The Magnesium Phosphate Formula is Mg₃(PO₄)₂, representing a white, odourless inorganic salt formed by the reaction of magnesium ions and phosphate ions. This compound is covered in NCERT Chemistry for Class 11 and Class 12, particularly in chapters dealing with ionic compounds, chemical bonding, and salt chemistry. It is also relevant for NEET aspirants studying biominerals and JEE Main candidates tackling stoichiometry and mole concept problems. This article covers the formula, structural representation, molar mass calculation, a complete chemistry formula sheet, three solved examples, CBSE exam tips, common mistakes, and JEE/NEET applications.
Key Magnesium Phosphate Formulas at a Glance
Quick reference for the most important formulas related to Magnesium Phosphate.
- Molecular formula: \( \text{Mg}_3(\text{PO}_4)_2 \)
- Molar mass: \( M = 3(24.31) + 2(30.97) + 8(16.00) = 262.87 \text{ g/mol} \)
- Ionic dissociation: \( \text{Mg}_3(\text{PO}_4)_2 \rightarrow 3\text{Mg}^{2+} + 2\text{PO}_4^{3-} \)
- Charge balance: \( 3 \times (+2) = 2 \times (-3) = 6 \)
- Number of moles: \( n = \frac{m}{M} \)
- Solubility product: \( K_{sp} = [\text{Mg}^{2+}]^3[\text{PO}_4^{3-}]^2 \)
What is the Magnesium Phosphate Formula?
The Magnesium Phosphate Formula is \( \text{Mg}_3(\text{PO}_4)_2 \). It represents an ionic compound formed between magnesium (Mg), a Group 2 alkaline earth metal, and the phosphate ion (PO₄³⁻). Magnesium carries a +2 charge, while the phosphate ion carries a −3 charge. To achieve electrical neutrality, three magnesium ions combine with two phosphate ions, giving the formula Mg₃(PO₄)₂.
This compound is studied in NCERT Class 11 Chemistry, Chapter 4 (Chemical Bonding and Molecular Structure) and Chapter 1 (Some Basic Concepts of Chemistry) for mole concept calculations. In Class 12, it appears in Chapter 4 (Chemical Kinetics) and ionic equilibrium topics. Magnesium phosphate occurs naturally as the mineral bobierrite. It is used in fertilisers, pharmaceuticals, and as a food additive (E343). Understanding its formula is essential for writing ionic equations, balancing reactions, and solving stoichiometry problems in CBSE and competitive exams.
Magnesium Phosphate Formula — Expression and Variables
The molecular formula of magnesium phosphate is written as:
\[ \text{Mg}_3(\text{PO}_4)_2 \]
The molar mass is calculated as:
\[ M = 3 \times 24.31 + 2 \times (30.97 + 4 \times 16.00) = 72.93 + 2 \times 94.97 = 72.93 + 189.94 = 262.87 \text{ g/mol} \]
| Symbol | Element / Ion | Quantity in Formula | Atomic / Molar Mass (g/mol) |
|---|---|---|---|
| Mg | Magnesium | 3 atoms | 24.31 |
| P | Phosphorus | 2 atoms | 30.97 |
| O | Oxygen | 8 atoms | 16.00 |
| Mg²⁺ | Magnesium ion | 3 ions | Charge: +2 |
| PO₄³⁻ | Phosphate ion | 2 ions | Charge: −3 |
| M | Molar mass of Mg₃(PO₄)₂ | — | 262.87 g/mol |
Derivation of the Formula
To derive the formula of magnesium phosphate, we use the criss-cross method of valencies.
Step 1: Identify the ions. Magnesium forms a cation Mg²⁺ (valency = 2). Phosphate is the anion PO₄³⁻ (valency = 3).
Step 2: Apply the criss-cross rule. The valency of Mg (2) becomes the subscript of PO₄, and the valency of PO₄ (3) becomes the subscript of Mg.
Step 3: Write the formula: \( \text{Mg}_3(\text{PO}_4)_2 \).
Step 4: Verify charge neutrality: \( 3 \times (+2) + 2 \times (-3) = +6 – 6 = 0 \). The formula is electrically neutral and correct.
