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learning goals
- Explain what complex ions or metal complexes are.
- Apply the concept of equilibrium in complex formation.
- Calculate the concentrations using the formation constant.
- Derive the total formation constant from stepwise formation constants.
- Derive the dissociation constant from the formation constant.
Metals are Lewis acids because of their positive charge. Dissolved in water, they react with water to form hydrated compounds such as \(\ce{Na(H2O)6+}\) and \(\ce{Cu(H2O)6^2+}\). These are called metal complexes or coordination compounds. These coordination reactions areLewis acid basereactions. The neutral molecules like \(\ce{H2O}\) and \(\ce{NH3}\) and anions like \(\ce{CN-}\), \(\ce{CH3COO-}\) are used as ligands designated. The coordination reaction can be represented by
\[\ce{CuSO4 + 6 H2O \rightleftharpoons} \ce{Cu(H2O)6^2+ + SO4^2-}\]
Typically, copper sulfate solids are hydrated with 5 water molecules per CuSO_4 complex ( \(\mathrm{ {\color{Periwinkle} CuSO_4\cdot(H_2O)_5}}\)) and their color is light blue. When heated, it loses crystal water and becomes \(\ce{CuSO4}\), which is colorless.
Most people know that when ammonia becomes a \(\mathrm{ {\color{Periwinkle} Cu(H_2O)_6^{2+}}}\)Solution, it turns deep blue. This is due to the formation of complexes:
\[ \color{Immergrün} {Cu(H_2O)_6^{2+} } + 4 NH_3 \: \rightleftharpoons {\color{Blue} Cu(H_2O)_2(NH_3)_4^{2+} + 4 H_2O} \]
In fact, the above reaction takes place stepwise. The \(\ce{H2O}\) molecules are shifted individually as the concentration of ammonia, \(\ce{[NH3]}\), increases. The more \(\ce{NH3}\) is bound to \(\ce{Cu^2+}\), the more intense the blue color becomes.
Ammonia forms complexes with many metals. It forms a very strong complex with \(\ce{Ag+}\), so that \(\ce{AgCl}\) dissolves solidly in ammonia solution.
\[\ce{AgCl_{\large{(s)}} + 2 NH3 \rightleftharpoons Ag(NH3)2+ + 2 Cl-}\]
However, the silver-ammonia complex is colorless.
Other frequently encountered ligands are \(\ce{CN-}\), \(\ce{SCN-}\), \(\ce{Cl-}\), ethylenediamine (\(\ce{NH2CH3CH3NH2}\) ) and acetate (\(\ce{CH3COO-}\)). For example,
\(\mathrm{{\color{Tan}Fe(H_2O)_6^{3+}} + SCN^-}\) | \(\right left harpoons\) | \(\mathrm{{\color{Rot} Fe(H_2O)_5SCN^{2+}} + H_2O}\) |
---|---|---|
braun | blood red |
formation constant of complexes
Complex | KF |
---|---|
\(\ce{Ag(NH3)2}\) | 1.6e7 |
\(\ce{Ag(S2O3)2^3-}\) | 1.7e13 |
\(\ce{Al(OH)4-}\) | 7.7e33 |
\(\ce{AlF6^3-}\) | 6.7e19 |
\(\ce{Zn(EDTA)^2-}\) | 3.8e16 |
The formation of complexes is also a thermodynamic phenomenon. For balance
\(\ce{Ag+ + 2 NH3 \rightleftharpoons Ag(NH3)2+}\),
the formation constant is very large,
\(K_{\ce f} = \ce{\dfrac{[Ag(NH3)2+]}{[Ag+] [NH3]^2}} = \textrm{1{,}6e7 M}^{-2}\)
because \(\ce{[Ag+]}\) is very small in such an equilibrium.
The formation constants of some other complexes are tabulated to the right. Although only three metal ions are involved, five ligands form the complexes, and the overall formation constants range from 1.6e7 to 7.7e33. EDTA is a complex organic molecule, \(\mathrm{( ^- OOCCH_2)_2}\ce{N-CH2-CH2-N(CH2COO- )2}\) with six sites (\(\ce{4\: O}\) and \(\ce{2\:N}\)) comprise the zinc ion in the zinc complex.
example 1
Calculate \(\ce{[Ag+]}\) in a solution with 0.10 M \(\ce{AgNO3}\) and 1.0 M \(\ce{NH3}\).
