Thermal Methods

Solution. Convert each loss to a percentage of the initial mass and match with the theoretical losses from §3.3:

Each observed % matches the theoretical % to within 0.1%, so the assignment is confirmed. The residue $20 - 2.46 - 3.84 - 6.02 = 7.68$ mg is CaO (theoretical $38.38\%$ of 20 mg = 7.68 mg). See Fig. 1 in §5 for the drawn thermogram.

Solution. Overall decomposition: $$2AgNO_3 \longrightarrow 2Ag + 2NO_2 + O_2$$

Molar mass of AgNO₃ = 169.87 g mol⁻¹. Theoretical mass loss: $\frac{2M_{NO_2} + M_{O_2}}{2M_{AgNO_3}} = \frac{124.01}{339.74} = 36.50\%$, so the theoretical residue (Ag) is $100 - 36.50 = 63.50\%$.

Observed residue: $15.9/25.0 = 0.636 = 63.6\%$, matching the theoretical 63.5% for metallic silver. Residue: Ag. (The intermediate nitrite stage $2AgNO_3 \rightarrow 2AgNO_2 + O_2$ accounts for $9.42\%$ of the loss; the remaining $27.08\%$ is $2AgNO_2 \rightarrow 2Ag + 2NO_2$.)

Solution. MgCO₃ decomposes first (350–600 °C), CaCO₃ second (650–900 °C); each step loses one CO₂ (44.01 g mol⁻¹). With $M_{MgCO_3} = 84.32$, $M_{CaCO_3} = 100.09$:

Step 1: $n_{MgCO_3} = 0.2087/44.01 = 4.743\times 10^{-3}$ mol → $m_{MgCO_3} = 4.743\times 10^{-3}\times 84.32 = 0.400$ g.

Step 2: $n_{CaCO_3} = 0.2638/44.01 = 5.994\times 10^{-3}$ mol → $m_{CaCO_3} = 5.994\times 10^{-3}\times 100.09 = 0.600$ g.

Check: $0.400 + 0.600 = 1.000$ g ✓. Metal ions by gravimetric factors:

$m_{Ca^{2+}} = 0.600\times 40.08/100.09 = 0.240$ g,   $m_{Mg^{2+}} = 0.400\times 24.31/84.32 = 0.115$ g.

Solution. Weight loss below ~150 °C is absorbed moisture: $0.040/5.000\times 100 = 0.80\%$ water. The weighed mass is therefore only 99.20% Na₂CO₃ — every standardisation made with it carries a ≈0.8% systematic error. Action: dry the salt at the prescribed temperature (for Na₂CO₃, 270–300 °C) and cool in a desiccator before weighing; the thermogram must then be flat to 150 °C.

Solution. Observed loss: $0.368/2.500 = 0.1472 = 14.72\%$. With $M_{BaCl_2} = 208.23$ and $M_{H_2O} = 18.02$:

$$\frac{18.02\,n}{208.23 + 18.02\,n} = 0.1472 \;\Rightarrow\; 15.36\,n = 30.65 \;\Rightarrow\; n \approx 2$$

The hydrate is BaCl₂·2H₂O (theoretical loss $36.03/244.26 = 14.75\%$).

Solution. Classification (see §3.1): (1) Isothermal (static) TGA — temperature constant, mass recorded vs time; (2) Dynamic (conventional) TGA — temperature increased continuously (linearly), mass recorded vs temperature; (3) Quasi-isothermal TGA — temperature held constant while mass changes, raised only when mass is constant.

AgNO₃ thermogram. Plateau AB: no mass change — AgNO₃ (m.p. 212 °C, no mass loss on melting) is thermally stable up to ~473 °C. Portion BC: weight loss — decomposition $2AgNO_3 \rightarrow 2Ag + 2NO_2 + O_2$, via the nitrite intermediate $2AgNO_3 \rightarrow 2AgNO_2 + O_2$; the inflection point on BC is the temperature of maximum rate of loss. Plateau CD: from ~608 °C the mass is constant — the stable residue is metallic silver (theoretical residue 63.5%, loss 36.5%).

Solution. Same question as 2020 MSCH-102 above: isothermal (constant T, mass vs time), dynamic (linear T rise, mass vs T), quasi-isothermal (T held while mass changes). AgNO₃: AB plateau (stable to ~473 °C), BC decomposition to Ag + NO₂ + O₂ (complete ~608 °C, inflection point = max rate), CD plateau of metallic Ag residue.