Structural Formula of Magnesium Phosphate
The structural formula of magnesium phosphate shows the ionic bonds between three Mg²⁺ cations and two PO₄³⁻ anions. In the phosphate ion, the central phosphorus atom forms four P–O bonds. Three of these are single bonds and one is a double bond (or all four are equivalent due to resonance). The phosphate ion is tetrahedral in shape, with a bond angle of approximately 109.5°.
The overall compound is ionic. There are no covalent bonds between magnesium and phosphate. The Mg²⁺ ions are held in place by electrostatic attraction to the PO₄³⁻ ions. In the crystal lattice, each magnesium ion is surrounded by phosphate ions and vice versa, forming a stable ionic solid.
The structural representation can be shown as:
\[ 3\text{Mg}^{2+} + 2\text{PO}_4^{3-} \rightarrow \text{Mg}_3(\text{PO}_4)_2 \]
The phosphate ion itself has the structural formula:
\[ \text{PO}_4^{3-}: \text{ Tetrahedral, P at centre, 4 O atoms at corners} \]
Magnesium phosphate is insoluble in water under normal conditions, but it dissolves in dilute acids. It exists in anhydrous form as well as hydrated forms such as trimagnesium phosphate octahydrate, Mg₃(PO₄)₂·8H₂O.
Complete Chemistry Formula Sheet: Magnesium and Phosphate Compounds
| Formula Name | Expression | Variables / Ions | Molar Mass (g/mol) | NCERT Chapter |
|---|---|---|---|---|
| Magnesium Phosphate | \( \text{Mg}_3(\text{PO}_4)_2 \) | Mg²⁺, PO₄³⁻ | 262.87 | Class 11, Ch 1 & 4 |
| Magnesium Chloride | \( \text{MgCl}_2 \) | Mg²⁺, Cl⁻ | 95.21 | Class 11, Ch 10 |
| Magnesium Oxide | \( \text{MgO} \) | Mg²⁺, O²⁻ | 40.30 | Class 11, Ch 10 |
| Magnesium Sulphate | \( \text{MgSO}_4 \) | Mg²⁺, SO₄²⁻ | 120.37 | Class 11, Ch 10 |
| Magnesium Hydroxide | \( \text{Mg(OH)}_2 \) | Mg²⁺, OH⁻ | 58.32 | Class 11, Ch 10 |
| Magnesium Carbonate | \( \text{MgCO}_3 \) | Mg²⁺, CO₃²⁻ | 84.31 | Class 11, Ch 10 |
| Sodium Phosphate | \( \text{Na}_3\text{PO}_4 \) | Na⁺, PO₄³⁻ | 163.94 | Class 11, Ch 1 |
| Calcium Phosphate | \( \text{Ca}_3(\text{PO}_4)_2 \) | Ca²⁺, PO₄³⁻ | 310.18 | Class 11, Ch 1 |
| Barium Phosphate | \( \text{Ba}_3(\text{PO}_4)_2 \) | Ba²⁺, PO₄³⁻ | 601.93 | Class 11, Ch 1 |
| Phosphoric Acid | \( \text{H}_3\text{PO}_4 \) | H⁺, PO₄³⁻ | 97.99 | Class 12, Ch 7 |
| Ammonium Phosphate | \( (\text{NH}_4)_3\text{PO}_4 \) | NH₄⁺, PO₄³⁻ | 149.09 | Class 11, Ch 1 |
Magnesium Phosphate Formula — Solved Examples
Example 1 (Class 9-10 Level): Finding the Molar Mass of Magnesium Phosphate
Problem: Calculate the molar mass of magnesium phosphate, Mg₃(PO₄)₂. Use atomic masses: Mg = 24.31, P = 30.97, O = 16.00 g/mol.
Given: Formula = Mg₃(PO₄)₂; Atomic masses: Mg = 24.31, P = 30.97, O = 16.00 g/mol
Step 1: Count each atom in the formula. Mg: 3 atoms; P: 2 atoms; O: 4 × 2 = 8 atoms.
Step 2: Multiply each atomic mass by the number of atoms.
