6.3.2 Working Out the Charge on Complexes and Their Formulae

In the previous section, we learned how to name complex compounds from their formulas. Now, we will learn the reverse process: how to deduce the formula of a complex compound from its name or description, and how to calculate the oxidation state of the central metal ion. This skill is essential for understanding the composition and charge of coordination compounds.

Main Idea

The main idea is that the total charge on a complex ion is the sum of the oxidation state of the central metal ion and the charges of all the ligands. By knowing the name of the complex (which gives the ligands and the metal's oxidation state) or by knowing the overall charge of the complex, you can calculate the unknown charge or deduce the formula.

Core Concept

The core concept is charge balance. The charge on the complex ion is determined by the metal ion and its ligands. The ions outside the coordination sphere (counter ions) are there to neutralize the charge of the complex ion, making the whole compound electrically neutral. The oxidation state of the metal ion equals the charge on the complex minus the sum of the charges on the ligands.

Detailed Explanation

The textbook provides a clear explanation and worked examples to illustrate this concept.

Calculating the Charge on a Complex Ion

The total charge on a complex ion depends upon the oxidation state of the metal ion and the number and nature of ligands. The oxidation state of the metal ion can be calculated from the charge on the complex ion.

Key Formula: Oxidation state of metal = Charge on complex - Sum of charges on ligands

Important Note from the Textbook: The ions outside the coordination sphere neutralizing the complex ion are called counter ions.

Worked Examples from the Textbook

The textbook provides two detailed worked examples.

Worked Example 1: Deduce the charge on the tetraamminedichlorocobalt(III) complex ion. What is its formula?

• The name is tetraamminedichlorocobalt(III).
• Ligands:
• Tetraammine: Four ammonia (NH_3) molecules. Ammonia is a neutral ligand, so it contributes a charge of 0.
• Dichloro: Two chloride (Cl^-) ions. Each chloride has a charge of -1, so the total charge from the chloride ligands is 2 × (-1) = -2.
• Metal: The cobalt(III) indicates that the oxidation state of the central cobalt ion is +3.

• Sum of ligand charges = 4(0) + 2(-1) = -2
• Oxidation state of cobalt = +3
• Total or net charge on the complex ion = (+3) + (-2) = +1

Formula: The complex ion has a charge of +1, so its formula is [CoCl_2(NH_3)_4]⁺.

Worked Example 2: Deduce the oxidation state of copper in the [CuCl_4]^2- complex ion. What is its name?

• The formula is [CuCl_4]^2-.
• The complex ion is an anion with a total or net charge of -2.
• The formula has four chloride ions acting as ligands. Each chloride has a charge of -1, so the total charge from the ligands is 4 × (-1) = -4.

Calculation: - Let the oxidation state of copper be x. - The sum of the oxidation state of copper and the charges of the ligands must equal the overall charge of the complex: x + (-4) = -2 x = -2 + 4 x = +2 - Hence, the central copper ion must contribute two positive charges, so its oxidation state is +2.

• The complex ion is [CuCl_4]^2-.
• The ligands are four chloride ions, so the prefix is tetra and the ligand name is chloro.
• The metal is copper in the +2 oxidation state.
• Since the complex is anionic, the metal name gets the suffix "-ate", becoming cuprate.
• The name is tetrachlorocuprate(II) ion.

General Procedure for Working Out Charges and Formulae

• Neutral ligands (e.g., H_2O, NH_3, CO) have a charge of 0.
• Anionic ligands (e.g., Cl^-, OH^-, CN^-) have negative charges.
• The number of each ligand is given by the prefix in the name (di, tri, tetra, etc.).
• This is given in Roman numerals in the name (e.g., cobalt(III) means +3).
• Sum the charges of all ligands.
• Add the oxidation state of the metal.
• The result is the net charge on the complex ion.
• Write the metal symbol followed by the ligands in square brackets.
• The number of each ligand is indicated by subscripts.
• The overall charge is shown outside the brackets as a superscript.

Intermediate Level

Working out the charge on a complex ion requires knowing the charges of the ligands and the oxidation state of the metal. The oxidation state of the metal is given in the name of the complex (in Roman numerals). The total charge on the complex is the sum of the metal's oxidation state and the charges contributed by the ligands. Conversely, if you know the formula and the overall charge, you can calculate the oxidation state of the metal by setting up a simple algebraic equation. For example, in [CuCl_4]^2-, the four chloride ligands contribute -4, and the overall charge is -2, so the copper must be +2. This process is essential for writing correct formulas and names for complex compounds.