Solution. The curve has three parts: AB — horizontal, AgNO₃ stable to ~473 °C (melting at 212 °C causes no mass change); BC — descending, decomposition $2AgNO_3 \rightarrow 2Ag + 2NO_2 + O_2$, complete by ~608 °C; CD — horizontal, constant mass of metallic silver residue (theoretical loss 36.5%, cf. Example 4.2).

Solution. See §2.6: (i) dimension → dilatometry, dilatometer; (ii) enthalpy → DSC, differential scanning calorimeter; (iii) mass → TGA, thermobalance; (iv) temperature → DTA, DTA apparatus; (v) optical property → thermo-microscopy, hot-stage microscope.

Solution. Identical question as 2020 MSCH-102 above: (i) dilatometry/dilatometer, (ii) DSC/calorimeter, (iii) TGA/thermobalance, (iv) DTA/DTA apparatus, (v) thermo-microscopy/hot-stage microscope.

Solution. Same five pairs again (see §2.6): (i) dilatometry, (ii) DSC, (iii) TGA, (iv) DTA, (v) thermo-microscopy — with the matching instruments: dilatometer, scanning calorimeter, thermobalance, DTA apparatus, hot-stage microscope.

Solution. Fourth appearance of this table: (i) dimension → dilatometry (dilatometer); (ii) enthalpy → DSC (differential scanning calorimeter); (iii) mass → TGA (thermobalance); (iv) temperature → DTA (DTA apparatus); (v) optical property → thermo-microscopy (hot-stage microscope).

Solution. Detection: run a TGA thermogram — absorbed moisture appears as a weight loss below ~100–150 °C before any decomposition (cf. Example 4.4); "loss on drying" or Karl Fischer titration confirms it. Removal: dry the substance in an oven at the prescribed temperature for that standard (e.g. ~110 °C for 2 h, or 270–300 °C for Na₂CO₃) and cool in a desiccator over a desiccant; the thermogram must then be flat below 150 °C.

Thermo-microscopy (sample watched under a microscope on a hot stage) — three applications: (1) melting-point determination; (2) detection of phase transitions and polymorphism; (3) study of dehydration/decomposition/sublimation behaviour (a fourth: crystal identification).

Solution. Factors (see §3.5): heating rate; furnace atmosphere (inert vs reactive, static vs flowing); furnace geometry/thermocouple position; sample weight; particle size; sample packing and crucible material; buoyancy/convection effects.

Moisture: detect by a TGA weight loss below ~100–150 °C (loss on drying); remove by oven-drying at the temperature prescribed for that standard and cooling in a desiccator. Absorbed water inflates the weighed mass and ruins the standardisation.

Solution. Detect with the thermobalance: absorbed moisture gives a low-temperature (< ~150 °C) weight-loss step (Example 4.4: 0.80% water in Na₂CO₃). Remove by drying at the standard's prescribed temperature and storing in a desiccator; re-check that the thermogram is flat below 150 °C before use.

Solution. Thermo-microscopy is the observation of a sample under a microscope while it is heated on a hot stage (optical property vs temperature). Three applications: (1) melting-point determination; (2) detection of phase transitions and polymorphism; (3) study of dehydration, decomposition and sublimation behaviour.

Solution. Classification: isothermal (constant T, mass vs time), dynamic (continuous/linear T rise, mass vs T), quasi-isothermal (T held while mass changes). Calcium oxalate monohydrate (see §3.3, Fig. 1): step 1, 100–250 °C, −H₂O (12.33%) → CaC₂O₄; step 2, 400–500 °C, −CO (19.17%) → CaCO₃; step 3, 600–850 °C, −CO₂ (30.12%) → CaO residue (38.38%). Each plateau is the stable intermediate.

Solution. As in the 2021 question above and Fig. 1: three steps — (1) 100–250 °C loss of H₂O, 12.33%, giving anhydrous CaC₂O₄; (2) 400–500 °C loss of CO, 19.17%, giving CaCO₃; (3) 600–850 °C loss of CO₂, 30.12%, leaving CaO. Molar mass 146.11 g mol⁻¹; the three % losses are $18.02/146.11$, $28.01/146.11$, $44.01/146.11$.

Solution. (See §2.5.) A higher heating rate $\beta$ shifts every DTA peak to higher temperature (thermal lag), makes peaks taller but broader (greater ΔT, higher sensitivity), and reduces resolution — close events merge. A lower heating rate gives sharper, better-resolved peaks at lower temperatures but smaller signals and longer runs. The same shift applies to TGA steps.

Solution. Any three: (1) determination of thermal stability and decomposition temperatures; (2) compositional analysis — hydrates, carbonates, and mixtures (e.g. CaCO₃/MgCO₃); (3) determination of moisture and volatile content (also: checking primary standards; kinetics of solid-state reactions; purity of minerals; polymer degradation and filler content).

