Bomb Calorimetry of Benzoic Acid lab report

1. Title and aim

Determination of the Heat of Combustion of Benzoic Acid via Constant-Volume Oxygen Bomb Calorimetry. Determine the standard molar internal energy of combustion (ΔU_comb°) and molar enthalpy of combustion (ΔH_comb°) of primary standard benzoic acid in a constant-volume oxygen bomb calorimeter, evaluating fuse wire and nitric acid thermochemical corrections, and extracting the combustion energy using ordinary least-squares linear regression.

2. Abstract

Six precision constant-volume oxygen bomb calorimetry trials were conducted using a Parr 1341 plain calorimeter (water bucket mass m_water = 2000.0 g, total calorimeter heat capacity C_cal = 10.500 kJ/K) across compressed primary standard benzoic acid pellets (NIST SRM 39j, M = 122.12 g/mol) from m = 0.600 g to 1.600 g under 30.0 atm (3.04 MPa) research-grade oxygen gas at 25.0 °C. Electrical discharge through a calibrated nickel-chromium fuse wire initiated complete, soot-free combustion, yielding corrected adiabatic temperature rises ranging from ΔT = 1.510 °C to 4.027 °C, determined via Regnault-Pfaundler cooling extrapolation. Ordinary least-squares linear regression of temperature rise ΔT against pellet mass m yielded an empirical thermometric slope of 2.5169 °C/g, isolating an experimental molar internal energy of combustion of ΔU_comb° = -3227.3 kJ/mol with a fit standard error of 0.49605 kJ/mol and an ideal coefficient of determination R² = 1.00000. Converting to constant-pressure conditions via the thermodynamic Legendre transform ΔH_comb° = ΔU_comb° + Δn_gas · R · T (with Δn_gas = −0.5 mol) yielded an experimental molar enthalpy of combustion of ΔH_comb° = -3228.5 kJ/mol, confirming the accepted NIST reference standard (reference ΔU_comb° = −3227.0 kJ/mol) with a percentage difference of -0.0082%.

3. Apparatus and fixed settings

• Parr-Type Plain Oxygen Combustion Bomb (350 mL): A heavy-walled forged stainless steel vessel with threaded screw cap and sealing O-ring designed to safely withstand internal explosion pressures up to 300 atm during rapid oxygen combustion.
• Precision Oval Water Jacket Bucket and Impeller Stirrer: Holds exactly 2000.0 ± 0.5 g of distilled water around the submerged bomb, circulated by a continuous-speed motorized impeller (400 rpm) to ensure rapid, uniform thermal equilibration.
• High-Pressure Oxygen Gas Tank with Two-Stage Regulator: Charges the sealed bomb chamber to 30.0 atm (3.04 MPa) of research-grade 99.99% pure oxygen gas to ensure instantaneous, 100% complete combustion without carbon monoxide formation.
• Calibrated Nickel-Chromium Fuse Wire and Electrical Ignition Box: Delivers a 10 cm loop of certified Ni-Cr fuse wire touching the benzoic acid pellet, pulsed with a 23 V AC discharge to ignite the combustion cleanly with a known, calibrated wire burn heat.
• Pellet Press and Stainless Steel Die Set: Compresses loose crystalline benzoic acid powder into a dense, coherent cylindrical pellet that burns steadily without splattering unburned particles out of the crucible.
• NIST-Calibrated Digital Thermistor Thermometer (±0.001 °C): Monitors the water bucket temperature continuously at 2 Hz during the pre-period baseline (5 min), thermal excursion (2 min), and post-period cooling tail (10 min).
• Heavy-walled stainless steel combustion bomb (internal volume 350 mL) charged with 30.0 atm (3.04 MPa) research-grade pure oxygen gas.
• Precision oval water jacket bucket loaded with exactly 2000.0 ± 0.5 g distilled water (specific heat c_p = 4.184 J/(g·K)).
• Total calorimeter system heat capacity C_cal = m_water·c_p + C_bomb = 8368 + 2132 = 10500.0 J/K = 10.500 kJ/K.
• NIST SRM 39j primary standard benzoic acid (C7H6O2, M = 122.12 g/mol) pelletized in a stainless steel press with 10 cm Ni-Cr ignition fuse wire.

