Calculation of Equivalent Weight of Ferrous Ammonium Sulphate

Precisely calculate the equivalent weight of Ferrous Ammonium Sulphate (Mohr's Salt) and understand the underlying chemistry.

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What is Equivalent Weight of Ferrous Ammonium Sulphate?

The equivalent weight of Ferrous Ammonium Sulphate (also known as Mohr's Salt, Fe(NH₄)₂(SO₄)₂·6H₂O) is a fundamental concept in quantitative chemical analysis, particularly in redox titrations. It represents the mass of the substance that will combine with or displace one equivalent of hydrogen or, more broadly, it's the molar mass of the substance divided by its n-factor (or valence change). For Ferrous Ammonium Sulphate, which contains iron in the +2 oxidation state (Fe²⁺), the most common reaction involves its oxidation to the +3 state (Fe³⁺). Therefore, its equivalent weight is crucial for accurately determining its concentration or purity when used as a primary standard or a titrant.

Who should use it? This calculation is essential for:

• Chemistry students and educators performing laboratory experiments.
• Quality control analysts in industries like pharmaceuticals, food, and water treatment.
• Researchers in analytical chemistry and materials science.
• Anyone involved in precise chemical measurements and standardization.

Common misconceptions include assuming the n-factor is always 2 (like in acid-base titrations where it might be related to the number of replaceable hydrogens or hydroxides) or failing to account for the specific redox reaction occurring. The n-factor is context-dependent and directly relates to the change in oxidation states of the elements involved in the redox process.

Equivalent Weight of Ferrous Ammonium Sulphate Formula and Mathematical Explanation

The calculation of the equivalent weight of Ferrous Ammonium Sulphate (FAS) hinges on two primary methods: one based on its intrinsic properties (molar mass and n-factor) and another derived from experimental titration data.

Method 1: Using Molar Mass and n-factor

The most direct way to calculate the equivalent weight is using the definition:

Equivalent Weight (EW) = Molar Mass (M) / n-factor (n)

Where:

• Molar Mass (M): This is the sum of the atomic masses of all atoms in the chemical formula Fe(NH₄)₂(SO₄)₂·6H₂O. Using standard atomic masses (Fe=55.845, N=14.007, H=1.008, S=32.06, O=15.999), the molar mass is approximately 392.14 g/mol.
• n-factor (n): This represents the number of electrons transferred per molecule of the substance in a specific redox reaction. In the most common application, FAS is used as a reducing agent, where Fe²⁺ is oxidized to Fe³⁺. The change in oxidation state for iron is from +2 to +3, meaning it loses 1 electron per Fe atom. Since there is one iron atom per formula unit of FAS, the n-factor is 1.

Therefore, for the oxidation of Fe²⁺ to Fe³⁺:

EW = 392.14 g/mol / 1 = 392.14 g/eq

Method 2: Using Titration Data

In practice, FAS is often standardized by titration, commonly with potassium permanganate (KMnO₄) in acidic medium. The reaction is:

5 Fe²⁺ + MnO₄⁻ + 8 H⁺ → 5 Fe³⁺ + Mn²⁺ + 4 H₂O

From this balanced equation, we see that 5 moles of Fe²⁺ (and thus 5 moles of FAS) react with 1 mole of MnO₄⁻.

The moles of titrant (KMnO₄) used are calculated as:

Moles Titrant = Molarity of Titrant (mol/L) × Volume of Titrant (L)

Since the stoichiometric ratio of FAS to KMnO₄ is 5:1, the moles of FAS in the sample are:

Moles FAS = Moles Titrant × 5

The mass of FAS present in the sample is given by:

Mass FAS = Moles FAS × Molar Mass of FAS

The equivalent weight can then be determined experimentally if the mass of the sample and the volume/molarity of the titrant are known, often to verify the purity or concentration of the FAS sample.

The calculator uses the primary definition (Molar Mass / n-factor) as the core calculation for 'Equivalent Weight', but also computes moles based on titration data to show consistency and provide intermediate results.

Variables Table

Variable	Meaning	Unit	Typical Range / Value
M	Molar Mass of Ferrous Ammonium Sulphate	g/mol	~392.14
n	n-factor (Valence Change)	–	1 (for Fe²⁺ → Fe³⁺)
EW	Equivalent Weight	g/eq	~392.14
MFAS	Mass of FAS Sample	g	Variable (e.g., 0.5 – 5.0)
MTitrant	Molarity of Titrant	mol/L	Variable (e.g., 0.01 – 0.1)
VTitrant	Volume of Titrant Used	mL	Variable (e.g., 5 – 50)
Ratio	Stoichiometric Ratio (FAS : Titrant)	–	5 (for KMnO₄ titration)

Practical Examples (Real-World Use Cases)

Example 1: Standardizing a KMnO₄ Solution

A chemist needs to standardize a potassium permanganate (KMnO₄) solution using a known mass of pure Ferrous Ammonium Sulphate (FAS). They dissolve 1.9607 grams (equivalent to exactly 0.005 moles of FAS) of pure FAS in dilute sulfuric acid and titrate it with the KMnO₄ solution. The titration requires 20.00 mL of KMnO₄ solution to reach the endpoint.