Solution. The thermobalance (see Fig. 2): a recording microbalance with the sample crucible hanging on a wire inside a programmable furnace (thermocouple at the sample); a furnace programmer/controller imposes the temperature programme; a purge-gas system (N₂/Ar or air) controls the atmosphere; a recorder plots mass vs temperature/time. Label all five blocks and the gas flow.

Solution. See §3.5: instrumental — heating rate, furnace atmosphere, furnace geometry/thermocouple position; sample — sample weight, particle size, packing and crucible material/shape, buoyancy and convection effects.

Solution. Classification: isothermal, dynamic (conventional), quasi-isothermal (§3.1). Three factors: heating rate; furnace atmosphere; sample weight (also: particle size, crucible, buoyancy).

Ca²⁺/Mg²⁺ from CaCO₃ + MgCO₃: heat the mixture on the thermobalance. MgCO₃ decomposes first (~350–600 °C): $MgCO_3 \rightarrow MgO + CO_2$; CaCO₃ decomposes later (~650–900 °C): $CaCO_3 \rightarrow CaO + CO_2$. The first CO₂ loss gives the MgCO₃ mass, the second the CaCO₃ mass; convert with the gravimetric factors $M_{Ca}/M_{CaCO_3}$ and $M_{Mg}/M_{MgCO_3}$ to Ca²⁺ and Mg²⁺. Fully worked with numbers in Example 4.3 (0.600 g CaCO₃ → 0.240 g Ca²⁺; 0.400 g MgCO₃ → 0.115 g Mg²⁺).

Solution. Fully worked in Example 4.1. Step 1 (100–250 °C, 12.3%): H₂O — theoretical $18.02/146.11 = 12.33\%$, dehydration to CaC₂O₄. Step 2 (400–500 °C, 19.2%): CO — theoretical $28.01/146.11 = 19.17\%$, giving CaCO₃. Step 3 (700–850 °C, 30.1%): CO₂ — theoretical $44.01/146.11 = 30.12\%$, leaving CaO (7.68 mg residue). The qualitative thermogram is Fig. 1: three descending steps separated by flat plateaus of CaC₂O₄·H₂O → CaC₂O₄ → CaCO₃ → CaO.

Solution. As in the 2024 main question above: the two carbonates decompose at well-separated temperatures — MgCO₃ → MgO + CO₂ (~350–600 °C), CaCO₃ → CaO + CO₂ (~650–900 °C). From the first step's CO₂ loss, $m_{MgCO_3} = \Delta m_1\times M_{MgCO_3}/M_{CO_2}$; from the second, $m_{CaCO_3} = \Delta m_2\times M_{CaCO_3}/M_{CO_2}$. See the worked numbers in Example 4.3.

Solution. Same as 2022 Q(c): (1) thermal stability/decomposition studies; (2) compositional analysis of hydrates, carbonates and mixtures; (3) moisture/volatile content and checking primary standards (also: solid-state reaction kinetics; mineral purity; polymer degradation).

A. A thermogram is the plot of sample mass (% mass) vs temperature (or time) under a controlled temperature programme. From it you read: (1) thermal stability (first plateau), (2) composition (% loss per step identifies the lost species), (3) purity/moisture (unexpected low-T step), (4) kinetic behaviour (step positions shift with heating rate).

A. (1) Isothermal — constant T, mass vs time. (2) Dynamic — linear T rise, mass vs T (routine mode). (3) Quasi-isothermal — T held while mass changes, raised when mass is constant.

A. The TGA instrument: a recording microbalance whose crucible hangs in a programmable furnace. Components: (1) recording balance, (2) furnace, (3) furnace programmer/controller, (4) purge-gas system + recorder.

A. It decomposes in three sharp, well-separated steps of known stoichiometry — H₂O (12.33%), CO (19.17%), CO₂ (30.12%) — so both the temperature scale and the mass scale of a thermobalance can be checked against it.

A. DTA measures the temperature difference $\Delta T$ between sample and reference (semi-quantitative); DSC measures the heat flow needed to keep them at equal temperature (quantitative — gives enthalpies).

A. Higher — the sample lags the furnace. Steps and DTA peaks move to higher T, broaden, and resolution worsens (close steps merge); sensitivity increases.

A. Mass → TGA; temperature → DTA; enthalpy → DSC; dimension → dilatometry; optical property → thermo-microscopy.

A. Detect: TGA weight loss below ~150 °C (loss on drying). Remove: dry at the temperature prescribed for that standard, cool in a desiccator; confirm the thermogram is flat below 150 °C.