Complex Formation Equilibria between Ag(I) and Thioureas in Propan-2-ol

The complex formation equilibria between Ag(I) and thiourea (Tu), Nmethyl-Thiourea (MeTu), N,N-dimethyl-Thiourea (Me 2 Tu), N,N,N,N Tetramethyl-Thiourea (Me 4 Tu), N-ethyl-Thiourea (EtTu), N,N diethyl-Thiourea (Et 2 Tu), and N,N-Ethylen-Thiourea (EnTu) in propan-2-ol as solvent medium have been investigated by potentiometry within the temperature range 10C–40C and self-determined ionic medium by (AgNO 3 ) concentration range 6.36 ⋅ 10–3.83 ⋅ 10−5 m⋅dm (no background electrolyte added). The experimental results can be interpreted with the stepwise formation of tris-coordinated complexes AgL n (n = 1–3; hereafter charge is omitted). The stability constants log β n and the standard thermodynamic changes in enthalpy (ΔH n ) and entropy (ΔS n ) for overall complex formation reactions Ag(I) + nL = AgL n (n = 1–3) have been evaluated. The reactions are exothermic in nature and entropy disfavored for all the investigated ligands.The standard enthalpy and entropy changes for the stepwise reactions AgL n−1 + L = AgL n have been evaluated by difference Δ(ΔH∘ n ) = ΔH ∘


Introduction
In homogeneous equilibria, the solvent medium operates simultaneously on both reactants and products and influences the chemical reactions with counteracting actions which originate from solute-solvent and solvent-solvent interactions.The quantitative balance of such interactions together with the solute-solute interactions determines the actual position of the chemical equilibrium [1][2][3][4][5].
Systematic investigations on single series of reactions but different solvents are of utmost importance for disclosing the role of both the solvents and the various elements of the series on the metal-to-ligand interactions.
Thioureas and in general thiocarbonyl compounds are soft ligands which in hard solvents coordinate to soft metal ions via sulfur atom(s) [6,7].They show relevant chemical affinities towards Ag(I) forming in hydroxyl solvents complexes with high thermodynamic stability ( [8,9] and cited references).
In hydrogen donor solvents, thioureas undergo simultaneous solvation both at the sulfur atom via the acceptor atom(s) of the solvent and, when not exhaustively Nalkylated, to the hydrogen atoms via the donor atom(s) of the solvent.
In hard solvents, in comparison with other metal ions in their ordinary oxidation states, silver ion has remarkable oxidizing properties which suggest that Ag(I) undergoes no strong solvation in such solvents.
The coordination of thiocarbonyl compounds to soft metal ions occurs via sulphur atom(s).The coordination to Ag(I) involves desolvation of both the acceptor Ag(I) and the donor atoms of the ligand and the reinforcement the bond between the hydrogen atoms of the amide groups of the coordinated ligand(s) and the oxygen atom of the solvating solvent [8,9].
In this contribution, the results of investigations on thermodynamics of complex formation equilibria between Ag(I) and thiourea or N-alkyl-substituted thioureas in propan-2-ol are reported.The investigation has been performed by potentiometry at different temperatures ( = 283.16-313.16K).Standard free energy changes (Δ ∘ ) for the complex formation reactions have been deduced from the stability constants, while standard enthalpy and entropy changes, Δ ∘ and Δ ∘ , from the dependence of Δ ∘ on temperature.
The water content of the reagent solutions and solvent was periodically checked by KF method.

Measurements.
Potentiometric measurements have been carried out in thermostated cell.The cell is reproduced in Scheme 1.
The ligand total concentration in the titrated solution ranges from No supporting electrolyte has been added.The ionic strength of the solutions is self-determined by [AgNO 3 ] tot .
In order to prepare stable and colorless solutions to be titrated with ligand, the initial solution has been prepared by adding the suitable amount of AgNO 3 solution to solution containing the ligand in concentration 1.33 × 10 −4 m⋅dm −3 under continuous stirring.
For every Ag(I)-Ligand system, the experimental results consist of about 4200 experimental points uniformly distributed over eight different temperatures.The original primary experimental data can be obtained on request from the author(s) free of charge.] tot * = var.

Calculations. The Nernst equation
free : molar concentration of solvated (free) ligand-describes the response of the electrode system to the variable composition of the investigated solution.For each single titration, the experimental set of data {Δ exp , [Ag(I)] tot , [L] tot } has been processed until the sum of the squared residuals  = Σ  (Δ exp − Δ cal ) 2 has been minimized with respect to Δ 0 and {ln   } by using an original routine "ad hoc" conceived, written, and implemented by one of the authors.Details about the algorithm, the listing, calculations, and so on can be freely obtained from the authors.
As to the composition of the investigated systems, the lowest number of successive AgL  complexes, which adequately describe the set of experimental data, has been assumed.
The calculated Δ 0 values at each temperature from the titration curves were always consistent with the values experimentally deduced from Δ versus ln [Ag(I)] tot relationships in absence of ligand.