Mg: \( 3 \times 24.31 = 72.93 \) g/mol
P: \( 2 \times 30.97 = 61.94 \) g/mol
O: \( 8 \times 16.00 = 128.00 \) g/mol
Step 3: Add all contributions: \( M = 72.93 + 61.94 + 128.00 = 262.87 \) g/mol
Answer
The molar mass of Magnesium Phosphate, Mg₃(PO₄)₂, is 262.87 g/mol.
Example 2 (Class 11-12 Level): Number of Moles and Ions
Problem: How many moles of Mg²⁺ and PO₄³⁻ ions are present in 52.574 g of magnesium phosphate?
Given: Mass of Mg₃(PO₄)₂ = 52.574 g; Molar mass = 262.87 g/mol
Step 1: Calculate moles of Mg₃(PO₄)₂.
\[ n = \frac{m}{M} = \frac{52.574}{262.87} = 0.200 \text{ mol} \]
Step 2: Write the dissociation equation.
\[ \text{Mg}_3(\text{PO}_4)_2 \rightarrow 3\text{Mg}^{2+} + 2\text{PO}_4^{3-} \]
Step 3: Calculate moles of each ion.
Moles of Mg²⁺ = \( 3 \times 0.200 = 0.600 \) mol
Moles of PO₄³⁻ = \( 2 \times 0.200 = 0.400 \) mol
Step 4: Calculate number of ions using Avogadro’s number \( N_A = 6.022 \times 10^{23} \).
Mg²⁺ ions = \( 0.600 \times 6.022 \times 10^{23} = 3.613 \times 10^{23} \)
PO₄³⁻ ions = \( 0.400 \times 6.022 \times 10^{23} = 2.409 \times 10^{23} \)
Answer
Moles of Mg²⁺ = 0.600 mol (3.613 × 10²³ ions); Moles of PO₄³⁻ = 0.400 mol (2.409 × 10²³ ions).
Example 3 (JEE/NEET Level): Solubility Product Calculation
Problem: The solubility of magnesium phosphate, Mg₃(PO₄)₂, in water at 25°C is \( s \) mol/L. Derive an expression for its solubility product \( K_{sp} \) in terms of \( s \). If \( s = 1.0 \times 10^{-4} \) mol/L, calculate \( K_{sp} \).
Given: Solubility = \( s \) mol/L; Dissociation: \( \text{Mg}_3(\text{PO}_4)_2 \rightarrow 3\text{Mg}^{2+} + 2\text{PO}_4^{3-} \)
Step 1: Write ion concentrations in terms of \( s \).
\( [\text{Mg}^{2+}] = 3s \); \( [\text{PO}_4^{3-}] = 2s \)
Step 2: Write the expression for \( K_{sp} \).
\[ K_{sp} = [\text{Mg}^{2+}]^3[\text{PO}_4^{3-}]^2 = (3s)^3(2s)^2 \]
Step 3: Expand the expression.
\[ K_{sp} = 27s^3 \times 4s^2 = 108s^5 \]
Step 4: Substitute \( s = 1.0 \times 10^{-4} \) mol/L.
\[ K_{sp} = 108 \times (1.0 \times 10^{-4})^5 = 108 \times 10^{-20} = 1.08 \times 10^{-18} \]
Answer
\( K_{sp} = 108s^5 \). For \( s = 1.0 \times 10^{-4} \) mol/L, \( K_{sp} = \mathbf{1.08 \times 10^{-18}} \).
CBSE Exam Tips 2025-26
- Memorise the criss-cross method: Always swap valencies to write ionic formulas. For Mg²⁺ (valency 2) and PO₄³⁻ (valency 3), the formula is Mg₃(PO₄)₂. We recommend practising this with at least 10 different ionic pairs.
- Verify charge neutrality: After writing any ionic formula, always check that the total positive charge equals the total negative charge. This single step eliminates most formula-writing errors.
- Molar mass calculation: In CBSE 2025-26 board exams, molar mass questions carry 2-3 marks. Write each step clearly. Show atomic masses, multiplication, and final addition separately.
- Distinguish hydrated forms: Magnesium phosphate exists as anhydrous Mg₃(PO₄)₂ and hydrated Mg₃(PO₄)₂·8H₂O. CBSE questions sometimes specify which form to use for calculations.
- Ionic equation writing: For reactions involving Mg₃(PO₄)₂, practise writing both molecular and net ionic equations. This is frequently tested in Class 11 and Class 12 practical-based questions.
