes occur at all three temperatures and can be divided into dissolution, supersaturation, and precipitation, according to three distinct kinetic curves. Kurnakovite was the final phase transition (terminal secondary mineral) within the chloropinnoite-boric acid solution. The dissolution rate of chloropinnoite (the dissolution stage) could be described by second order pseudo-homogeneous reaction model. According to the spectroscopy data, geochemical mechanism of kurnakovite was identified. The new geochemical hypothesis well explains the geochemical mechanism of kurnakovite minerals on the QTP.     

An experimental study of anorthosite dissolution in lunar picritic magmas: Implications for crustal assimilation processes

Experiments characterizing the kinetics of anorthosite dissolution in lunar picritic magmas (very low-Ti, low-Ti, and high-Ti picritic glasses) were conducted at 0.6 GPa and 1250-1400 °C using the dissolution couple method. Reaction between the anorthosite and lunar picritic magmas at 1250-1300 °C produced a spinel + melt layer. Reaction between the anorthosite and an olivine-saturated low-Ti magma at 1250-1300 °C produced a crystal-free region between the spinel + melt layer and the olivine-saturated magma. The anorthosite dissolution experiments conducted at 1400 °C simply dissolved anorthosite and did not result in a crystal-bearing region. The rate of anorthosite dissolution strongly depends on temperature and composition of the reacting melt. Concentration profiles that develop during anorthosite dissolution are nonlinear and extend from the picritic glass compositions to anorthite. These profiles feature a large and continuous variation in melt density and viscosity from the anorthosite-melt interface to the initial picritic magmas. In both the low-Ti and high-Ti magmas the diffusive fluxes of TiO₂, Al₂O₃, and SiO₂ are strongly coupled to the concentration gradients of CaO and FeO. Anorthosite dissolution may play an important role in producing the chemical variability of the lunar picritic magmas, the origin of spinel in the lunar basalts and picritic glasses, and the petrogenesis of the high-Al basalts.     

Mechanisms of orthopyroxene dissolution in silica-undersaturated melts at 1 atmosphere and implications for the origin of silica-rich glass in mantle xenoliths

Experiments dissolving orthopyroxene (En₉₃) in a variety of Si-undersaturated alkaline melts at 1 atmosphere and variable f _O2 demonstrate that orthopyroxene dissolves to form olivine, Si-rich melt and clinopyroxene. These phases form a texturally and chemically distinct boundary layer around the partly dissolved orthopyroxene crystals. The occurrence of clinopyroxene in the boundary layer is due to inward diffusion of Ca from the solvent melt to the boundary layer causing clinopyroxene saturation. Compositional profiles through the solvent and the boundary layer for a number of experiments demonstrate rapid diffusion of cations across the boundary layer – solvent interface. SiO₂ diffuses outward from the boundary layer whereas CaO and Al₂O₃ diffuse toward the Si-enriched boundary layer melt. The rate of Al diffusion is slower under reducing conditions compared to the rates in experiments performed in air. Concentrations of FeO and MgO in the boundary layer and solvent are approximately equal indicating rapid diffusion and attainment of equilibrium despite ongoing crystallisation of clinopyroxene within the boundary layer. The behaviour of Na₂O and K₂O is strongly affected by f _O2. Under reducing conditions Na₂O and K₂O concentrations are approximately equal in the boundary layer and solvent indicating normal diffusion down the concentration gradient and attainment of equilibrium. Under oxidising conditions, K₂O and to a lesser extent Na₂O, have compositional profiles indicative of uphill diffusion likely due to their preference for more polymerised Si- and Al-rich melts. Under reduced conditions Al-enrichment in the boundary layer melt is not as extreme and uphill diffusion did not occur. The composition of the solvent melt after the experiments indicates that it was contaminated by the boundary layer by convective mixing due to the onset of hydrodynamic instabilities brought on by density and viscosity contrasts between the two melts. Despite using a wide variety of solvent melt compositions we find that the boundary layer melts converge toward a common composition at high SiO₂ contents. The composition of glass generated by orthopyroxene dissolution at 1 atmosphere is similar in many respects to Si-rich glass found in many orthopyroxene-rich mantle xenoliths that have been attributed to high pressure in situ processes including mantle metasomatism. The results of this study suggest that at least some Si-rich melts are likely to have formed by dissolution of xenolith orthopyroxene at low pressure possibly by their Si-undersaturated host magmas. Received: 30 August 1996 / Accepted: 15 April 1998     

A zinc oxide-coated nanoporous carbon adsorbent for lead removal from water: Optimization, equilibrium modeling, and kinetics studies

