THE GEOCHEMISTRY OF NATURAL WATERS

1. 1 THE GEOCHEMISTRY OF NATURAL WATERS CHEMICAL KINETICS CHAPTER 2f - Kehew (2001)

2. 2 LEARNING OBJECTIVES Be introduced to some of the basic principles of chemical kinetics. Learn what is meant by reaction order. Become familiar with some basic rate-law expressions. Learn about the Arrhenius equation. Gain an appreciation for the factors controlling mineral precipitation and dissolution rates. The first part of this lecture deals with Chemical Kinetics, or the study of the rates of chemical reactions. We will cover only some of the very basic principles here, including learning about rate laws, reaction order, the Arrhenius equation (which governs how rates depend on temperature), and the kinetics of mineral precipitation and dissolution. In the second part of the lecture, we will start discussing acid-base reactions and the carbonate system. The first part of this lecture deals with Chemical Kinetics, or the study of the rates of chemical reactions. We will cover only some of the very basic principles here, including learning about rate laws, reaction order, the Arrhenius equation (which governs how rates depend on temperature), and the kinetics of mineral precipitation and dissolution. In the second part of the lecture, we will start discussing acid-base reactions and the carbonate system.

3. 3 TEMPERATURE-DEPENDENCE OF RATES Arrhenius equation Higher temperatures lead to faster chemical reactions. A general rule of thumb: an increase of 10°C in temperature generally leads to a doubling of reaction rate. The temperature dependence of rates is given by the well-known Arrhenius equation. It tells us that the rate constant is equal to a constant (k0) times the exponent of (-Ea/RT). Ea is the activation energy and is given in Joules or calories, R is the gas constant (8.314 J K-1 mol-1 or 1.987 cal K-1 mol-1), and T is the absolute temperature in K. Both Ea and k0 are constants, so as T increases, (-Ea/RT) becomes increasingly less negative, such that k increases exponentially with increasing temperature. Thus, reaction rates increase dramatically with temperature. It turns out that, for most geochemically relevant reactions, Ea varies over a comparatively restricted range. Thus, a rough rule of thumb is that an increase of 10°C will lead to an increase in the reaction rate by a factor of approximately 2. The temperature dependence of rates is given by the well-known Arrhenius equation. It tells us that the rate constant is equal to a constant (k0) times the exponent of (-Ea/RT). Ea is the activation energy and is given in Joules or calories, R is the gas constant (8.314 J K-1 mol-1 or 1.987 cal K-1 mol-1), and T is the absolute temperature in K. Both Ea and k0 are constants, so as T increases, (-Ea/RT) becomes increasingly less negative, such that k increases exponentially with increasing temperature. Thus, reaction rates increase dramatically with temperature. It turns out that, for most geochemically relevant reactions, Ea varies over a comparatively restricted range. Thus, a rough rule of thumb is that an increase of 10°C will lead to an increase in the reaction rate by a factor of approximately 2.

4. 4 ACTIVATION ENERGY BARRIER As mentioned in the slide, Ea represents the height of an energy barrier. In the absence of this energy barrier, the system would spontaneously shift from the reactants to the products, because the products occur at a lower energy, and thermodynamics tells us that the reaction should proceed in such a direction as to lower the energy of the system. However, a barrier to this reaction exists; thermodynamics can predict the relative change in energy between reactants and products, but it cannot predict the existence of or the magnitude of the energy barrier. The constant k0 in the Arrhenius equation is called the pre-exponential factor. Among other things, it is a measure of the number of attempts the system makes to get over the energy barrier per unit time. As mentioned in the slide, Ea represents the height of an energy barrier. In the absence of this energy barrier, the system would spontaneously shift from the reactants to the products, because the products occur at a lower energy, and thermodynamics tells us that the reaction should proceed in such a direction as to lower the energy of the system. However, a barrier to this reaction exists; thermodynamics can predict the relative change in energy between reactants and products, but it cannot predict the existence of or the magnitude of the energy barrier. The constant k0 in the Arrhenius equation is called the pre-exponential factor. Among other things, it is a measure of the number of attempts the system makes to get over the energy barrier per unit time.