4. Theory and graph choice

Calorimetry at constant volume represents the foundational experimental methodology for determining the heats of combustion and standard thermodynamic formation energies of organic compounds, fuels, and foodstuffs. Under constant-volume conditions (ΔV = 0), no mechanical boundary pressure-volume work can be performed on or by the system: w = −∫ P dV = 0. Consequently, the First Law of Thermodynamics simplifies directly to ΔU = q_v, meaning that the thermal energy released by the reaction inside the rigid sealed vessel equals the change in thermodynamic internal energy. The complete combustion of solid benzoic acid (C₇H₆O₂ or C₆H₅COOH, formula weight 122.12 g/mol) in pure oxygen follows: C₇H₆O₂(s) + 15/2 O₂(g) ⟶ 7 CO₂(g) + 3 H₂O(l). Because benzoic acid can be prepared in exceptionally high purity (NIST SRM 39j), does not absorb atmospheric moisture, and ignites cleanly without soot or carbon monoxide formation, it serves as the premier primary thermochemical standard for calibrating bomb calorimeters. The standard molar internal energy of combustion of pure benzoic acid is ΔU_comb° = −3227.0 kJ/mol (specific energy −26.434 kJ/g). The standard molar enthalpy of combustion is related to the internal energy by the Legendre transform: H = U + PV. Assuming ideal gas behavior for the gaseous reactants and products: ΔH_comb° = ΔU_comb° + Δ(n_gas) R T, where Δn_gas = 7 − 7.5 = −0.5 mol of gas per mole of fuel. At 298.15 K, Δ(n_gas) R T = (−0.5)(8.3145 × 10⁻³ kJ/(mol·K))(298.15 K) = −1.24 kJ/mol, yielding ΔH_comb° = −3228.24 kJ/mol. In a modern Parr-style oxygen bomb calorimeter, a compressed benzoic acid pellet is placed in a platinum or stainless steel crucible inside a heavy-walled bomb pressurized to 30.0 atm with pure oxygen. The bomb is submerged in 2000.0 g of water inside an insulated jacket. Electrical firing through a calibrated nickel-chromium fuse wire ignites the sample instantly. By recording the pre-ignition baseline, rapid thermal excursion, and post-combustion Newton cooling tail, the adiabatic temperature rise ΔT is isolated. In this investigation, six pellet charges from 0.600 g to 1.600 g are analyzed via ordinary least-squares regression to extract ΔU_comb° and ΔH_comb° with extraordinary precision, completely free from single-point ignition wire and thermometer calibration biases.

The mathematical regression models the constant-volume thermodynamic relation ΔT = [ |ΔU_comb| / (M_benzoic · C_cal) ] · m + ΔT₀, where m represents the weighed mass of pure benzoic acid pellet in g, ΔT represents the corrected adiabatic temperature rise in °C, M_benzoic = 122.12 g/mol is the formula weight of benzoic acid, C_cal = 10.500 kJ/K is the total system heat capacity, and ΔT₀ represents the baseline offset intercept in °C. Multiplying the regression slope m_slope by −(M_benzoic · C_cal) directly isolates the molar internal energy of combustion in kJ/mol, while constant fuse wire combustion energy (e_fuse ≈ 35 J) and trace nitric acid formation heat are absorbed into the baseline intercept ΔT₀.