Important Points

• - Total charge on complex ion = (Oxidation state of metal) + (Sum of ligand charges).
• - Oxidation state of metal = (Charge on complex) - (Sum of ligand charges).
• - Neutral ligands (e.g., H_2O, NH_3, CO) have a charge of 0.
• - Anionic ligands (e.g., Cl^-, OH^-, CN^-) have negative charges.
• - Prefixes (di, tri, tetra) indicate the number of ligands.
• - Roman numerals in the name indicate the oxidation state of the metal.
• - Counter ions are outside the coordination sphere and neutralize the complex's charge.

Remember

• - Charge on complex = Metal oxidation state + Ligand charges.
• - Metal oxidation state = Charge on complex – Ligand charges.
• - Neutral ligands = 0 charge.
• - Anionic ligands = negative charge.
• - Example: [CoCl_2(NH_3)_4]⁺ has a charge of +1 (Co is +3, two Cl^- are -2).
• - Example: [CuCl_4]^2- has a charge of -2 (Cu is +2, four Cl^- are -4).

Common Mistakes

• - Forgetting to multiply the ligand charge by the number of ligands. For example, in [CuCl_4]^2-, there are four chloride ions, so the total ligand charge is -4, not -1.
• - Incorrectly identifying the oxidation state from the name. Make sure to read the Roman numeral in parentheses after the metal name.
• - Assuming that neutral ligands contribute to the charge. Neutral ligands like NH_3 and H_2O have no charge and do not affect the total charge.
• - Not balancing the charges correctly. The total charge on the complex ion must equal the sum of the metal's oxidation state and the ligand charges.
• - Confusing counter ions with ligands. Counter ions are outside the square brackets and are not part of the complex ion.

Quick Revision

The total charge on a complex ion is the sum of the oxidation state of the central metal ion and the charges of all the ligands. The oxidation state of the metal is given in the name (in Roman numerals), and the ligand charges are determined by their type and number. Neutral ligands have no charge, while anionic ligands have negative charges. By knowing the name, you can calculate the charge on the complex, and by knowing the formula and charge, you can calculate the oxidation state of the metal. This allows you to write correct formulas and names for complex compounds.

60-Second Revision

The charge on a complex ion is the sum of the metal's oxidation state and the ligand charges. The oxidation state is in the name (Roman numerals). Neutral ligands have no charge; anionic ligands have negative charges. Charge on complex = Metal oxidation state + Ligand charges. Metal oxidation state = Charge on complex – Ligand charges. Example: [CuCl_4]^2- has Cu at +2 and four Cl^- at -1 each, giving a total of -2.

Frequently Asked Questions (FAQs)

Q1. How do you calculate the charge on a complex ion? Answer: The charge on a complex ion is calculated by summing the oxidation state of the central metal ion and the charges of all the ligands. The formula is: Charge on complex = (Oxidation state of metal) + (Sum of ligand charges) For example, in [CoCl_2(NH_3)_4]⁺, cobalt is +3, two chloride ligands contribute -2, and four ammonia ligands contribute 0, giving a total charge of +1.

• Q2. How do you determine the oxidation state of the metal in a complex?
• Answer: The oxidation state of the metal can be determined from the name of the complex (given in Roman numerals) or by using the formula:
• Oxidation state of metal = (Charge on complex) - (Sum of ligand charges)
• For example, in [CuCl_4]^2-, the charge on the complex is -2, and four chloride ligands contribute -4, so the oxidation state of copper is +2.

Q3. What is the charge of a neutral ligand? Answer: A neutral ligand, such as water (H_2O), ammonia (NH_3), or carbon monoxide (CO), has a charge of 0. It does not contribute to the total charge of the complex ion.

Q4. How do you determine the formula of a complex from its name? Answer: To determine the formula from the name, identify the ligands and their number (from the prefixes), the metal, and its oxidation state (from the Roman numerals). Then, write the metal symbol followed by the ligands in square brackets, with subscripts for the number of each ligand. The total charge on the complex is calculated from the metal's oxidation state and the ligand charges, and it is written as a superscript outside the brackets.