Solution
Let \(\mathrm{M = [Ag^+]}\) simplify the formulation. The equilibrium equation and the concentration are:
\(\begin{array}{cccccl}\ce{Ag+ &+ &2 NH3 &\rightleftharpoons &Ag(NH3)2+} &\hspace{10px}K_{\ce f} = \textrm{1.6e7 M}^{ -2}\\
x &&1.00-0.20+x &&0.10-x &
\end{array}\)
\(\dfrac{0.10-x}{x (0.80+x)^2} = \textrm{1.6e7 M}^{-2}\)
\(x = \textrm{9{,}7e-9 M}\)
DISCUSSION
If we assume \(x \ce M = \ce{[Ag(NH3)2+]}\), the calculation becomes very difficult. Try it and find out why.
Suppose we now introduce 0.10M\(\ce{Cl-}\)to balance; does a precipitate form? For\(\ce{AgCl}\),Ksp= 1.8e-10.
Ans. Da 9.7e-9*0.10 = 9.7e-10 >Ksp, a precipitate forms.
example 2
What is the solubility of \(\ce{AgCl}\) in a solution containing 1.0 M \(\ce{NH3}\)? For \(\ce{Ag(NH3)2+}\),KF= 1.6e7, and for \(\ce{AgCl}\),Ksp= 1.8e-10.
Solution
First consider the equilibria:
\(\ce{AgCl \rightleftharpoons Ag+ + Cl-} \hspace{15px} K_{\ce{sp}} = \textrm{1.8e-10 M}^2\)
\(\ce{Ag+ + 2 NH3 \rightleftharpoons Ag(NH3)2+} \hspace{15px} K_{\ce f} = \textrm{1{,}6e7 M}^{-2}\)
Adding the two equations gives the following equilibrium equation.
\(\begin{array}{cccccccl}\ce{AgCl &+ &2 NH3 &\rightleftharpoons &Ag(NH3)2+ &+ &Cl-} &\:\:\: K = K_{\ce{sp}} K_ {\ce f} = \textrm{2.9e-3}\\
&&1.0-x &&x &&x &\:\:\: \Leftarrow \textrm{equilibrium concentrations}
\end{array}\)
where x is the molar solubility of \(\ce{AgCl}\).
\(\dfrac{x^2}{(1.0-x)^2} = \textrm{2.9e-3}\)
\(\dfrac{x}{(1,0-x)} = 0,054\)
\(x = \textrm{0,051 M}\)
DISCUSSION
Answer the following questions and watch the discussion inExample 1.
The solubility product of\(\ce{AgBr}\)is 5.0e-13M2. Estimate the molar solubility of\(\ce{AgBr}\)in 1.0 Mio\(\ce{NH3}\)Solution.
Ans. 2.8e-3 M
Gradual formation constants and overall constants
As already indicated, the formation of a complex occurs stepwise. The formation constants in these steps are called stepwise formation constants.
For the reaction
\[\ce{Ag+ + NH3 \rightleftharpoons Ag(NH3)+}\]
\[K_{\ce{\large f_{\Large 1}}} = \ce{\dfrac{[Ag(NH3)+]}{[Ag+] [NH3]}} = \textrm{2{,}2e3 M}\ ]
And for the reaction
\[\ce{Ag(NH3)+ + NH3 \rightleftharpoons Ag(NH3)2+}\]
\[K_{\ce{\large f_{\Large 2}}} = \ce{\dfrac{[Ag(NH3)2+]}{[Ag(NH3)+] [NH3]}} = \textrm{ 7.2e3 M}\]
And of course, for the overall reaction,
\[\ce{Ag+ + 2 NH3 \rightleftHarpoons Ag(NH3)2+}\]
\[K_{\ce{\large f}} = \ce{\dfrac{[Ag(NH3)2+]}{[Ag+] [NH3]+}} = K_{\ce{\large f_{\Large 1}}} \times K_{\ce{\large f_{\Large 2}}} = \textrm{1.6e7 M}^2\]
A generalized formula is
\[K_{\ce{\large f}} = K_{\ce{\large f_{\Large 1}}} \times K_{\ce{\large f_{\Large 2}}} \times K_{\ ce{\large f_{\Large 3}}} \times \: ...\]
dissociation constants and the formation constants
The reverse reaction of complex formation is called dissociation, and the equilibrium constant is called dissociation constantKD.