• Inputs:
  • Molar Mass of FAS = 392.14 g/mol
  • n-factor = 1
  • Mass of FAS = 1.9607 g
  • Titrant Molarity (to find) = ?
  • Titrant Volume = 20.00 mL
  • Stoichiometric Ratio (FAS:KMnO₄) = 5:1
• Calculations:
  • Moles of FAS = Mass / Molar Mass = 1.9607 g / 392.14 g/mol = 0.005 mol
  • Moles of Titrant (KMnO₄) = Moles FAS / Stoichiometric Ratio = 0.005 mol / 5 = 0.001 mol
  • Volume of Titrant in Liters = 20.00 mL / 1000 mL/L = 0.020 L
  • Molarity of Titrant = Moles Titrant / Volume Titrant (L) = 0.001 mol / 0.020 L = 0.05 mol/L
  • Equivalent Weight of FAS = Molar Mass / n-factor = 392.14 g/mol / 1 = 392.14 g/eq
• Interpretation: The titration indicates that the KMnO₄ solution has a molarity of 0.05 M. The calculated equivalent weight of the FAS sample (392.14 g/eq) confirms its purity, assuming the n-factor is correctly identified as 1 for the Fe²⁺ → Fe³⁺ transition.

Example 2: Determining Purity of an FAS Sample

A laboratory receives a batch of Ferrous Ammonium Sulphate and wants to check its purity. They prepare a solution by dissolving 2.500 g of the sample. This solution is then titrated against a standardized 0.1000 M KMnO₄ solution, and the titration consumes 22.50 mL of the KMnO₄ solution.

• Inputs:
  • Molar Mass of FAS = 392.14 g/mol
  • n-factor = 1
  • Mass of FAS Sample = 2.500 g
  • Titrant Molarity (KMnO₄) = 0.1000 mol/L
  • Titrant Volume = 22.50 mL
  • Stoichiometric Ratio (FAS:KMnO₄) = 5:1
• Calculations:
  • Moles of Titrant (KMnO₄) = Molarity × Volume (L) = 0.1000 mol/L × (22.50 mL / 1000 mL/L) = 0.002250 mol
  • Moles of FAS in sample = Moles Titrant × Stoichiometric Ratio = 0.002250 mol × 5 = 0.01125 mol
  • Theoretical Moles of FAS if 100% pure = Mass / Molar Mass = 2.500 g / 392.14 g/mol ≈ 0.006375 mol
  • Purity = (Actual Moles FAS / Theoretical Moles FAS) × 100% = (0.01125 mol / 0.006375 mol) × 100% ≈ 176.6%
  • Equivalent Weight Calculated from titration = Mass of FAS / Moles of FAS = 2.500 g / 0.01125 mol ≈ 222.22 g/eq
• Interpretation: The calculated purity of ~176.6% is impossible, suggesting an error in the assumptions or titration. A purity greater than 100% usually indicates that the titrant solution (KMnO₄) was not as concentrated as assumed (i.e., its actual molarity was lower than 0.1000 M), or the FAS sample contained impurities that reacted differently. If we assume the FAS sample *is* pure and the molarity of KMnO4 is unknown, then the calculated moles of FAS (0.006375 mol from the mass) would mean that 0.006375 mol / 5 = 0.001275 mol of KMnO4 should have been used. The actual volume used (22.50 mL) implies the molarity of KMnO4 is 0.001275 mol / 0.02250 L = 0.0567 M, not 0.1 M. If we assume the 0.1 M KMnO4 is correct, and the FAS sample is impure, the calculated equivalent weight of 222.22 g/eq suggests the sample is significantly impure or the reaction stoichiometry is misunderstood for the specific conditions. The *true* equivalent weight of pure FAS remains 392.14 g/eq. This example highlights how titration results are used to *determine* unknowns, not just calculate a fixed value.

How to Use This Equivalent Weight Calculator

Using the Equivalent Weight of Ferrous Ammonium Sulphate Calculator is straightforward:

1. Enter Molar Mass: Input the precise molar mass of Ferrous Ammonium Sulphate. The default value (392.14 g/mol) is standard, but verify if your source uses slightly different atomic masses.
2. Specify n-factor: Enter the n-factor, which is typically 1 for the common oxidation of Fe²⁺ to Fe³⁺. Adjust only if a different reaction is considered.
3. Input Sample Mass: Enter the exact mass of the Ferrous Ammonium Sulphate sample you are working with (in grams).
4. Provide Titrant Details: Enter the molarity (concentration in mol/L) of the titrant solution (e.g., KMnO₄) and the volume (in mL) that was consumed during the titration.
5. Verify Stoichiometric Ratio: Ensure the stoichiometric ratio between FAS and the titrant is correct for the balanced redox reaction. For FAS titrated with KMnO₄, it's 5:1. This field is often pre-filled for common titrations.
6. Click 'Calculate': Press the 'Calculate' button.

