A study of the hydration of the alkali metal ions in aqueous solution

Abstract

The hydration of the alkali metal ions in aqueous solution has been studied by large angle X-ray scattering (LAXS) and double difference infrared spectroscopy (DDIR). The structures of the dimethyl sulfoxide solvated alkali metal ions in solution have been determined to support the studies in aqueous solution. The results of the LAXS and DDIR measurements show that the sodium, potassium, rubidium and cesium ions all are weakly hydrated with only a single shell of water molecules. The smaller lithium ion is more strongly hydrated, most probably with a second hydration shell present. The influence of the rubidium and cesium ions on the water structure was found to be very weak, and it was not possible to quantify this effect in a reliable way due to insufficient separation of the O-D stretching bands of partially deuterated water bound to these metal ions and the O-D stretching bands of the bulk water. Aqueous solutions of sodium, potassium and cesium iodide and cesium and lithium hydroxide have been studied by LAXS and M-O bond distances have been determined fairly accurately except for lithium. However, the number of water molecules binding to the alkali metal ions is very difficult to determine from the LAXS measurements as the number of distances and the temperature factor are strongly correlated. A thorough analysis of M-O bond distances in solid alkali metal compounds with ligands binding through oxygen has been made from available structure databases. There is relatively strong correlation between M-O bond distances and coordination numbers also for the alkali metal ions even though the M-O interactions are weak and the number of complexes of potassium, rubidium and cesium with well-defined coordination geometry is very small. The mean M-O bond distance in the hydrated sodium, potassium, rubidium and cesium ions in aqueous solution have been determined to be 2.43(2), 2.81(1), 2.98(1) and 3.07(1) Å, which corresponds to six-, seven-, eight- and eight-coordination. These coordination numbers are supported by the linear relationship of the hydration enthalpies and the M-O bond distances. This correlation indicates that the hydrated lithium ion is four-coordinate in aqueous solution. New ionic radii are proposed for four- and six-coordinate lithium(I), 0.60 and 0.79 Å, respectively, as well as for five- and six-coordinate sodium(I), 1.02 and 1.07 Å, respectively. The ionic radii for six- and seven-coordinate K(+), 1.38 and 1.46 Å, respectively, and eight-coordinate Rb(+) and Cs(+), 1.64 and 1.73 Å, respectively, are confirmed from previous studies. The M-O bond distances in dimethyl sulfoxide solvated sodium, potassium, rubidium and cesium ions in solution are very similar to those observed in aqueous solution.

Figure 1

(a) HDO in bulk water, ν_O–D = 2509 cm^–1, d_{O(···D)–O} = 2.89 Å. (b) HDO affected by a structure making cation, ν_O–D < 2509 cm^–1, d_{O(···D)–O} < 2.89 Å. (c) HDO affected by a structure breaking cation, ν_O–D > 2509 cm^–1, d_{O(···D)–O} > 2.89 Å. O–D bond strength is indicated by the line thickness, and orange color represent a D atom.

Figure 2

Crystal structures of neutral, homoleptic, Li⁺ hydrates. The dashed line is drawn between mean values for four- and six-coordination (geometrically approved atoms). Error bars correspond to two standard deviations. The sums of the radii given by Shannon and the oxygen radius are shown as orange crosses.

Figure 3

Crystal structures of neutral, monodentate non-ether Li⁺ complexes. The dashed line is drawn between mean values for four- and six-coordination (geometrically approved atoms). Error bars correspond to two standard deviations. The sums of the radii given by Shannon and the oxygen radius are shown as orange crosses.

Figure 4

Crystal structures of neutral, homoleptic, Na⁺ hydrates. The dashed line is drawn between mean values for five- and six-coordination (geometrically approved atoms). Error bars correspond to ±2 standard deviations. The sums of the radii given by Shannon and the oxygen radius are shown as orange crosses. A green circle represents the experimental M–O distance determined by LAXS for six-coordination in this study.

