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• W1990813114 abstract "The requirements of any experimental investigation of a reaction, such as dissolution or precipitation, at the solid-liquid interface are delineated, and it is shown that no previously adopted experimental method successfully meets all of these criteria. A new strategy for studying such reactions is therefore proposed, and described specifically for the dissolution kinetics of calcium carbonate in acidic aqueous solution. This technique involves locating a calcite crystal in part of one wall of a rectangular duct, through which reactant flows under laminar conditions, and positioning either an amperometric or potentiometric detector electrode immediately adjacent to and downstream of the crystal. The rate of the reaction at the crystal surface is then followed by measuring the concentration of the reactant or products reaching the electrode as a function of solution flow rate. In this way both transport (to the crystal and detection system) and the surface topography of the crystal are defined and controllable, and, most importantly, the concentrations interrogated by the detector electrode are those pertaining at the crystal surface and not the bulk values, which are those probed with other (previous) methods. A mechanistic model for the dissolution reaction at pH < 4, <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML overflow=scroll> <mml:msup> <mml:mrow> <mml:mi mathvariant=normal>H</mml:mi> </mml:mrow> <mml:mo>+</mml:mo> </mml:msup> <mml:mo>+</mml:mo> <mml:msub> <mml:mrow> <mml:mi mathvariant=normal>CaCO</mml:mi> </mml:mrow> <mml:mn>3</mml:mn> </mml:msub> <mml:mrow> <mml:mo stretchy=false>→</mml:mo> </mml:mrow> <mml:mspace width=thinmathspace /> <mml:mrow> <mml:mi mathvariant=normal>C</mml:mi> </mml:mrow> <mml:msup> <mml:mrow> <mml:mi mathvariant=normal>a</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> <mml:mo>+</mml:mo> </mml:mrow> </mml:msup> <mml:mspace width=thinmathspace /> <mml:mo>+</mml:mo> <mml:msubsup> <mml:mrow> <mml:mi mathvariant=normal>HCO</mml:mi> </mml:mrow> <mml:mn>3</mml:mn> <mml:mo>−</mml:mo> </mml:msubsup> </mml:math> , is developed, and it is recognized that half-, first- and second-order reactions in surface H + constitute possible candidate heterogeneous processes. The model also takes the following homogeneous (solution) reactions into account: <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML overflow=scroll> <mml:msubsup> <mml:mrow> <mml:mi mathvariant=normal>HCO</mml:mi> </mml:mrow> <mml:mn>3</mml:mn> <mml:mo>−</mml:mo> </mml:msubsup> <mml:mspace width=thinmathspace /> <mml:mo>+</mml:mo> <mml:msup> <mml:mrow> <mml:mi mathvariant=normal>H</mml:mi> </mml:mrow> <mml:mo>+</mml:mo> </mml:msup> <mml:mrow> <mml:mo stretchy=false>⇌</mml:mo> </mml:mrow> <mml:mspace width=thinmathspace /> <mml:msub> <mml:mrow> <mml:mi mathvariant=normal>H</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msub> <mml:mrow> <mml:mi mathvariant=normal>C</mml:mi> </mml:mrow> <mml:msub> <mml:mrow> <mml:mi mathvariant=normal>O</mml:mi> </mml:mrow> <mml:mn>3</mml:mn> </mml:msub> <mml:mspace width=thinmathspace /> <mml:mrow> <mml:mover> <mml:mo stretchy=false>⟶</mml:mo> <mml:mrow> <mml:msub> <mml:mi>k</mml:mi> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi mathvariant=normal>H</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msub> <mml:mrow> <mml:mi mathvariant=normal>C</mml:mi> </mml:mrow> <mml:msub> <mml:mrow> <mml:mi mathvariant=normal>O</mml:mi> </mml:mrow> <mml:mn>3</mml:mn> </mml:msub> </mml:mrow> </mml:msub> </mml:mrow> </mml:mover> </mml:mrow> <mml:mspace width=thinmathspace /> <mml:mrow> <mml:mi mathvariant=normal>C</mml:mi> </mml:mrow> <mml:msub> <mml:mrow> <mml:mi mathvariant=normal>O</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msub> <mml:mspace width=thinmathspace /> <mml:mo>+</mml:mo> <mml:msub> <mml:mrow> <mml:mi mathvariant=normal>H</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msub> <mml:mrow> <mml:mi mathvariant=normal>O</mml:mi> </mml:mrow> </mml:math> , <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML overflow=scroll> <mml:msub> <mml:mi>K</mml:mi> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi mathvariant=normal>H</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msub> <mml:mrow> <mml:mi mathvariant=normal>C</mml:mi> </mml:mrow> <mml:msub> <mml:mrow> <mml:mi mathvariant=normal>O</mml:mi> </mml:mrow> <mml:mn>3</mml:mn> </mml:msub> </mml:mrow> </mml:msub> <mml:mspace width=thinmathspace /> <mml:mo>=</mml:mo> <mml:mspace width=thinmathspace /> <mml:mspace width=thinmathspace /> <mml:msub> <mml:mi>a</mml:mi> <mml:mrow> <mml:mi mathvariant=normal>H</mml:mi> </mml:mrow> </mml:msub> <mml:mspace width=thinmathspace /> <mml:mo>+</mml:mo> <mml:mspace width=thinmathspace /> <mml:msub> <mml:mi>a</mml:mi> <mml:mrow> <mml:msubsup> <mml:mrow> <mml:mi mathvariant=normal>HCO</mml:mi> </mml:mrow> <mml:mn>3</mml:mn> <mml:mo>−</mml:mo> </mml:msubsup> </mml:mrow> </mml:msub> <mml:mspace width=thinmathspace /> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:mspace width=thinmathspace /> <mml:msub> <mml:mi>a</mml:mi> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi mathvariant=normal>H</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msub> <mml:mrow> <mml:mi mathvariant=normal>C</mml:mi> </mml:mrow> <mml:msub> <mml:mrow> <mml:mi mathvariant=normal>O</mml:mi> </mml:mrow> <mml:mn>3</mml:mn> </mml:msub> </mml:mrow> </mml:msub> </mml:math> The backward implicit finite difference method is used to provide theory for the proposed flow cell experiment. Specifically this relates the rate of an n th order process at the crystal surface to the transport-limited current at an amperometric detector electrode, as a function of solution flow rate and cell-crystal-electrode geometry. The computational method selected allows both the full parabolic velocity profile and any value of n to be considered. The validity of the numerical approach is checked by invoking the Lévêque approximation (linearizing the parabolic velocity profile) and solving the problem analytically for n = 0 and 1. The numerical method is extended so that both parallel heterogeneous and homogeneous reactions are covered, specifically so that theory describing the mechanistic model can be derived as related to the flow cell experiment. The design and construction of the necessary experimental apparatus is described, along with experiments devised to prove the validity of the experimental approach. The results of flow cell dissolution experiments carried out with 0.25–1.0 mM HCl solutions are presented, and it is shown for the first time that the reaction between H + and calcite is not transport-controlled. Assuming <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML overflow=scroll> <mml:msub> <mml:mi>k</mml:mi> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi mathvariant=normal>H</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msub> <mml:mrow> <mml:mi mathvariant=normal>C</mml:mi> </mml:mrow> <mml:msub> <mml:mrow> <mml:mi mathvariant=normal>O</mml:mi> </mml:mrow> <mml:mn>3</mml:mn> </mml:msub> </mml:mrow> </mml:msub> <mml:mspace width=thinmathspace /> <mml:mo>=</mml:mo> <mml:mspace width=thinmathspace /> <mml:mspace width=thinmathspace /> <mml:mn>20</mml:mn> <mml:mspace width=thinmathspace /> <mml:msup> <mml:mrow> <mml:mi mathvariant=normal>s</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> <mml:mspace width=thinmathspace /> <mml:mrow> <mml:mi mathvariant=normal>and</mml:mi> </mml:mrow> <mml:mspace width=thinmathspace /> <mml:msub> <mml:mi>K</mml:mi> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi mathvariant=normal>H</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msub> <mml:mrow> <mml:mi mathvariant=normal>C</mml:mi> </mml:mrow> <mml:msub> <mml:mrow> <mml:mi mathvariant=normal>O</mml:mi> </mml:mrow> <mml:mn>3</mml:mn> </mml:msub> </mml:mrow> </mml:msub> <mml:mspace width=thinmathspace /> <mml:mo>=</mml:mo> <mml:mspace width=thinmathspace /> <mml:mn>3.06</mml:mn> <mml:mspace width=thinmathspace /> <mml:mspace width=thinmathspace /> <mml:mrow> <mml:mo>×</mml:mo> </mml:mrow> <mml:mspace width=thinmathspace /> <mml:mspace width=thinmathspace /> <mml:mrow> <mml:mn>1</mml:mn> </mml:mrow> <mml:msup> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>4</mml:mn> </mml:mrow> </mml:msup> <mml:msub> <mml:mspace width=thinmathspace /> <mml:mrow> <mml:mi mathvariant=normal>M</mml:mi> </mml:mrow> </mml:msub> </mml:math> , a best fit to the data is obtained for a first-order heterogeneous process with a rate constant of (0.043 ± 0.015) cm s -1 ." @default.
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• W1990813114 date "1990-02-06" @default.
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• W1990813114 title "The dissolution of calcite in aqueous solution at pH < 4: kinetics and mechanism" @default.
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• W1990813114 doi "https://doi.org/10.1098/rsta.1990.0001" @default.
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