Predict complex geometry, formula and charge
Use coordination number and ligand charge to describe common complex shapes and construct complex-ion formulae.
A Level; Cambridge International Chemistry 9701, 2028–2030 syllabus, Topic 28. Use the first-row transition elements titanium to copper and the species explicitly named in the syllabus. Where redox potentials or stability constants are needed, use the values supplied in the question. Colour descriptions can depend on conditions and concentration. Written practice is self-checked
Before you begin
- Use electron configurations, oxidation numbers, ionic equations, equilibrium expressions and the AS redox and bonding models.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What is the ideal bond angle in a linear complex?
What you will learn
- Describe linear, square-planar, tetrahedral and octahedral geometry and bond angles
- Calculate coordination number from the donor atoms
- Construct a complex formula and charge from the metal oxidation state, ligand and coordination number
Match shape to coordination number
The syllabus names linear, square-planar, tetrahedral and octahedral complex geometries. Their ideal bond angles are 180°, 90°, about 109.5° and 90° respectively. A square-planar complex has four donor atoms in one plane; a tetrahedral complex has four donor atoms directed to the corners of a tetrahedron.
An octahedral complex has six donor atoms around the central metal. When ligands are bidentate, count their donor atoms rather than their number of molecules to determine coordination number.
Construct formulae by charge accounting
Write the central metal first, then place ligands inside square brackets. Use the specified coordination number or geometry to choose how many donor atoms are attached. Find the total charge by adding the metal-ion charge to the charge of every ligand.
For example, Co³⁺ with six neutral NH₃ ligands gives [Co(NH₃)₆]³⁺. With four Cl⁻ ligands around Co²⁺, the formula [CoCl₄]²⁻ has total charge +2 + 4(−1) = −2.
Pause and explain
What is the charge of [CoCl₄]²⁻ if Co is +2?
Worked example
Write the formula and charge of a complex containing Cu²⁺ with four NH₃ ligands, and state its geometry if it is square planar.
Show the worked solution
- NH₃ is neutral and monodentate.
- Four NH₃ ligands give coordination number 4.
- Add ligand charges to the Cu²⁺ charge.
Answer [Cu(NH₃)₄]²⁺; the four donor atoms are square planar with 90° adjacent bond angles.
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Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
State the geometry and ideal angle for a complex with four donor atoms arranged at the corners of a tetrahedron.
Give me a hint
Identify the named geometry before giving its characteristic angle.
Compare my reasoning
- The geometry is tetrahedral.
- Use the ideal tetrahedral angle.
- Do not substitute the square-planar angle.
Tetrahedral, with an ideal bond angle of about 109.5°.
Look for these in your work
- Geometry named
- Angle correct
- Square-planar case distinguished
A complex has one Ni²⁺, two bidentate en ligands and two monodentate water ligands. Give the coordination number and overall charge.
Give me a hint
Count donors separately, then add ligand charges.
Compare my reasoning
- Two en ligands contribute four donor atoms.
- Two H₂O ligands contribute two donor atoms.
- en and H₂O are neutral, so the charge remains +2.
Coordination number 6; formula [Ni(en)₂(H₂O)₂]²⁺.
Look for these in your work
- Donors counted correctly
- Coordination number found
- Neutral ligands handled correctly
Construct the formula and charge for a tetrahedral complex with Fe³⁺ and four CN⁻ ligands.
Give me a hint
Use four monodentate ligands and sum all formal charges.
Compare my reasoning
- Place Fe and four CN ligands in brackets.
- Four CN⁻ contribute −4.
- Add Fe³⁺ to obtain the total charge.
[Fe(CN)₄]⁻, because +3 + 4(−1) = −1.
Look for these in your work
- Ligand number matches coordination
- Bracketed formula written
- Total charge calculated
Common mistakes
- Adding neutral ligands as if they were charged
- Using the ligand count instead of coordination number with en
- Mixing tetrahedral and square-planar angles
- Forgetting brackets around the complex ion
What can you explain now?
What is the ideal bond angle in a linear complex?
Compare with the explanation
180°
The two ligand directions lie on opposite sides of the central metal.
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Make it stick
How do you get coordination number, complex charge, shape and bond angle from a metal ion and its ligands?
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.