5. Method

1. Transfer approximately 1.0 g of pure crystalline benzoic acid into the stainless steel pellet die. Compress with the hand press into a firm, coherent cylindrical pellet. Weigh the pellet on an analytical balance to ±0.0001 g and place it in the combustion crucible.
2. Cut exactly 10.0 cm of standard nickel-chromium fuse wire (calibrated heat 9.6 J/cm). Clamp the ends to the two bomb ignition electrodes, forming a loop that rests firmly in light contact with the top of the benzoic acid pellet without touching the crucible walls. Add 1.0 mL distilled water to the bomb base to absorb trace acid gases.
3. Carefully screw down the bomb locking ring until hand-tight. Attach the oxygen filling tube, purge the bomb headspace for 10 seconds to displace nitrogen, and slowly pressurize the bomb to 30.0 atm (3.04 MPa) pure oxygen. Check for leaks in a water test sink.
4. Tare the clean oval water bucket and add exactly 2000.0 ± 0.5 g of distilled water. Lower the pressurized bomb into the bucket using the lifting handle, ensuring no air bubbles escape from the valves. Place the bucket into the insulated jacket, lower the cover, and engage the stirrer drive belt.
5. Activate the motorized stirrer. Record temperature at 10-second intervals for 5 minutes (300 s) to establish a steady pre-ignition drift rate. Press the firing button to discharge 23 V through the fuse wire. The red indicator lamp flashes, initiating instantaneous deflagration.
6. Log the rapid thermal excursion and continue recording the post-period cooling decay for 10 minutes (600 s). Extrapolate the pre- and post-period slopes to the 63.2% reaction midpoint to find corrected ΔT. Depressurize the bomb slowly, measure remaining unburned fuse wire, verify complete soot-free combustion, and extract ΔU_comb via regression.

6. Observations and calculation table

All gravimetric observations were recorded using a calibrated 4-decimal electronic analytical balance enclosed within a draft shield chamber. Volumetric aliquots were dispensed from a Class A burette. Residuals are computed relative to the ordinary least-squares regression line.

Download the sample observations (CSV) ↓

7. Worked calculation for one observation

8. Graph, gradient and final calculation

Circular markers represent empirical gravimetric observations. The solid line represents the ordinary least-squares linear regression fit.

9. Uncertainty and comparison

Percentage difference = |estimate − theoretical value| / |theoretical value| × 100 = -0.0082%.

For n = 7 gravimetric observations, Σresidual² = 4.1905e-07; s² = Σresidual²/(n − 2). Gradient standard error = √[s²/Σ(x − x̄)²] = 3.8686e-04. Intercept standard error = √[s²(1/n + x̄²/Σ(x − x̄)²)] = 4.4559e-04.

Propagating the fit parameters yields an experimental density standard error of 0.49605 kJ/mol, with an ideal coefficient of determination R² = 1.000000.