\p\ce{Ag(NH3)2+ \rightleftharpoons Ag+ + 2 NH3}, \hspace{10px} K_{\ce d}.\]
Obviously we have
\pK_{\ce d} = \dfrac{1}{K_{\ce f}}\]
Similar to stepwise formation constants, we can also apply the concept to give a stepwise dissociation constant.
Example 3
Calculate \(\ce{[Ag+]}\) when mixing equal volumes of 0.10 M \(\ce{AgNO3}\) and 0.10 M \(\ce{Na2S2O3}\) solutions what resultsKF= 1,7e13 M-2for \(\ce{Ag(S2O3)2^3-}\).
Solution
When mixing the solutions \(\ce{[Ag(S2O3)2^3- ]} = \textrm{0.05 M}\). Let \(x \ce M = \ce{[Ag+]}\) be in equilibrium. In this case, the dissociation equilibrium equation is more appropriate than the formation equilibrium equation.
\(\begin{array}{ccccc}
\ce{Ag(S2O3)2^3- &\rightleftHarpunen &Ag+ &+ &2 S2O3^3-}\\
0,05-x &&x &&2 x
\end{array}\)
\(\dfrac{x (2 x)^2}{0,05-x} = \dfrac{1}{\textrm{1,7e13}} = \textrm{5,9e-14 M}^2\)
SinceXis very small, 0.05-X~ 0.050 and
\(\ce{[Ag+]} = x = \left(\dfrac{\textrm{5.9e-14}}{4} \right)^{1/3} = \textrm{2.5e-5 M}\ )
The approximation is justified.
DISCUSSION
If you use the formation equilibrium equation and put \(\ce{[Ag(S2O3)2^3- ]} = x\), the equation is very difficult to solve.
Questions
- Which of the following is a complex ion?
\(\ce{CH4}\), \(\ce{H2O}\), \(\ce{NH3}\), \(\ce{Al(OH)4-}\), \(\ce{ CCl4}\), \(\ce{CO3^2-}\), \(\ce{NH4+}\)
- To a sample of 9.0 ml solution with \(\ce{[NH3]} = \mathrm{1.1 M}\) add 1.0 ml 0.1 M \(\ce{AgNO3}\) solution given. Calculate \(\ce{[Ag+]}\). Assume the final volume is 10.0 mL. TheKFfor \(\ce{Ag(NH3)2} = \mathrm{1{,}6e7}\).
- Calculate the dissociation constantKDfor \(\ce{Ag(NH3)+}\), ifKFfor \(\ce{Ag(NH3)2} = \mathrm{1{,}6e7}\).
- The solubility product of \(\ce{AgBr}\) is 5.0e-13 M2, AndKF= 1,6e7 M-2for \(\ce{Ag(NH3)2+}\). Estimate the molar solubility of \(\ce{AgBr}\) in a 1.0 M \(\ce{NH3}\) solution.
- The solubility product of \(\ce{AgI}\) is 8.3e-17 M2, AndKF= 1,6e7 M-2for \(\ce{Ag(NH3)2+}\). Estimate the molar solubility of \(\ce{AgI}\) in a 1.0 M \(\ce{NH3}\) solution.
- The solubility product of \(\ce{AgBr}\) is 5.0e-13 M2, AndKF= 1,7e13 M-2for \(\ce{Ag(S2O3)2^3-}\). Estimate the molar solubility of \(\ce{AgBr}\) in a 1.0 M \(\ce{Na2S2O3}\) solution.
solutions
- Answer\(\ce{Al(OH)4-}\)
Hold...
Explain what complex ions or metal complexes are. - Answer\(\ce{[Ag+]} = \textrm{6.25e-10}\)
Hold...
Suppose \(\ce{[Ag+]} = x\), then\(\begin{array}{cccccl}
\ce{Ag+ &+ &2 NH3 &\rightleftharpoons &Ag(NH3)2+}, &K_{\ce f} = \textrm{1.6e7}\\
x &&1.0 &&0.01 &\leftarrow \textrm{equilibrium concentration}
\end{array}\)\(\dfrac{0.01}{x 1.0^2} = \textrm{1.6e7}\); \(x =\: ?\)
Apply the concept of equilibrium in complex formation.