Results and Discussion
The experimental data for every system at every temperature can be described by the presence in solution of three stepwisely formed AgL  ( = 1-3) complexes.The estimated residual (Δ exp − Δ cal ) values were in agreement with the estimated experimental error (≈ ±2 mV) and symmetrically distributed around the calculated values.
The overall stability constants (log 10   ) for the complexing reactions Ag(I) + L = AgL  , as primary deduced directly from the experimental {Δ exp , [L] tot } data, are reported in Table 1.In Table 2, the most probable Ag(I) + L = AgL  values of thermodynamic parameters at 25 ∘ C, as deduced by linear regression from {Δ ∘ , } data of Table 1, are reported.The predominance diagrams and the formation curves for both Ag(I)-thiourea and Ag(I)-substituted thioureas systems show large ligand concentration ranges with prevalence of the monocoordinated AgL.Both predominance diagrams and formation curves are not reported for they can be easily visualized by means of software available from the web or from the authors.
In the coordination of the third ligand AgL 2 + L = AgL 3 , the affinity range is comparable with the previous one.
The overall complexing reactions are simultaneously exothermal and entropy disfavored.The alkyl substituents influence sensitively the enthalpy and the entropy changes affecting both the parameters in parallel way: positive (negative) changes in Δ ∘ values correspond to positive (negative) changes in Δ ∘ values.
In the stepwise complexing reactions the influence of the alkyi-substituents manifests in reversed order in the subsequent coordination levels of the reacting substratum.
For the reaction series Ag(I) + L () = AgL () (L () = variable) the sequence of stepwise enthalpy changes Δ(Δ and the same for the sequence of stepwise entropy changes.For the reaction series AgL () + L () = AgL () 2 the sequences are almost totally reversed.
The standard enthalpy changes for the stepwise complex formation reactions AgL −1 + L = AgL  show less favourable sometimes positive values for the coordination of the second ligand in respect both to the first and the third coordinations.The values are readily counterbalanced by the respective changes in entropy changes which follow the same pattern (Figure 1).From the results by now obtained, the following relationships ), it can be assumed as general behavior for the stepwise complex formation reactions between Ag(I) and substituted thiourea ligands in hard solvents.
Between the enthalpy and the entropy changes, linear compensative relationships occur for the stepwise complex formation (Figure 2).

Remarks
The actual results strengthen previous remarks on thermodynamics of complex formation between Ag(I) and thioureas in Table 2: Most probable stability constants (log  ,   as m − ⋅ dm 3 ), standard free energy Δ ∘ (as kJ⋅m −1 ), enthalpy Δ ∘ (as kJ⋅m −1 ), and entropy Δ ∘ changes (as kJ⋅K −1 ⋅m −1 ) at  = 298.2K and ionic strength self-determined by [AgNO 3 ] = 6.36 × 10 −6 − 3.83 × 10 −5 m⋅dm −3 for the overall complexing reactions Ag(I)+L = AgL  .hydroxyl hard solvents and the tendency of the complexed central ion to bind further ligand [10][11][12][13][14][15].The substratum to ligand affinities is contained within ranges of free energy changes which are related to the coordination levels of the substrata: the higher the coordination level of the reacting substrata, the narrower the amplitude of the free energy ranges.In addition, more thermodynamically stable is the coordinatively unsaturated reacting substratum, lower is the tendency to coordinate further ligands.So, it can be affirmed that the coordinated ligands affect the coordinating ability of the central ion in inverse way to their global mutual affinity towards the central ion.In some cases the influence leads to nonlinear (exponential) free energy relationships [14,15] and coordinatively unsaturated, but very stable complexes for very high metal-to-ligand affinities do not bind further ligands although the central ion is not exhaustively coordinated.

Ligand
The comparatively examined substratum-to-ligand affinity sequences (Figure 1) at coordination level of the reacting substratum  = 0 or  = 1 confirm the stated sentence: to higher (lower) affinity of the ligand L towards Ag(I) with respect to ligand L  at  = 0 (Δ ∘ for the reaction Ag(I) + L = AgL >(<) Δ ∘ for the reaction Ag(I) + L  = Ag L  ) it corresponds reversed affinity sequence of the same ligands towards the respective mono-coordinated substrata.On comparing the sequences for mono-and biscoordinated substrata, identical behaviors are found.2).The general sequence of the substratum to ligand affinity, enthalpy, and entropy changes (i) in the reactions of AgL  ( = 1-3) substrata with the same ligands as dependent on the coordination level of the reacting substratum, (ii) in the reactions AgL () −1 + L = AgL ()  ( = 1-3) in dependence on the alkyl substitution at the same coordination level and (iii) the concurrent changes in the corresponding Δ ∘ and Δ ∘ are evident.Such parallelism in the Δ ∘ and Δ ∘ occurs very often in homologous series of reactions [10][11][12][13].
The enthalpy changes show exothermic overall complex formation reactions but at the same time temperature unfavoured (negative entropy changes).The dissection in successive stepwise contribution for single ligand complexing reactions AgL −1 + L = AgL  discloses unmonotonous trend in dependence on the coordination level : the first and third coordination (Figure 1) are more enthalpy favoured (entropy disfavored), whereas the second coordination involves less favorable sometimes positive enthalpy changes counterbalanced by more favorable sometimes positive entropy changes.
By taking into account the compensative enthalpyentropy relationships (Figure 2), it can be concluded that the systems maintain their stiffness on the occurrence of the first and third coordination whilst the stiffness is lost on the second complexing reaction.Probably the solvation of the respective reacting substratum is maintained during the first and third coordination and sensitive desolvation process occurs in the second coordination.