Gravimetric Analysis- Two Essential Equations Explained

What Is Gravimetric Analysis?

Gravimetric analysis is one of the oldest analytical techniques in chemistry. You isolate an analyte as a solid, weigh it with high precision, and calculate its concentration from the mass. No spectrophotometers, no calibration curves. Just mass.

It's slow, but when done right, it's incredibly accurate. The technique relies on stoichiometric precipitation—you convert your target ion into a pure, insoluble compound you can filter, wash, and weigh.

Two equations do most of the heavy lifting in gravimetric calculations. Master these, and you can handle virtually any gravimetric problem.

The Two Essential Equations

Equation 1: Mass of Analyte from Precipitate Mass

This is the core calculation. You filter a precipitate, dry it, weigh it, then back-calculate how much analyte was in your original sample.

The equation:

Mass_analyte = Mass_precipitate × (Molar mass_analyte / Molar mass_precipitate) × (Stoichiometric coefficient_analyte / Stoichiometric coefficient_precipitate)

The ratio of molar masses is called the gravimetric factor. It's the conversion factor between precipitate mass and analyte mass.

Example: You precipitate chloride as AgCl. You isolated 0.5234 g of AgCl. How much chlorine (as Cl⁻) was in your sample?

• Gravimetric factor = Molar mass of Cl⁻ (35.45) / Molar mass of AgCl (143.32)
• Mass of Cl⁻ = 0.5234 × (35.45 / 143.32)
• Mass of Cl⁻ = 0.5234 × 0.2473 = 0.1294 g

Equation 2: Percent Analyte in the Original Sample

Most labs need the result as a percentage, not an absolute mass. This equation combines the first with a simple division by sample mass.

The equation:

% Analyte = (Mass_analyte / Mass_sample) × 100

Example: Your 0.4123 g sample yielded 0.1294 g of Cl⁻. What is the percent chlorine in the sample?

• % Cl = (0.1294 / 0.4123) × 100
• % Cl = 0.3139 × 100 = 31.39%

Working Through a Complete Problem

Let's put it together with a real-world scenario.

Problem: A 0.8765 g sample of a nickel ore is dissolved and treated with dimethylglyoxime to precipitate nickel dimethylglyoximate (Ni(DMG)₂). The dried precipitate weighs 1.2456 g. Calculate the percent nickel in the ore.

Step 1: Identify the relevant molar masses

• Ni: 58.69 g/mol
• Ni(DMG)₂: 288.91 g/mol

Step 2: Calculate the gravimetric factor

• GF = 58.69 / 288.91 = 0.2031

Step 3: Find mass of nickel

• Mass Ni = 1.2456 × 0.2031 = 0.2530 g

Step 4: Calculate percent nickel

• % Ni = (0.2530 / 0.8765) × 100 = 28.87%

Common Gravimetric Factors for Reference

These come up constantly in gravimetric work. Save this table:

Where It Goes Wrong

These equations assume your precipitate is 100% pure. In reality, several things destroy accuracy:

• Co-precipitation: Other ions stick to your precipitate. You weigh more than you should, giving inflated analyte values.
• Incomplete precipitation: Some analyte stays in solution. You weigh less, giving low results.
• hygroscopic precipitates: Compounds that absorb water from air. Your mass is too high.
• Thermal decomposition: Heating to dry the precipitate can cause it to decompose into a different compound with different mass.

This is why gravimetric analysis requires careful control of conditions, proper washing, and consistent drying/ignition protocols.

When to Use Gravimetric Analysis

It's not the fastest method, but it excels in specific situations:

• High-accuracy requirement where relative standard deviations under 0.1% are needed
• Analytes present at >1% concentration
• Reference method for validating other techniques
• When you need traceability to SI units without calibration standards

For trace analysis or rapid screening, look elsewhere. Gravimetric work is slow—plan for 2-4 hours minimum per determination, often overnight for complete drying.