- Answer=KD= 6,25e-8
Hold...
Derive the dissociation constant from the formation constant and show that \(K_{\ce d} = \dfrac{1}{K_{\ce f}}\). - AnswerMolar solubility = 2.8e-3 M
A notice...
reviewexample 2. - AnswerMolar solubility = 3.6e-5 M
Discussion...
The solubilities for \(\ce{AgCl}\), \(\ce{AgBr}\) and \(\ce{AgI}\) in 1.0 M \(\ce{NH3}\) solution are 0.051, 0.0028 and .0.000036m - AnswerThe molar solubility is 0.49 M
Discussion...
Use the method ofexample 2, but no approximation possible.
Credits and Attributions
Chung (Peter) Chieh(Em. Professor, Chemie @University of Waterloo)
(Video) Transition Metal Complexes
FAQs
What metals form coordination complexes? ›
Aluminum, tin, and lead, for example, form complexes such as the AlF63-, SnCl42- and PbI42- ions. Alfred Werner developed a model of coordination complexs which explains the following observations.
How do you find the coordination number of metal in metal complex? ›- Identify the central atom in the chemical formula. ...
- Locate the atom, molecule, or ion nearest the central metal atom. ...
- Add the number of atoms of the nearest atom/molecule/ions. ...
- Find the total number of nearest atoms.
Examples include tungsten hexachloride, WCl6, osmium tetroxide, OsO4, and platinum hexafluoride, PtF6. Compounds of the first series transition metals in higher oxidation states are strong oxidants and thus are readily reduced.
What are the factor affecting the formation of metal complexes? ›The stability of metal complexes is governed by two different aspects that are thermodynamic and kinetic stability.
What is an example of coordination complex? ›An example of a coordination complex is hexaaquo cobalt dichloride, Co(H2O)6Cl2. This compound contains a Co2+ ion. This electrophilic metal ion is coordinated by six nucleophilic water ligands. Because the water molecules are neutral, the complex still has a 2+ charge overall.
How are metal complexes formed? ›How are complex ions formed? A complex ion is formed by a Lewis acid–base interaction between a metal ion and a ligand. The positively charged metal ion acts as a Lewis acid, and the ligand, which contains one or more lone electron pairs, acts as a Lewis base.
What is the easiest way to find coordination number? ›Coordination number isthe number of atoms, ions, or molecules that a central atom holds as its nearest neighbours in a complex or coordination compound. For example: In [Mo(CN)8]4–, The central metal Mo is linked to eight cyanide ion, thus the metal atom has coordination number 8.
What determines coordination number of complex? ›The coordination number of a compound is determined by the type and number of ions or other species surrounding a central ion. Often the color of a compound is affected by the specific materials coordinated to that central ion.
What are 4 coordinate complexes? ›Tetrahedral and square planar complexes have a coordination number of four; trigonal bipyramidal and square pyramidal complexes have a coordination number of five; and octahedral complexes have a coordination number of six.
What are metal complexes also called? ›Metal complexes, also known as coordination compounds, include virtually all metal compounds.
Why are metal complexes important? ›
Metal complexes have become an emerging tool in drug discovery being widely used as therapeutic compounds to treat several human diseases such as carcinomas, lymphomas, infection control, diabetes, anti-inflammatory, and neurological disorders [8, 9].
What are the properties of metal complexes? ›Metal complexes vary in numerous properties (colours, photophysical characteristics, magnetism, reactivity, biological activity, catalytic behaviour, structure, etc.), and many of these are described by the authors who contributed to this issue and are briefly described in this editorial.
What increases the stability of metal complexes? ›Resonance increases the stability of the complexes. For example, acetylacetonate anion ligand shows resonance, and as a result it forms stable complexes upon reacting with metal ion (Figure 1).
What does the stability of metal complexes depend on? ›Stability of complexes mainly depends on two factors: Central Metal ion. Nature of ligands.
What are the factors affecting the stability of a metal complex in solution? ›Greater the charge (i.e. oxidation number) on the central metal ion, greater will be its attraction for the ligands. Hence, greater will be the stability of the complex.