A zinc oxide-coated nanoporous carbon sorbent was prepared by acid modification and ZnO functionalization of mesoporous carbon. The synthesized materials, such as mesoporous carbon, oxidized mesoporous carbon and zinc oxide-coated nanoporous carbon, were characterized by nitrogen adsorption–desorption analysis, Fourier transform infrared spectra, scanning electron microscopy, and transmission electron microscopy. ZnO on oxidized mesoporous carbon gradually increased with increase in the number of cycles. Furthermore, the effects of agitation time, initial metal ions concentration, adsorbent dose, temperature and pH on the efficiency of Pb(II) ion removal were investigated as the controllable factors by Taguchi method. The value of correlation coefficients showed that the equilibrium data fitted well to the Langmuir isotherm. Among the adsorbents, zinc oxide-coated nanoporous carbon showed the largest adsorption capacity of 522.8 mg/g (2.52 mmol/g) which was almost close to that of the zinc oxide-coated (2.38 mmol/g), indicating the monolayer spreading of ZnO onto the oxidized mesoporous carbon. The results of the present study suggest that ZnO-coated nanoporous carbon can be effectively used for Pb(II) adsorption from aqueous solution, whereas a part of acidic functional groups may be contributed to binding the Pb(II) for the oxidized mesoporous carbon and mesoporous carbon. Kinetic studies indicated that the overall adsorption process of Pb(II) followed the pseudo-second-order model. The ZnO-coated nanoporous carbon was regenerated and found to be suitable of reuse of the adsorbent for successive adsorption–desorption cycles without considerable loss of adsorption capacity.     

Transition from shoshonitic to adakitic magmatism in the eastern Pontides,NE Turkey: Implications for slab window melting

The formation of the eastern Pontides orogenic belt has been widely assigned to a northward subduction of the Neotethyan oceanic slab during the late Mesozoic–Cenozoic. Here we provide an alternate model based on new geological, geochemical and isotopic data. The magmatic activity in the far south of the belt started in the early Campanian with shoshonitic trachyandesites and associated pyroclastics. This sequence is covered by the late Campanian–early Maastrichtian reefal limestones and another stage of high-K volcanism represented by analcimized leucite-rich ultrapotassic rocks of the Maastrichtian–early Paleocene (?) ages. The shoshonitic and ultrapotassic rocks, with K₂O contents ranging from 0.26 to 6.95 wt.%, display broadly similar rare earth and multi-element distribution patterns. Both rock types are enriched in LILE and LREE and depleted in HFSE (Nb, Ta and Ti), suggesting a subduction-enriched mantle source for the magma generation. Subsequently, during the late Paleocene, a stage of acidic magmatism (SiO₂ of 53.25–73.61 wt.%) that shows adakitic geochemical characteristics including high Sr/Y (46–416) and La/Yb (11–51) and low Y (2.6–12.2 ppm), is documented characterized by melting of a mafic source such as the MORB crust with garnet in the residue. The adakitic magmatism began at ~ 56 Ma and migrated toward the north through time, culminating with porphyritic andesites (~ 47 Ma) that were emplaced in the Gumushane–Bayburt line and its vicinity. North of this line, coeval magmas show typical calc-alkaline nature and continued to develop toward further north until the middle to late Eocene. Based on the spatial and temporal variations in the magmas generated in the eastern Pontides orogenic belt, we propose a new geodynamic model to explain the tectonomagmatic evolution of these rocks and correlate the adakitic magmatism to ridge subduction and slab window process within a south-dipping subduction zone. Our model is in contrast to the previous proposals which envisage partial melting or delamination of thickened lower continental crust due to the collision in the south during the Paleocene–Eocene.     

Dissolution kinetics of a lunar glass simulant at 25 degrees C: the effect of pH and organic acids

The dissolution kinetics of a simulated lunar glass were examined at pH 3, 5, and 7. Additionally, the pH 7 experiments were conducted in the presence of citric and oxalic acid at concentrations of 2 and 20 mM. The organic acids were buffered at pH 7 to examine the effect of each molecule in their dissociated form. At pH 3, 5, and 7, the dissolution of the synthetic lunar glass was observed to proceed via a two-stage process. The first stage involved the parabolic release of Ca, Mg, Al, and Fe, and the linear release of Si. Dissolution was incongruent, creating a leached layer rich in Si and Ti which was verified by transmission electron microscopy (TEM). During the second stage the release of Ca, Mg, Al, and Fe was linear. A coupled diffusion/surface dissolution model was proposed for dissolution of the simulated lunar glass at pH 3, 5, and 7. During the first stage the initial release of mobile cations (i.e., Ca, Mg, Al, Fe) was limited by diffusion through the surface leached layer of the glass (parabolic release), while Si release was controlled by the hydrolysis of the Si-O-Al bonds at the glass surface (linear release). As dissolution continued, the mobile cations diffused from greater depths within the glass surface. A steady-state was then reached where the diffusion rate across the increased path lengths equalled the Si release rate from the surface. In the presence of the organic acids, the dissolution of the synthetic lunar glass proceeded by a one stage process. The release of Ca, Mg, Al, and Fe followed a parabolic relationship, while the release of Si was linear. The relative reactivity of the organic acids used in the experiments was citrate > oxalate. A thinner leached layer rich in Si/Ti, as compared to the pH experiments, was observed using TEM. Rate data suggest that the chemisorption of the organic anion to the surface silanol groups was responsible for enhanced dissolution in the presence of the organic acids. It is proposed that the increased rate of Si release is responsible for the one stage parabolic release of mobile cations and the relatively thin leached layer compared to experiments at pH 3 and 5.