- Use standard atomic masses: CBSE provides a data sheet in the exam. Our experts suggest confirming atomic masses from the NCERT appendix: Mg = 24, P = 31, O = 16 (rounded values are acceptable in board exams).
Common Mistakes to Avoid
- Mistake 1 — Writing MgPO₄ instead of Mg₃(PO₄)₂: Students forget to apply the criss-cross rule correctly. The charges must balance. Mg²⁺ and PO₄³⁻ require three Mg and two PO₄ groups, not a 1:1 ratio.
- Mistake 2 — Counting oxygen atoms incorrectly: The subscript 2 outside the bracket in (PO₄)₂ multiplies all atoms inside. There are 4 × 2 = 8 oxygen atoms, not 4. This error directly affects molar mass calculations.
- Mistake 3 — Confusing magnesium phosphate with magnesium phosphite: Phosphate is PO₄³⁻ (oxidation state of P = +5). Phosphite is PO₃³⁻ (P = +3). These are different compounds with different formulas.
- Mistake 4 — Incorrect Ksp expression: In the \( K_{sp} \) expression for Mg₃(PO₄)₂, students often write \( K_{sp} = [\text{Mg}^{2+}][\text{PO}_4^{3-}] \) without applying stoichiometric exponents. The correct form is \( K_{sp} = [\text{Mg}^{2+}]^3[\text{PO}_4^{3-}]^2 \).
- Mistake 5 — Ignoring brackets in formula: Writing Mg₃PO₄₂ instead of Mg₃(PO₄)₂ changes the meaning entirely. Brackets are mandatory when a polyatomic ion has a subscript greater than 1.
JEE/NEET Application of Magnesium Phosphate Formula
In our experience, JEE aspirants encounter magnesium phosphate primarily in three contexts: mole concept and stoichiometry, ionic equilibrium and solubility product, and qualitative analysis of cations and anions.
Application 1: Stoichiometry and Mole Concept (JEE Main)
JEE Main frequently tests percentage composition and mole-based calculations. For Mg₃(PO₄)₂ (molar mass = 262.87 g/mol), the percentage of magnesium is:
\[ \%\text{Mg} = \frac{3 \times 24.31}{262.87} \times 100 = \frac{72.93}{262.87} \times 100 \approx 27.74\% \]
This type of calculation appears in JEE Main Paper 1 under the “Some Basic Concepts of Chemistry” topic.
Application 2: Ionic Equilibrium and Ksp (JEE Advanced / NEET)
The solubility product concept for Mg₃(PO₄)₂ is a standard JEE Advanced problem type. The key relationship \( K_{sp} = 108s^5 \) (derived in Example 3 above) is a high-yield formula. NEET also tests this in the context of biological systems, since calcium and magnesium phosphates are components of bones and teeth.
Application 3: Bioinorganic Chemistry (NEET)
NEET Biology and Chemistry overlap in questions about biominerals. Magnesium phosphate is a component of struvite kidney stones and is relevant to phosphate metabolism. NEET aspirants should know that Mg₃(PO₄)₂ is sparingly soluble in water but dissolves readily in acidic conditions, which is why stomach acid can dissolve mineral salts. This connects to NCERT Biology Class 11, Chapter 16 (Digestion and Absorption).
Our experts suggest that JEE and NEET aspirants practise at least five Ksp problems involving 3:2 electrolytes (like Mg₃(PO₄)₂ and Ca₃(PO₄)₂) to master this pattern thoroughly.
FAQs on Magnesium Phosphate Formula
Explore More Chemistry Formulas
Now that you have mastered the Magnesium Phosphate Formula, strengthen your chemistry preparation with these related resources on ncertbooks.net. Explore the Complete Chemistry Formulas hub for a full list of ionic and covalent compound formulas. For more ionic compound practice, study the Barium Acetate Formula and the Zinc Bromide Formula, which follow the same criss-cross derivation method. You can also review the Ammonium Acetate Formula to understand how polyatomic ions behave in salt formation. For foundational mole concept and stoichiometry skills, visit our STP Formula article. All formula articles on ncertbooks.net are aligned with the latest NCERT textbooks and CBSE 2025-26 syllabus.