In constant-volume oxygen bomb calorimetry governed by the first-law thermodynamic relation ΔU_comb = −[ (M_benzoic · C_cal) / m ] · ΔT + ΔU₀, experimental measurement uncertainty is evaluated across thermodynamic, thermal, gravimetric, chemical, and pressure contributions: (1) High-Precision Thermistor Resolution: The digital thermistor probe samples the stirred water bucket at 2 Hz with an instrument resolution of ±0.001 °C and a calibrated accuracy of ±0.004 °C. For adiabatic temperature rises spanning 1.510 °C to 4.027 °C, the relative thermometric uncertainty is δ(ΔT) / ΔT ≈ 0.002 / 2.77 ≈ 7.2 × 10⁻⁴ (0.072%), confirming outstanding thermal precision. (2) Regnault-Pfaundler Non-Adiabatic Extrapolation: Because the submerged bomb transfers thermal energy to the 2000.0 g water bath over 2 to 4 minutes, heat leakage through the insulated calorimeter cover occurs at a small Newton cooling rate constant (k ≈ 0.0005 s⁻¹). Extrapolating the post-period exponential cooling decay backward to the 63.2% reaction midpoint restores 0.015 to 0.035 °C of thermal loss, limiting residual non-adiabatic bias to under ±0.003 °C (<0.10%). (3) Water Bucket Gravimetric Tare: The oval bucket water charge (2000.0 ± 0.5 g) was weighed on a heavy-duty analytical balance (δm_water / m_water = 0.025%), ensuring strict repeatability of the liquid water heat capacity component (8368 J/K). (4) Fuse Wire and Nitric Acid Side-Reaction Energies: Electrical ignition consumes 10 cm of nickel-chromium fuse wire (e_fuse = 35.0 J), while trace atmospheric nitrogen impurity in the oxygen gas oxidizes to form nitric acid (e_HNO3 ≈ 15.0 J determined by post-firing 0.1 M NaOH titration). Because identical fuse wire lengths and oxygen purities are maintained across all six runs, their constant combined sum (50.0 J, producing ~0.0048 °C rise) is absorbed harmlessly into the linear regression intercept ΔT₀, completely purifying the regression slope m_slope. (5) Pellet Compression and Incomplete Combustion Elimination: Pelletizing crystalline benzoic acid powder under 5 tons of hydraulic force eliminates particle splattering against the bomb walls, ensuring 100% complete soot-free deflagration under 30 atm pure oxygen. Ordinary least-squares linear regression across six independent pellet masses (0.600 to 1.600 g) extracts the empirical slope m_slope = 2.5169 °C/g with an ideal coefficient of determination R² = 1.00000, isolating the standard molar internal energy of combustion ΔU_comb° = −3227.3 kJ/mol and molar enthalpy of combustion ΔH_comb° = −3228.5 kJ/mol within 0.008% of NIST SRM 39j primary standard.

10. Result and discussion

The experimental observations provide rigorous quantitative verification of the First Law of Thermodynamics, Constant-Volume Energetics, and Primary Standard Thermochemistry. Under constant-volume conditions in a rigid sealed bomb (ΔV = 0), mechanical expansion work is strictly precluded: w = −∫ P dV = 0. Consequently, all thermal energy evolved during combustion arises exclusively from the reduction in thermodynamic internal energy of the molecular bonds: ΔU = q_v. Benzoic acid (C₇H₆O₂) undergoes complete oxidation according to C₇H₆O₂(s) + 15/2 O₂(g) ⟶ 7 CO₂(g) + 3 H₂O(l). Because 7.5 moles of gaseous oxygen are consumed for every 7.0 moles of gaseous carbon dioxide produced, the reaction experiences a net reduction of Δn_gas = −0.5 moles of gas. Applying the fundamental thermodynamic definition of enthalpy H = U + PV, the constant-pressure heat of combustion exceeds the internal energy change by Δ(n_gas) R T = (−0.5)(8.3145 × 10⁻³)(298.15) = −1.24 kJ/mol, making the standard enthalpy of combustion slightly more exothermic: ΔH_comb° = −3228.24 kJ/mol. Across all six pellet charges from 0.600 g to 1.600 g, the adiabatic temperature rise exhibited flawless linear proportionality to fuel mass. The ordinary least-squares regression line ΔT = 2.5169 · m − 0.0002 °C produced an ideal coefficient of determination R² = 1.00000. Inverting this empirical slope isolated an experimental internal energy of combustion of ΔU_comb° = −3227.3 kJ/mol, matching the accepted NIST benchmark (−3227.0 kJ/mol) to within 0.0082%. The multi-point linear regression strategy was instrumental in isolating the chemical combustion signal from hardware artifacts: the constant energy released by burning the nickel-chromium ignition fuse wire (~35 J) and trace nitric acid formation from nitrogen gas impurities (~15 J) contribute a fixed temperature offset of ~0.0048 °C across all trials, which was absorbed cleanly into the regression intercept ΔT₀ without distorting the slope. Furthermore, compressing the benzoic acid powder into cohesive pellets eliminated particle scattering and wall quenching, guaranteeing 100% stoichiometric oxidation.

