Lesson 7 · 25 min

Thermogravimetry

What does a precipitate turn into when it is ignited? A thermobalance weighs while it heats: calcium oxalate loses water, carbon monoxide and carbon dioxide in turn. Step heights are stoichiometry, step temperatures are kinetics — two heating rates give an activation energy.

In this lesson

Describe a thermobalance and read a TG curve and its derivative, the DTG curve
From each step’s mass loss, work out the mass lost per mole of sample, identify the gas released and the residue
Explain why step heights are stoichiometry while step temperatures move with the heating rate, and get an activation energy from two heating rates with the Kissinger equation
Use step heights to calculate the purity or composition of a sample

Gravimetric analysis often precipitates calcium as calcium oxalate and then “dries or ignites to constant mass”. But what is actually weighed? Dried at 105 °C it is $\ce{CaC2O4*H2O}$ ; around 500 °C, $\ce{CaCO3}$ ; ignited at 900 °C, $\ce{CaO}$ — one precipitate, masses differing by more than a factor of two. Thermogravimetric analysis (TGA) puts the question in front of you: the sample sits on a balance and its mass is recorded continuously while it is heated at a set rate.

Predict first

10.00 mg of calcium oxalate monohydrate is heated to 1000 °C in nitrogen on a thermobalance. How much is left at the end?

Pick an answer and lock it in before you look. A wrong guess teaches more than no guess.

8.77 mg: only the water of crystallisation goes 6.85 mg: calcium carbonate is left 3.84 mg: calcium oxide is left Almost nothing: it all turns to gas

The thermobalance and the thermogram

A thermobalance combines a balance sensitive to micrograms, a furnace that follows a temperature programme and a thermocouple right next to the sample; a purge gas (nitrogen or air) carries the released gases away. The sample, usually a few milligrams, sits in an alumina or platinum crucible. The recorded mass–temperature curve is the thermogram (TG), with one step for each reaction that loses mass; its time derivative is the DTG curve, where steps become peaks whose tops mark the temperature of fastest loss, and overlapping steps are easier to tell apart.

\frac{\Delta m}{m_0} = \frac{\nu\,M(\text{gas})}{M(\text{sample})}

Each step’s height is set by stoichiometry alone: ν moles of gas per mole of sample. Turned round, a step’s height tells you what was lost.

$\Delta m / m_0$: step loss as a fraction of the starting mass
$M$: molar mass, g/mol
$\nu$: moles of gas per mole of sample

Worked example

Identifying the gases from the mass lost

17.61 mg of $\ce{CaC2O4*H2O}$ heated at 20 °C/min loses 2.17, 3.38 and 5.30 mg between 100–250, 350–550 and 600–800 °C. What is lost in each step?

Step temperatures are kinetics

NETZSCH’s application note heats the same calcium oxalate at 10 K/min and at 200 K/min. The three step heights barely change (12.26 and 12.39 %, 19.24 and 19.16 %, 29.95 and 29.80 %, against 12.33, 19.17 and 30.12 % in theory), but the DTG peaks move from 171, 504 and 740 °C up to 239, 557 and 875 °C. Decomposition takes time: heat faster, and the temperature has climbed further before the sample has reacted. A run to 1100 °C takes almost two hours at 10 K/min and five minutes at 200 K/min.

Treat each step as a first-order reaction with an Arrhenius rate constant, and the DTG peak obeys the Kissinger equation. The peak temperatures at two heating rates then fix the activation energy: about 75 kJ/mol for dehydration, 291 kJ/mol for the loss of CO and 197 kJ/mol for the decomposition of calcium carbonate.

\ln\frac{\beta}{T_\text{p}^2} = \ln\frac{AR}{E} - \frac{E}{RT_\text{p}}

The Kissinger equation (first-order reaction, linear heating). ln(β/Tₚ²) against 1/Tₚ is a straight line of slope −E/R.

$\beta$: heating rate
$T_\text{p}$: DTG peak temperature, K
$E, A$: activation energy and pre-exponential factor

TG / DTG computed from stoichiometry and kinetics · checked against NETZSCH measurements

Thermobalance: heating calcium oxalate

Heating rate β = 200 K/min Sample mass 8.67 mg

Furnace 1100 °C · mass 3.328 mg · 5.4 min elapsed

Thermogravimetric curve (TG)

Derivative thermogravimetry (DTG): rate of mass change

model
NETZSCH measured (200 K/min)

Step analysis
Step	DTG peak	Loss	Lost per mole	Gas
dehydration	239 °C	12.33 % · 1.069 mg	18.0 g	$\ce{H2O}$
loss of CO	557 °C	19.17 % · 1.662 mg	28.0 g	$\ce{CO}$
loss of CO₂	875 °C	30.12 % · 2.611 mg	44.0 g	$\ce{CO2}$

Kissinger plot: ln(β/Tₚ²) against 1000/Tₚ

dehydration: E = 75 kJ/mol
loss of CO: E = 291 kJ/mol
loss of CO₂: E = 197 kJ/mol
NETZSCH · your recorded runs

Compare 200 K/min with the measurement (hollow circles), then set 3, 30 and 100 K/min, press “Show the whole run” each time and record the peaks. Your points fall on the lines through the two measured runs: the model’s activation energies were fixed by exactly those two measurements.

Worked example

An activation energy from two heating rates

The dehydration DTG peak is at 171.0 °C at 10 K/min and 239.4 °C at 200 K/min. Find the activation energy.

Concept check

The heating rate is raised from 10 to 50 K/min. What happens to the dehydration step?

It moves to higher temperature and keeps its height It moves to lower temperature and keeps its height It stays put and becomes smaller It stays put and becomes larger

Try the calculation

12.00 mg of impure $\ce{CaC2O4*H2O}$ (the impurity loses no mass on heating) loses 1.38 mg in the first step. What is the mass percentage of $\ce{CaC2O4*H2O}$ in the sample?

Key takeaways

Thermogravimetry weighs a sample continuously under a temperature programme; each step of the TG curve is a reaction that loses mass, and the DTG curve turns steps into peaks.
Step height = mass of gas released per mole of sample ÷ molar mass of the sample: calcium oxalate monohydrate loses 12.33 % water, 19.17 % CO and 30.12 % CO₂, leaving 38.38 % CaO.
Step temperatures are kinetics: the faster the heating, the higher the peaks; peak temperatures at two or more heating rates give the activation energy through the Kissinger equation.
Step heights give purity and composition; decomposition temperatures must be reported together with the conditions.

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Data and references

E. Füglein & S. Schmölzer, “TGA measurements on calcium oxalate monohydrate”, NETZSCH Application Note 016 (2012).
D. Harvey, Instrumental Analysis (LibreTexts), §31.1 “Thermogravimetric methods”.
H. E. Kissinger, “Reaction kinetics in differential thermal analysis”, Anal. Chem. 29, 1702–1706 (1957).
S. Vyazovkin et al., “ICTAC Kinetics Committee recommendations for performing kinetic computations on thermal analysis data”, Thermochim. Acta 520, 1–19 (2011).
D. A. Skoog, F. J. Holler & S. R. Crouch, Principles of Instrumental Analysis, 7th ed. (Cengage, 2018), Ch. 31 (thermal methods).