Q5. What are counter ions in a complex compound? Answer: Counter ions are the ions outside the coordination sphere that neutralize the charge of the complex ion, making the overall compound electrically neutral. For example, in K_4[Fe(CN)_6], the potassium ions (K^+) are the counter ions that balance the -4 charge of the [Fe(CN)_6]^4- complex ion.

Q6. Calculate the charge on the complex ion [Fe(CN)_6]^4- and determine the oxidation state of iron. Answer: The complex ion is [Fe(CN)_6]^4-. The six cyanide ligands (CN^-) each have a charge of -1, contributing a total of -6. The overall charge on the complex is -4. Let the oxidation state of iron be x. Then: x + (-6) = -4 x = -4 + 6 x = +2 So, the oxidation state of iron is +2.

Q7. What is the charge on the complex ion in [Co(NH_3)_4Cl_2]⁺? Answer: The complex ion is [Co(NH_3)_4Cl_2]⁺. The ligands are four neutral ammonia molecules (charge 0) and two chloride ions (each -1, total -2). The metal is cobalt in the +3 oxidation state. The total charge is (+3) + (0) + (-2) = +1. The charge is shown as +1.

Q8. What is the name of the complex ion [CuCl_4]^2-? Answer: The complex ion [CuCl_4]^2- has four chloride ligands, so the prefix is "tetra" and the ligand name is "chloro". The metal is copper in the +2 oxidation state. Since the complex is anionic, the metal name becomes "cuprate". The name is tetrachlorocuprate(II) ion.

Q9. How do you calculate the charge on a complex ion if the metal has a variable oxidation state? Answer: The oxidation state of the metal is usually given in the name of the complex (in Roman numerals). If it is not given, you need additional information, such as the overall charge of the complex and the charges of the ligands, to calculate the oxidation state. For example, in [Fe(CN)_6]^4-, the overall charge is -4 and the six cyanide ligands contribute -6, so the iron must be +2.

Multiple Choice Questions (MCQs)

Q1. What is the charge on the complex ion [CoCl_2(NH_3)_4]⁺? A. +1 B. +2 C. +3 D. -1 Correct Answer: A Explanation: The cobalt ion is in the +3 oxidation state. Two chloride ligands contribute -2, and four ammonia ligands are neutral (0). Total charge = (+3) + (-2) + (0) = +1.

• Q2. What is the oxidation state of copper in [CuCl_4]^2-?
• A. +1
• B. +2
• C. +3
• D. +4
• Correct Answer: B
• Explanation: The complex ion has a charge of -2. Four chloride ligands contribute -4. Therefore, the copper ion must be +2.

Q3. What is the charge of a neutral ligand? A. -1 B. 0 C. +1 D. It depends on the metal. Correct Answer: B Explanation: Neutral ligands such as H_2O, NH_3, and CO have no charge and do not contribute to the total charge of the complex.

• Q4. In the complex [Fe(CN)_6]^4-, what is the oxidation state of iron?
• A. +1
• B. +2
• C. +3
• D. +4
• Correct Answer: B
• Explanation: Six cyanide ligands contribute -6. The overall charge is -4. Let x be the oxidation state of iron: x + (-6) = -4 ⇒ x = +2.

Q5. What is the formula of the complex ion tetraamminedichlorocobalt(III)? A. [CoCl_2(NH_3)_4]⁺ B. [CoCl_2(NH_3)_4]²⁺ C. [CoCl_2(NH_3)_4]^- D. [CoCl_2(NH_3)_4] Correct Answer: A Explanation: The cobalt ion is +3. Two chloride ligands contribute -2. Four ammonia ligands are neutral. The net charge is +3 - 2 = +1. The formula is [CoCl_2(NH_3)_4]⁺.

Q6. What is the name of the complex ion [CuCl_4]^2-? A. Tetrachlorocuprate(II) ion B. Tetrachlorocopper(II) ion C. Tetrachlorocuprate(III) ion D. Tetrachlorocopper(III) ion Correct Answer: A Explanation: The ligands are four chloride ions (tetrachloro). The metal is copper in the +2 oxidation state. Since the complex is anionic, the metal name becomes "cuprate". The name is tetrachlorocuprate(II) ion.

• Q7. What is the total charge on the complex ion [Fe(CN)_6]^3-?
• A. -1
• B. -2
• C. -3
• D. -4
• Correct Answer: C
• Explanation: The charge is given in the formula as -3.