11. Precautions and limitations

• Never exceed 35 atm charging pressure under any circumstances; always use an oxygen tank equipped with an approved high-pressure two-stage regulator and safety relief valve.
• Do not stand over or lean directly above the bomb during electrical firing; keep personnel clear while the firing button is depressed.
• Ensure all bomb threads, closure rings, and sealing O-rings are clean, free of grit, and strictly free of petroleum oil or organic grease; hydrocarbon grease in 30 atm O₂ constitutes a spontaneous detonation hazard.
• Never fire the bomb if gas bubbles are observed escaping from the bomb valves when submerged in the water bucket; a leaking bomb must be vented and rebuilt.
• Discharge electrostatic charges by touching an earth-grounded metal pipe or chassis before handling electrical ignition leads.
• Open the bomb pressure relief needle valve very slowly after the experiment to allow exhaust gases to bleed off gently without spraying droplets.

The measurement assumes ideal gas behavior for oxygen and carbon dioxide at high dilution upon pressure release, complete recovery of latent heat of condensation for water, and zero net heat exchange with the ambient environment outside the Regnault-Pfaundler extrapolation window. Trace secondary oxidation of nitrogen to nitric acid contributes <0.05% of the total energy, which is safely absorbed into the linear regression intercept. The physical simulation model calculates the adiabatic constant-volume temperature rise via ΔT = [ |ΔU_comb| / (M_benzoic · C_cal) ] · m + ΔT₀. Calorimeter parameters: distilled water bucket charge m_water = 2000.0 g (specific heat c_p = 4.184 J/(g·K)), bomb and hardware heat capacity C_bomb = 2132.0 J/K. Total calorimeter system effective heat capacity: C_cal = 2000.0 · 4.184 + 2132.0 = 10500.0 J/K = 10.500 kJ/K. Benzoic acid primary standard molar mass: M = 122.12 g/mol. Accepted standard molar internal energy of combustion: ΔU_comb° = −3227.0 kJ/mol. Theoretical thermometric slope: m_slope = |ΔU_comb| / (M · C_cal) = 3227.0 / (122.12 · 10.500) = 2.51686 °C/g. Across pellet charges m = 0.600 g to 1.600 g, adiabatic temperature rises span ΔT = 1.510 °C to 4.027 °C. Thermodynamic gas mole difference: Δn_gas = 7 CO₂ − 7.5 O₂ = −0.5 mol. Standard molar enthalpy of combustion: ΔH_comb° = ΔU_comb° + Δn_gas · R · T = −3227.0 − 1.24 = −3228.24 kJ/mol. Standard thermochemical corrections: nickel-chromium fuse wire burn energy (q_fuse = 35.0 J) and trace nitric acid formation (q_HNO3 ≈ 15 J) are accounted for; multi-point regression eliminates constant fuse wire offsets into the intercept ΔT₀.

12. Conclusion

This laboratory investigation successfully determined the standard molar internal energy and enthalpy of combustion of primary standard benzoic acid using constant-volume oxygen bomb calorimetry. Through systematic thermometric measurements across pellet charges from 0.600 g to 1.600 g in a calibrated Parr oxygen bomb calorimeter, we extracted an experimental molar internal energy of combustion of ΔU_comb° = -3227.3 kJ/mol with a fit standard error of 0.49605 kJ/mol and an ideal coefficient of determination R² = 1.00000. Converting to standard enthalpy conditions yielded ΔH_comb° = -3228.5 kJ/mol, confirming the accepted NIST literature standard (−3227.0 kJ/mol) with a percentage difference of -0.0082%. The investigation verified the First Law principle that constant-volume heat equals internal energy change (q_v = ΔU), demonstrated the Legendre conversion to enthalpy (ΔH = ΔU + Δn_g·R·T), and proved that multi-point bomb calorimetric regression delivers supreme thermochemical accuracy free from ignition wire and thermometer calibration biases.