Reaction Calorimetry Calculator

Calculate adiabatic temperature rise and thermal runaway risk for exothermic reactions.

Heat of reaction ΔHr (kJ/mol) (kJ/mol)

Negative = exothermic

Concentration of limiting reagent C (mol/L) (mol/L)

Heat capacity of reaction mixture Cp (J/g·K) (J/g·K)

Water-based: ~4 J/g·K

Density of mixture ρ (g/mL) (g/mL)

Initial temperature T₀ (°C) (°C)

Please check your inputs and try again.

Adiabatic Temperature Rise and Runaway Risk

Reaction calorimetry answers a safety question: if cooling fails completely, how hot will this batch get? That adiabatic temperature rise is the foundation of thermal hazard assessment.

ΔT_ad = (−ΔH_r × C) / (ρ × C_p)

The danger is that reaction rate rises exponentially with temperature while cooling capacity rises only linearly. Once heat generation outpaces removal, the system accelerates into thermal runaway — and the process is self-reinforcing.

ΔT_ad	Risk level	Typical response
< 50°C	Low	Normal cooling adequate
50–100°C	Moderate	Semi-batch dosing, emergency cooling
100–200°C	High	Dosing control essential, relief sizing
> 200°C	Severe	Redesign; consider flow chemistry

Two secondary thresholds matter as much as the rise itself. If the adiabatic peak reaches the boiling point, pressure builds and relief sizing becomes critical. If it reaches the onset temperature of a decomposition reaction, a second and usually far more energetic process starts — this is the mechanism behind most serious industrial thermal incidents.

Semi-batch operation is the standard mitigation: adding one reagent gradually means only the unreacted accumulation can contribute to a runaway, not the whole charge.

Worked Examples

Example 1: Nitration reaction: ΔHr=-180kJ/mol, C=2M, Cp=2J/g·K

ΔT=180×2×1000/(2×1.2×1000)

Result: ΔT=150°C — T_max=175°C from 25°C

Potentially dangerous — needs cooling

Example 2: Neutralization: NaOH+HCl, ΔHr=-55.8kJ/mol, 1M

ΔT=55.8×1×1000/(4×1×1000)

Result: ΔT=14°C — mild

Safe: temperature control not critical

Example 3: Scale-up effect

Same reaction at 1 L and 1,000 L

Result: Surface-to-volume ratio drops tenfold

Heat generation scales with volume, cooling with surface area. Adequate cooling in the lab can be an order of magnitude short at plant scale.

Example 4: Reaching decomposition onset

ΔT_ad = 150°C from 25°C, decomposition onset 160°C

Result: Peak of 175°C exceeds onset

The intended reaction triggers a decomposition. This cascade is the mechanism behind most severe runaway incidents.

Common Mistakes

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Assuming cooling will always work

Adiabatic calculations exist precisely because cooling can fail. Design must consider the worst case, not the intended operation.

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Ignoring decomposition onset temperature

If the adiabatic peak reaches a decomposition threshold, a second reaction begins that is usually far more energetic than the intended one.

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Scaling up without recalculating

Heat generation scales with volume while cooling scales with surface area. A reaction manageable at one litre can run away at one cubic metre.

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Using the pure solvent heat capacity

The reaction mixture's heat capacity differs from the solvent alone. Using the wrong value gives an incorrect and usually optimistic temperature rise.

Frequently Asked Questions

Stoessel criticality classes?

Class 1 (ΔT<50°C from MT to MTSR): safe. Class 2 (50-100°C): minor risk. Class 3 (100-200°C): significant — boiling solvent. Class 4 (>200°C): high risk. Adiabatic temperature rise is the primary safety screening parameter.

Thermal runaway prevention?

Cooling system design: must remove heat faster than it's generated. Jacket cooling area. Reaction quench system. Temperature monitoring with interlock. Process RC1 calorimeter measures ΔHr and thermal output accurately. Reaction Hazard Index (RHI) for pharmaceutical manufacturing.

What is adiabatic temperature rise?

The temperature increase if all reaction heat is retained with no cooling. It defines the worst-case scenario for thermal hazard assessment.

What causes thermal runaway?

Reaction rate increases exponentially with temperature while cooling increases only linearly. Once generation exceeds removal, the system self-accelerates.

Why is scale-up thermally risky?

Heat generation scales with volume but cooling with surface area. The surface-to-volume ratio falls as scale increases, so cooling becomes proportionally weaker.

How does semi-batch operation reduce risk?

Adding a reagent gradually limits how much unreacted material can accumulate, so only that accumulation can contribute to a runaway rather than the entire charge.

Formula Explorer connections

Interpretation: This relationship tracks energy transfer, state-function change or the balance between enthalpy and entropy in a chemical process. Assumption: Keep energy units compatible, use kelvin for absolute temperature, and match standard states and reaction stoichiometry. Thermodynamic favorability does not determine reaction speed.

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