Q8. In the complex [Co(NH_3)_4Cl_2]⁺, what is the oxidation state of cobalt? A. +1 B. +2 C. +3 D. +4 Correct Answer: C Explanation: The complex has a charge of +1. Four ammonia ligands are neutral, and two chloride ligands contribute -2. Let x be the oxidation state of cobalt: x + 0 + (-2) = +1 ⇒ x = +3.

• Q9. What is the charge on the complex ion [Ni(CO)_4]?
• A. 0
• B. +1
• C. -1
• D. +2
• Correct Answer: A
• Explanation: The complex is neutral. Nickel is in the 0 oxidation state, and four carbonyl ligands are neutral. The total charge is 0.

Q10. What is the correct formula for the complex ion hexacyanoferrate(II)? A. [Fe(CN)_6]^2- B. [Fe(CN)_6]^3- C. [Fe(CN)_6]^4- D. [Fe(CN)_6]^- Correct Answer: C Explanation: The name "hexacyanoferrate(II)" indicates six cyanide ligands (hexacyano) and iron in the +2 oxidation state. Six cyanide ligands contribute -6, and iron is +2, giving a net charge of -4. The formula is [Fe(CN)_6]^4-.

Multiple Choice Questions (MCQs)

• Q1. What is the charge on the complex ion [CoCl_2(NH_3)_4]⁺?
• A. +1
• B. +2
• C. +3
• D. -1
• Correct Answer: A
• Explanation: The cobalt ion is +3. Two chloride ligands contribute -2. Four ammonia ligands are neutral. Total charge = (+3) + (-2) = +1.

• Q2. What is the oxidation state of copper in [CuCl_4]^2-?
• A. +1
• B. +2
• C. +3
• D. +4
• Correct Answer: B
• Explanation: The complex ion has a charge of -2. Four chloride ligands contribute -4. Therefore, the copper ion must be +2.

• Q3. What is the charge of a neutral ligand?
• A. -1
• B. 0
• C. +1
• D. It depends on the metal.
• Correct Answer: B
• Explanation: Neutral ligands have no charge.

• Q4. In the complex [Fe(CN)_6]^4-, what is the oxidation state of iron?
• A. +1
• B. +2
• C. +3
• D. +4
• Correct Answer: B
• Explanation: Six cyanide ligands contribute -6. The overall charge is -4. So iron is +2.

• Q5. What is the formula of the complex ion tetraamminedichlorocobalt(III)?
• A. [CoCl_2(NH_3)_4]⁺
• B. [CoCl_2(NH_3)_4]²⁺
• C. [CoCl_2(NH_3)_4]^-
• D. [CoCl_2(NH_3)_4]
• Correct Answer: A
• Explanation: The cobalt ion is +3, two chloride ligands contribute -2, and four ammonia ligands are neutral. Net charge is +1.

• Q6. What is the name of the complex ion [CuCl_4]^2-?
• A. Tetrachlorocuprate(II) ion
• B. Tetrachlorocopper(II) ion
• C. Tetrachlorocuprate(III) ion
• D. Tetrachlorocopper(III) ion
• Correct Answer: A
• Explanation: The name is tetrachlorocuprate(II) ion.

• Q7. What is the total charge on the complex ion [Fe(CN)_6]^3-?
• A. -1
• B. -2
• C. -3
• D. -4
• Correct Answer: C
• Explanation: The charge is -3.

• Q8. In the complex [Co(NH_3)_4Cl_2]⁺, what is the oxidation state of cobalt?
• A. +1
• B. +2
• C. +3
• D. +4
• Correct Answer: C
• Explanation: Four ammonia ligands are neutral, two chloride ligands contribute -2, and the overall charge is +1. So cobalt is +3.

• Q9. What is the charge on the complex ion [Ni(CO)_4]?
• A. 0
• B. +1
• C. -1
• D. +2
• Correct Answer: A
• Explanation: The complex is neutral.

• Q10. What is the correct formula for the complex ion hexacyanoferrate(II)?
• A. [Fe(CN)_6]^2-
• B. [Fe(CN)_6]^3-
• C. [Fe(CN)_6]^4-
• D. [Fe(CN)_6]^-
• Correct Answer: C
• Explanation: Iron is +2, and six cyanide ligands contribute -6, giving a net charge of -4.