5. 5 MINERAL DISSOLUTION - I Experimental studies have shown that the rate of mineral dissolution is a function of the degree of undersaturation, i.e., the following reaction applies: The more undersaturated the solution with respect to a mineral, the faster it will dissolve. As the solution approaches saturation, the rate of dissolution will decrease. As we have already pointed out, the farther a reaction is from equilibrium, the faster it will proceed. Near equilibrium, the reaction rate must slow to zero. The equation shown in the slide above reflects this fact in the case of mineral dissolution reactions. When the solution is far from saturation with a mineral, the SI << 0, i.e., IAP << KSP. Under these conditions, (1 - IAP/KSP) ? 1 and not very sensitive to the exact value of IAP, and hence the solution composition. So when the solution is sufficiently far from saturation with the mineral, the rate of dissolution is independent of the exact saturation state, but the dissolution rate will be relatively fast. As the solution nears saturation with respect to the mineral, IAP becomes a significant fraction of KSP, and dissolution slows. Finally, at saturation, IAP = KSP, and the dissolution rate becomes zero. As we have already pointed out, the farther a reaction is from equilibrium, the faster it will proceed. Near equilibrium, the reaction rate must slow to zero. The equation shown in the slide above reflects this fact in the case of mineral dissolution reactions. When the solution is far from saturation with a mineral, the SI << 0, i.e., IAP << KSP. Under these conditions, (1 - IAP/KSP) ? 1 and not very sensitive to the exact value of IAP, and hence the solution composition. So when the solution is sufficiently far from saturation with the mineral, the rate of dissolution is independent of the exact saturation state, but the dissolution rate will be relatively fast. As the solution nears saturation with respect to the mineral, IAP becomes a significant fraction of KSP, and dissolution slows. Finally, at saturation, IAP = KSP, and the dissolution rate becomes zero.

6. 6 MINERAL DISSOLUTION - II Mineral dissolution rates also depend on surface area. Greater surface area leads to faster dissolution. It is also often found that experimentally measured rates of dissolution appear to decrease with time after the start of the experiment. Why? Partially leached layer on surface retards the migration of ions through the altered layer. Initial rapid rate due to higher dissolution rate of smaller particles; rate slows when smaller particles have been removed. Dissolution rates of minerals are also known to depend strongly on surface area. It is common experience that more finely subdivided solids dissolve faster than the same mass of coarser solids. For example, a whole 100-gram calcite crystal dissolves much more slowly in dilute acid than the same 100 grams of calcite ground to a fine powder. This is a reflection of the greater surface area of the latter per unit mass. A final complication in mineral dissolution kinetics is the following. It has often been found experimentally that, initial rates of dissolution are quite fast, but then they slow with time. Early on, this was thought to indicate the universal development of partially leached layers on the surface of minerals as dissolution proceeded. This leached layer was thought to impede further reaction progress by retarding the diffusion of ions across the leached layer. Although leached layers may form in some instances, it has subsequently been found that the change in mineral dissolution rate with time results from the fast dissolution of very fine particles at the start of the experiment, with the rate of dissolution slowing when all the fine particles were removed by dissolution. It was found that, when the solid starting materials in mineral dissolution experiments were properly pretreated to remove the fine particles, the initial rapid dissolution phase often is eliminated. Dissolution rates of minerals are also known to depend strongly on surface area. It is common experience that more finely subdivided solids dissolve faster than the same mass of coarser solids. For example, a whole 100-gram calcite crystal dissolves much more slowly in dilute acid than the same 100 grams of calcite ground to a fine powder. This is a reflection of the greater surface area of the latter per unit mass. A final complication in mineral dissolution kinetics is the following. It has often been found experimentally that, initial rates of dissolution are quite fast, but then they slow with time. Early on, this was thought to indicate the universal development of partially leached layers on the surface of minerals as dissolution proceeded. This leached layer was thought to impede further reaction progress by retarding the diffusion of ions across the leached layer. Although leached layers may form in some instances, it has subsequently been found that the change in mineral dissolution rate with time results from the fast dissolution of very fine particles at the start of the experiment, with the rate of dissolution slowing when all the fine particles were removed by dissolution. It was found that, when the solid starting materials in mineral dissolution experiments were properly pretreated to remove the fine particles, the initial rapid dissolution phase often is eliminated.

