Writing Formulas from Complex Names

Introduction

Reading a coordination formula into a name is only half the skill. A name can be reversed into a formula by identifying the metal oxidation state, ligand identities and counts, bracket charge and any outer counter-ion. The sequence matters. Guessing the counter-ion subscript before computing complex charge produces common errors.

Core explanation

Consider hexaamminecobalt(III) chloride. “Hexaammine” means six neutral NH₃ ligands; cobalt(III) means a formal +3 metal center. The bracketed ion is therefore [Co(NH₃)₆]³⁺. Chloride is the external −1 anion, so three chloride ions are needed to balance the +3 charge. The salt formula is [Co(NH₃)₆]Cl₃. Do not put the three chlorides inside the brackets; the name says chloride counter-ion, not chlorido ligand.

For potassium hexacyanidoferrate(II), “hexacyanido” supplies six CN⁻ ligands, and ferrate(II) identifies Fe(+2) in an anionic complex. Charge on [Fe(CN)₆] is +2 + 6(−1) = −4. Each potassium is +1, requiring four K⁺ ions. The full formula is K₄[Fe(CN)₆]. The -ate ending signals an anionic bracketed component, but the exact magnitude −4 still comes from the charge sum.

For diamminedichloridoplatinum(II), two NH₃ ligands are neutral and two coordinated chloride ligands total −2. Pt(II) contributes +2, giving a neutral complex [Pt(NH₃)₂Cl₂]. No counter-ion is required. The chlorido word ensures the two chlorides lie inside brackets; the absence of a following salt anion is consistent with a neutral bracket.

Polydentate ligands require careful parentheses. Tris(ethane-1,2-diamine)cobalt(III) nitrate contains three neutral en molecules attached to Co(+3), giving [Co(en)₃]³⁺. Three nitrate ions balance it, producing Co(en)₃₃. The “tris” prefix counts complete en ligands, not individual nitrogen donor atoms. The coordination number is six, but the ligand subscript is three.

A name may specify cis or trans before the rest of the complex. That descriptor changes spatial arrangement, not elemental counts or charges. Both cis- and trans-diamminedichloridoplatinum(II) have [Pt(NH₃)₂Cl₂] as their composition; a structural drawing or cis/trans label is needed to distinguish them. Similarly, linkage names can indicate which end of an ambidentate ligand attaches without changing the raw empirical formula.

To check a constructed formula, convert it back mentally: count each ligand, calculate the metal's state from total charge, verify the anionic or cationic name ending, and confirm the outer ions balance. A formula that fails this reverse check was assembled incorrectly. This method works across many examples because it uses charge conservation rather than memorising isolated names.

Be careful with metal roots. Ferrate means an anionic iron complex; it does not directly state iron's oxidation state. The numeral does that. Likewise, the name of an outer ion, such as chloride or nitrate, gives its ordinary charge. A student must combine all pieces to produce the final subscript.

Step-by-step reasoning

1. Extract metal identity and Roman-numeral oxidation state. 2. Translate ligand names and prefixes into formulas inside brackets. 3. Sum metal and ligand formal charges to find bracket charge. 4. Identify external cation or anion from the salt name. 5. Choose the smallest whole-number ratio that makes the salt neutral. 6. Check by reading the new formula back into a name.

Visual explanation

Write a flow from “hexaamminecobalt(III)” to Co³⁺ + 6NH₃ to [Co(NH₃)₆]³⁺. A second arrow brings in three Cl⁻ to give [Co(NH₃)₆]Cl₃. Show the ligand subscript inside and counter-ion subscript outside.

Real-world analogy

Building a recipe from its name requires first identifying the ingredients and quantities, then choosing how many servings make a balanced batch. The complex name supplies inner ingredients; charge balance determines outer ion quantities.

Real-world example

Chemical inventory systems rely on an unambiguous formula as well as a name. Confusing potassium hexacyanidoferrate(II) with the (III) salt changes the potassium ratio from four to three and describes a different redox state.

Why?

Why does potassium hexacyanidoferrate(II) need four K⁺ ions? Fe(+2) plus six CN⁻ ligands gives a bracketed charge of −4, so four monovalent potassium ions are necessary for neutrality.

Common misconception

“The metal's Roman numeral equals the number of counter-ions.” This happens for hexaamminecobalt(III) chloride because its ligands are neutral, but fails for ferrate(II) with six anionic cyanides.

Worked example

Construct the formula of pentaamminechloridocobalt(III) chloride. Five NH₃ are neutral and one coordinated Cl⁻ is −1. Co(+3) gives the bracket [Co(NH₃)₅Cl]²⁺. Each external chloride is −1, so two are required: [Co(NH₃)₅Cl]Cl₂. The name contains chlorido for the inner ligand and chloride for the outer ion.

Quick check

1. What formula corresponds to diamminedichloridoplatinum(II)? Answer: [Pt(NH₃)₂Cl₂], a neutral coordination entity.

Exam focus

Compute bracket charge explicitly before adding counter-ions. Put coordinated chlorido inside brackets and ordinary chloride outside. Do a reverse naming check to catch misplaced subscripts.

Advanced insight

For a salt containing a polyatomic counter-ion, use parentheses when more than one copy is required, as in Co(en)₃₃. Parentheses are formula grouping symbols, whereas square brackets mark the coordination sphere.

Summary

Convert names to formulas by building the inner coordination entity, summing formal charges and balancing with outer ions. Prefixes count ligands; Roman numerals state the metal oxidation state. Geometry descriptors may distinguish structures without changing composition.

Practice questions

1. Write hexaamminecobalt(III) chloride as a formula. Answer: [Co(NH₃)₆]Cl₃. 2. Write potassium hexacyanidoferrate(II) as a formula. Answer: K₄[Fe(CN)₆]. 3. What is the bracket charge in pentaamminechloridocobalt(III) chloride? Answer: +2, from Co(+3) and one Cl⁻ ligand. 4. Does cis versus trans change the formula [Pt(NH₃)₂Cl₂]? Answer: No. It changes the spatial arrangement of the same attached groups.