What bonding is in metal complexes? ›A complex ion has a metal ion at its center with a number of other molecules or ions surrounding it. These can be considered to be attached to the central ion by coordinate (dative covalent) bonds (in some cases, the bonding is actually more complicated than that.
What does coordination complex mean? ›A coordination complex is the product of a Lewis acid-base reaction in which neutral molecules or anions (called ligands) bond to a central metal atom (or ion) by coordinate covalent bonds. Ligands are Lewis bases - they contain at least one pair of electrons to donate to a metal atom/ion.
What are the properties of coordination complexes? ›Coordination compounds generally display a variety of distinctive physical and chemical properties, such as colour, magnetic susceptibility, solubility and volatility, an ability to undergo oxidation-reduction reactions, and catalytic activity.
What is the information about metal complexes? ›A metal complex consists of a central metal atom or ion that is bonded to one or more ligands, which are ions or molecules that contain one or more pairs of electrons that can be shared with the metal. Metal complexes can be neutral, positively charged, or negatively charged.
What is the structure of metal complexes? ›Metal complexes consist of a central metal atom or ion surrounded by several atoms, ions or molecules, called ligands. Ligands are ions or molecules that can have an independent existence, and are attached to the central metal atom or ion. Examples of ligands are halide ions, carbon monoxide, ammonia, cyanide ion, etc.
Where are metal complexes used? ›
While electron transfer reactions of metal complexes have been used for various applications in chemistry, these processes have also found utilization for medicinal purposes. One example of introducing redox active groups is the replacement of phenyl substituents in an organic compound with a metallocene moiety.
How do you write coordination formula? ›Hint: The coordination complex formula is written in square brackets. First, the chemical symbol of the central metal atom is written and then the ligands. In some cases, we have some metal atom which is before the complete name, then such an atom should be written before the square bracket.
How do you calculate coordinate numbers? ›For molecules and polyatomic ions the coordination number of an atom is determined by simply counting the other atoms to which it is bonded (by either single or multiple bonds). For example, [Cr(NH3)2Cl2Br2]− has Cr3+ as its central cation, which has a coordination number of 6 and is described as hexacoordinate.
What is coordination number 6 examples? ›Coordination Number Examples
Pt and Fe are linked to six ligands, Cl and H 2 O, respectively. [Cr(NH 3 ) 2 Cl 2 Br 2 ] – is another example. Because the total number of atoms/ions/molecules linked to Cr is discovered to be 6, the core atom Cr has coordination number 6.
In ligand field theory, the inner d orbitals of the central atom or ion are assumed to be affected by the presence of the ligands. The number of orbitals made available for bonding, hence the coordination number, depends on the geometrical arrangement of the ligands and the strength of the ligand field.
Which coordination complex is most stable? ›The stability of a complex increases by chelation. Therefore, the most stable complex is [Fe(C2O4)3]3−.
What causes a change in coordination number? ›The coordination number of a cation can be changed as the vacancy migrates from one site to another. Changing the coordination number should be related the valence variation of the cation due to the electron band structure modified by symmetry and the separation between the cation and the oxygen anion.
What are the 3 coordinate systems? ›There are three commonly used coordinate systems: Cartesian, cylindrical and spherical. In this chapter, we will describe a Cartesian coordinate system and a cylindrical coordinate system.
What are all 3 coordinates? ›The Cartesian coordinates of a point in three dimensions are a triplet of numbers (x,y,z). The three numbers, or coordinates, specify the signed distance from the origin along the x, y, and z-axes, respectively.
What are the 3 types of ligands? ›Ligands can be anions, cations, and neutral molecules.
What is the importance of coordination compounds? ›
A major application of coordination compounds is their use as catalysts, which serve to alter the rate of chemical reactions. Certain complex metal catalysts, for example, play a key role in the production of polyethylene and polypropylene.
What is the conclusion for coordination chemistry? ›CONCLUSION: So to conclude The Coordination compounds are chemical compounds that are made up of an array of anions or neutral molecules that are attached to a central atom by covalent bonds that are formed by the coordination of the anions or neutral molecules.
What do you think is the most important use of metal? ›Metals are tremendously important to a high energy society: they transport electricity in the electrical grid, and provide many services. Various manufacturing processes around the world uses more than 3 gigatonnes of metal every year.
What are the 3 main properties of metals? ›Metals are good conductors of heat and electricity, and are malleable (they can be hammered into sheets) and ductile (they can be drawn into wire).