7. 7 MINERAL PRECIPITATION A nucleation barrier exists that must be overcome before small mineral precipitates will be stable and grow. This nucleation barrier means that mineral precipitation will not occur until a critical degree of supersaturation is attained. Some foreign substances can affect precipitation kinetics. For example, Mg, phosphate and organics can inhibit the precipitation of calcite. For a mineral to precipitate from solution, two steps must be completed: 1) nucleation; and 2) growth. Nucleation is the process by which the first stable crystallite appears. Growth is the process by which a stable nucleus increases in size. A solution near saturation is a dynamic system; there will be local fluctuations within the solution that may lead several ions or molecules suddenly to congregate together and form the initial building blocks of a mineral. If the solution is undersaturated with the mineral, these crystallites will always simply redissolve. If the solution is saturated or supersaturated with the mineral, we would expect the crystallite to be stable, and perhaps even grow. However, this neglects the effect of the surface energy. It takes energy to create a new surface, and this expenditure of energy makes the formation of a small crystallite, with a high ratio of surface area to volume, unstable, even if the solution is saturated with the mineral. However, volume increases more rapidly than surface area, so larger crystallites have a relatively smaller contribution from the unfavorable surface energy term. This means that, if a crystallite (nucleus) reaches a certain critical size, it will be stable and grow. To insure that random fluctuations will give rise to a nucleus larger than the critical size, the solution must be supersaturated to a certain extent, e.g., the supercooling required to freeze a lake in winter. Another complication in mineral precipitation kinetics is that some foreign substances can inhibit nucleation and/or crystal growth by adsorbing onto critical sites on the surface of the nucleus or growing crystal. For a mineral to precipitate from solution, two steps must be completed: 1) nucleation; and 2) growth. Nucleation is the process by which the first stable crystallite appears. Growth is the process by which a stable nucleus increases in size. A solution near saturation is a dynamic system; there will be local fluctuations within the solution that may lead several ions or molecules suddenly to congregate together and form the initial building blocks of a mineral. If the solution is undersaturated with the mineral, these crystallites will always simply redissolve. If the solution is saturated or supersaturated with the mineral, we would expect the crystallite to be stable, and perhaps even grow. However, this neglects the effect of the surface energy. It takes energy to create a new surface, and this expenditure of energy makes the formation of a small crystallite, with a high ratio of surface area to volume, unstable, even if the solution is saturated with the mineral. However, volume increases more rapidly than surface area, so larger crystallites have a relatively smaller contribution from the unfavorable surface energy term. This means that, if a crystallite (nucleus) reaches a certain critical size, it will be stable and grow. To insure that random fluctuations will give rise to a nucleus larger than the critical size, the solution must be supersaturated to a certain extent, e.g., the supercooling required to freeze a lake in winter. Another complication in mineral precipitation kinetics is that some foreign substances can inhibit nucleation and/or crystal growth by adsorbing onto critical sites on the surface of the nucleus or growing crystal.

8. 8 CRYSTAL NUCLEATION This slide shows the Gibbs free energy of an incipient crystallite as a function of its radius (assuming that crystallites can be approximated as spheres; assumption of other shapes does not change the essential details). It is assumed that the solution is saturated with the mineral in question. When random fluctuations in the solution cause very small crystallites (with a radius less than the critical radius) to aggregate, these crystallites have a positive Gibbs free energy owing to unfavorable surface energy. Growth of a crystallite with a radius less than the critical radius would result in a further increase in the Gibbs free energy, so the crystallite falls back down to the left of the above diagram and redissolves. If random fluctuations produce a crystallite of larger than critical size, then the favorable Gibbs free energy of precipitation will outweigh the unfavorable surface energy, and the crystallite (nucleus) will continue to grow, which will allow it to decrease its Gibbs free energy. A crystallite of larger than critical size can fall down to the right of the above diagram. This slide shows the Gibbs free energy of an incipient crystallite as a function of its radius (assuming that crystallites can be approximated as spheres; assumption of other shapes does not change the essential details). It is assumed that the solution is saturated with the mineral in question. When random fluctuations in the solution cause very small crystallites (with a radius less than the critical radius) to aggregate, these crystallites have a positive Gibbs free energy owing to unfavorable surface energy. Growth of a crystallite with a radius less than the critical radius would result in a further increase in the Gibbs free energy, so the crystallite falls back down to the left of the above diagram and redissolves. If random fluctuations produce a crystallite of larger than critical size, then the favorable Gibbs free energy of precipitation will outweigh the unfavorable surface energy, and the crystallite (nucleus) will continue to grow, which will allow it to decrease its Gibbs free energy. A crystallite of larger than critical size can fall down to the right of the above diagram.