Reading Results:

• The primary result displayed prominently is the Equivalent Weight in g/eq, calculated as Molar Mass / n-factor.
• Intermediate values show the calculated moles of FAS and moles of titrant used, offering insight into the stoichiometry of the reaction based on your inputs.
• The table summarizes your input parameters for easy verification.
• The chart visually compares the mass of the sample you entered against the calculated equivalent weight.

Decision Guidance: If you are performing a titration to determine purity, compare the calculated equivalent weight from your titration data (if you input mass and titration values) against the theoretical value (392.14 g/eq). Significant deviations can indicate impurities in your FAS sample, issues with the titrant's concentration, or procedural errors. Use the 'Copy Results' button to save or share your findings.

Key Factors That Affect Equivalent Weight Calculations

While the core calculation of equivalent weight (Molar Mass / n-factor) is straightforward for a pure substance, its practical application and determination via titration are influenced by several factors:

1. Purity of the Substance: The calculated equivalent weight is only accurate if the Ferrous Ammonium Sulphate sample is pure. Impurities can lead to incorrect calculations, especially when determining concentration via titration. High purity FAS is crucial for its use as a primary standard.
2. Accuracy of Molar Mass: While standard atomic masses are used, slight variations or the use of unhydrated forms can alter the theoretical molar mass, impacting the calculated equivalent weight. Always use the correct formula weight.
3. Correct n-factor Identification: The n-factor is critical and depends entirely on the specific chemical reaction. For FAS, the most common use involves the oxidation of Fe²⁺ to Fe³⁺, giving an n-factor of 1. If FAS were involved in a reaction where iron changed its oxidation state by, say, 2 (hypothetically), the n-factor would change, altering the equivalent weight.
4. Titrant Molarity Precision: When using titration to determine purity or standardize a solution, the accuracy of the titrant's known molarity is paramount. An incorrectly assumed molarity will lead to incorrect results for the analyte (FAS in this case).
5. Volume Measurement Accuracy: Precise measurement of the titrant volume using calibrated equipment (burettes, pipettes) is essential. Small errors in volume can significantly affect the calculated moles and, consequently, the purity or concentration derived.
6. Reaction Completeness and Stoichiometry: The redox reaction must go to completion, and the balanced chemical equation must accurately reflect the stoichiometry. Incomplete reactions or side reactions can lead to endpoint inaccuracies. The 5:1 ratio for FAS:KMnO₄ is critical.
7. Endpoint Detection: Accurate identification of the titration endpoint (e.g., the first persistent faint pink color in KMnO₄ titrations) is vital. An improperly identified endpoint leads to incorrect volume readings.
8. Acidic Medium Control: For titrations involving KMnO₄ and Fe²⁺, maintaining an acidic medium (usually with H₂SO₄) is crucial. In neutral or alkaline solutions, KMnO₄ can decompose, forming MnO₂, leading to inaccurate results.

Frequently Asked Questions (FAQ)

Q1: What is the standard n-factor for Ferrous Ammonium Sulphate?

For the most common application where Fe²⁺ is oxidized to Fe³⁺, the n-factor is 1. This means each mole of FAS loses one mole of electrons.

Q2: Can the equivalent weight be different from 392.14 g/eq?

Yes, theoretically, if FAS participates in a reaction where the change in oxidation state of iron is different from 1. However, in standard analytical practice, the n-factor is almost always taken as 1.

Q3: Why is the stoichiometric ratio typically 5:1 when titrating FAS with KMnO₄?

This ratio comes from the balanced redox reaction: 5 Fe²⁺ + MnO₄⁻ + 8 H⁺ → 5 Fe³⁺ + Mn²⁺ + 4 H₂O. It shows that 5 moles of Fe²⁺ (from FAS) react with 1 mole of MnO₄⁻.

Q4: What happens if I use the sample mass to calculate the equivalent weight directly?

If you use the sample mass and the titration data (titrant molarity and volume) to calculate an 'equivalent weight', you are effectively determining the *actual* equivalent weight of the substance *as per the titration results*. If this differs significantly from the theoretical value (392.14 g/eq), it implies the sample is impure or the titrant concentration is not as assumed.

Q5: Is Ferrous Ammonium Sulphate a primary standard?

Yes, pure Ferrous Ammonium Sulphate is often considered a primary standard for standardization of oxidizing agents like potassium permanganate, provided it is of high purity and stored correctly (to prevent oxidation by air).

Q6: How should Ferrous Ammonium Sulphate be stored?

It should be stored in tightly sealed containers in a cool, dark place to minimize oxidation by atmospheric oxygen and prevent dehydration or clumping. Adding a small amount of dilute sulfuric acid can help preserve the Fe²⁺ state.

Q7: What is the difference between equivalent weight and molar mass?

Molar mass is the mass of one mole of a substance (in g/mol). Equivalent weight is the mass of a substance that reacts with one equivalent of another reactant in a specific reaction (in g/eq). It is calculated as Molar Mass / n-factor.

Q8: Can this calculator be used for other iron(II) salts?

The principle applies, but you would need to adjust the Molar Mass input to match the specific salt and confirm the correct n-factor for the reaction being considered. The stoichiometric ratio in titrations would also likely change.

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