Figure 5

Crystal structures of neutral, non-ether, monodentate Na⁺ complexes. The dashed line is drawn between mean values for five- and six-coordination (geometrically approved atoms). Error bars correspond to ±2 standard deviations. The sums of the radii given by Shannon and the oxygen radius are shown as orange crosses. A green circle represents the experimental M–O distance determined by LAXS for six-coordination in this study.

Figure 6

Crystal structures of potassium THF solvates. The error bar corresponds to ±2 standard deviations. The sums of the radii given by Shannon and the oxygen radius are shown as orange crosses. The dashed line is drawn 0.02 Å above average values for six- and seven-coordination in order to correct for the smaller size of THF oxygen relative to water oxygen (see text). A green circle represents the experimental M–O distance determined by LAXS for seven-coordination in this study.

Figure 7

(Top) LAXS radial distribution curves for a 2.001 mol·dm^–3 aqueous solution of cesium iodide. Upper part: Separate model contributions (offset: 20) of the hydrated cesium ion (black line), the hydrated iodide ion (red line) and the aqueous bulk (blue line). (Middle) Experimental RDF: D(r) – 4πr²ρ_o (red line), sum of model contributions (black line) and the difference between experimental and calculated functions (blue line). (Bottom) Reduced LAXS intensity functions s·i(s) (solid line); model s·i_calc(s) (dashed line).

Figure 8

(Top) LAXS radial distribution curves for a 2.007 mol·dm^–3 aqueous solution of potassium iodide. Upper part: Separate model contributions (offset: 12) of the hydrated potassium ion (black line), the hydrated iodide ion (red line) and the aqueous bulk (blue line). (Middle) Experimental RDF: D(r) – 4πr²ρ_o (red line), sum of model contributions (black line) and the difference between experimental and calculated functions (blue line). (Bottom) Reduced LAXS intensity functions s·i(s) (solid line); model s·i_calc(s) (dashed line).

Figure 9

(Top) LAXS radial distribution curves for a 2.007 mol·dm^–3 aqueous solution of sodium iodide. Upper part: Separate model contributions (offset: 14) of the hydrated sodium ion (black line), the hydrated iodide ion (red line) and the aqueous bulk (blue line). (Middle) Experimental RDF: D(r) – 4πr²ρ_o (red line), sum of model contributions (black line) and the difference between experimental and calculated functions (blue line). (Bottom) Reduced LAXS intensity functions s·i(s) (solid line); model s·i_calc(s) (dashed line).

Figure 10

Affected spectrum for NaI(aq), KI(aq), RbI(aq) and CsI(aq). The spectrum can be divided into two main contributions, both of which are discussed in the text. The dashed line shows the position of the wavenumber 2509 cm^–1 where bulk water HDO is located.

Figure 11

Affected spectrum for NaClO₄(aq) and LiClO₄(aq). The orange line represents the contribution from the anion (iodide) and the green line the contribution from the alkali metal cation. The dashed line shows the position of the wavenumber 2509 cm^–1 where bulk water affected HDO is located. Thin black lines show the Gaussian peaks that are combined to produce the cationic contribution.

Figure 12

A two-dimensional approximation of the three-dimensional hydrogen bonded network of water: (a) bulk water, (b) around a structure making ion, (c) around a structure breaking ion. The limitations associated with showing a three-dimensional network in two dimensions, such as incomplete bond illustration, have to be accepted. The effects on water structure are exaggerated in the figure.

Figure 13

Heats of hydration as a function of the inverse metal oxygen distance. Dashed trendlines are shown for the occurring hydration numbers 4, 6, 7, 8, 9, 10, and 12. Experimental values from this and a previous work are shown in red-white circles, and a possible linear relationship is shown with a solid line. Other values are based on crystal structures whereof values within blue circles are from the radii proposed in Table 1 and all other values are from Shannon radii of different coordination numbers, ref (37).

Figure 14

The relationship between determined ionic radii (diamonds), surface area (triangles) and volume (squares) for the alkali metal ions. Determined values for ionic radii are those proposed in this and previous papers based on experiments in aqueous solution. The radii for six- and four-coordinate Li⁺ respectively are also shown in open diamonds. Higher degree linear regression functions for volume and area have been forced through the origin while the second degree function for radii is unconstrained.