What are the 4 main properties of metals? ›Metals are lustrous, malleable, ductile, good conductors of heat and electricity.
Which metal complex is most stable? ›∴ Of the given complexes [Co(en)3]Cl2 is most stable.
What are the factors influencing stability of complexes? ›The stability of complex ion depend upon charge, size electronegativity of metal ion. Greater the charge of metal ion greater would be the stability. As size of metal ion decreases stability of metal ion increases complex ion more stable if chelating ligand present.
What factors affect stability? ›Common factors that affect this stability include temperature, light, pH, oxidation and enzymatic degradation. Special considerations are also required when dealing with chiral molecules, deuterated internal standards and large biomolecules.
Which of the two complexes is more stable and why? ›Thermodynamically it is favoured that a complex having monodentate ligand tends to react with either polydentate or bidentate ligands in order to form a chelate complex, as this is driven by entropy. Thus, bidentate or polydentate are considered to be more stable.
Which one of the following metal complexes is not stable? ›Cobalt with odd atomic number (=27) does not form a monometallic carbonyl compound. Thus, [Co(CO)6]3+ is least stable among the given.
What are two factors that affect the stability of an object? ›
Ans. In order to measure the stability of an object, two factors need to be determined that are the width of the object's base and the height of the object's centre of mass. The position of the centre helps one to know whether the object will remain standing or tip over.
What two things can affect the stability of a structure? ›It is found that the primary factors affecting deep beam structure stability are deep beam thickness, cable pre-tension and cable spacing.
Which elements can form coordination compounds? ›The transition elements and main group elements can form coordination compounds, or complexes, in which a central metal atom or ion is bonded to one or more ligands by coordinate covalent bonds. Ligands with more than one donor atom are called polydentate ligands and form chelates.
What metal can form complex ion? ›The transition metals are able to form complexes, where a metal ion is at the centre of multiple other compounds bonded to them. This happens as the central metal ion can accept electrons being donated to it to form a bond.
Which elements form complexes? ›Transition elements have a tendency to form complexes more than s and p block elements. So they are able to form complexes with the groups which are able to donate an electron pair. The cations of d-block elements have a strong tendency to form complexes. Hence transition element form complexes.
Can metals form coordinate bond? ›Often, metal ions can form many coordinate covalent bonds by accepting multiple lone pairs of electrons. A coordinate covalent bond can be represented as an arrow, with the species shown at the arrowhead representing the electron pair acceptor and the species at the base representing an electron pair donor.
Why do transition metals form more stable complex? ›Transition metals generally form more complex or coordination compound because they have empty valence shell orbitals that can accept pair of an electron from lewis base (ligand) That means ligands must contain one pair (at least) of the non-bonding electron that can be donated to the metal ion.
What are the properties of coordination compounds? ›Coordination compounds generally display a variety of distinctive physical and chemical properties, such as colour, magnetic susceptibility, solubility and volatility, an ability to undergo oxidation-reduction reactions, and catalytic activity.
How is coordination complex formed? ›A coordination complex is the product of a Lewis acid-base reaction in which neutral molecules or anions (called ligands) bond to a central metal atom (or ion) by coordinate covalent bonds. Ligands are Lewis bases - they contain at least one pair of electrons to donate to a metal atom/ion.
What is the structure of coordination complexes? ›A coordination complex consists of a central atom or ion, which is usually metallic and is called the coordination centre, and a surrounding array of bound molecules or ions, that are in turn known as ligands or complexing agents.
Do metals form complex ions? ›
Small, highly charged metal ions have the greatest tendency to act as Lewis acids and form complex ions. The equilibrium constant for the formation of the complex ion is the formation constant (Kf).
How many types of complexes are there in chemistry? ›There are three types of complexes: (i) Cationic complexes: These are the complexes in which the complex ion carries a net positive charge. Example: [Ni(NH3)6]2+,[Cr(NH3)6]3+ etc, (ii) (ii) Anionic complexes: These are the complexes in which the complex ion carries a net negative charge.
How do you form complexes? ›Complex formation involves an exchange of coordinated water, directly bonded to the central actinide ion, for ligands on the condition that the ligand has an affinity for the actinide ion strong enough to compete with that of the coordinated water.