CHM110H5 Chap.8 Calorimetry, Enthalpy and Hess's Law
Calorimetry, Enthalpy and Hess's Law
Enthalpy as heat at constant pressure
Most reactions you run in the CHM110H5 lab happen in open containers, so pressure stays fixed while the system is free to expand or contract. Internal energy alone is awkward under those conditions because some energy leaves as pressure-volume work.
The course therefore works with enthalpy, defined as H = E + PV, and its change equals the heat absorbed by the system at constant pressure. A positive change means the system took in heat; a negative change means it gave heat away.
Temperature, phase and chemical bonding all contribute to how much enthalpy a sample holds, and every quantitative calculation in Experiment 5 rests on measuring heat flow through a temperature change.
Heat capacity and the calorimeter balance
Heat absorbed by a sample is the product of its mass, its specific heat capacity and its temperature change, q = m c ΔT.
Water is taken as 4.18 J per gram per kelvin with a density of 1.00 g/mL. Because temperature differences are identical on the Celsius and Kelvin scales, either works. The coffee-cup calorimeter is two stacked Styrofoam cups inside a beaker, with a lid, a stir bar and a clamped thermometer. It is treated as adiabatic, so every heat term inside it must add to zero.
The cup itself soaks up a little heat, summarised by one constant, the calorimeter heat capacity, found by mixing a weighed portion of warm water into a weighed portion of room-temperature water and solving the balance for the single unknown.
Reading the final temperature properly
Mixing takes a few seconds, and the cup begins losing heat to the room immediately.
For that reason you log the temperature every 15 seconds for four minutes, plot it against time, and extend the straight cooling tail back to the moment the two waters met. That extrapolated value should sit above every reading you actually recorded.
Using the raw maximum instead underestimates the temperature change of the cold water and inflates the calorimeter constant, which then distorts every reaction enthalpy measured later with the same cup.
Hess's law and magnesium oxide
Burning magnesium in oxygen is too violent for a foam cup, yet its enthalpy is exactly what the experiment targets.
Hess's law says the overall heat of a reaction does not depend on how many steps it takes, so you measure two convenient reactions instead: magnesium metal dissolving in dilute hydrochloric acid, and magnesium oxide dissolving in the same acid. Combining the first, the reverse of the second, and the literature enthalpy for forming liquid water (−285.8 kJ/mol) reproduces the formation of MgO from its elements.
Results are reported to three significant digits along with a percent error against the accepted value, and the discussion should name where heat escaped or mass was misjudged.
What this chapter covers
- 01
Enthalpy as constant-pressure heat
- 02
The sign of q from q = m c ΔT
- 03
Calorimeter calibration with warm and cold water
- 04
Extrapolating T-final from a cooling curve
- 05
Reaction enthalpy per mole of limiting reagent
- 06
Hess cycle for MgO formation
- 07
State functions, heat, work and the first law
Worked example · free
Finding the heat capacity of a coffee-cup calorimeter
- 1Cold water warms: q1 = 50.1 × 4.18 × (34.1 − 22.0) = 209.4 × 12.1 = +2534 J (heat absorbed).
- 1Warm water cools: q2 = 49.8 × 4.18 × (34.1 − 47.5) = 208.2 × (−13.4) = −2789 J (heat released).
- 2Adiabatic balance: q1 + Ccal(34.1 − 22.0) + q2 = 0, so Ccal × 12.1 K = 2789 − 2534 = 255 J.
- 1Divide: Ccal = 255 J ÷ 12.1 K = 21.1 J/K.
- 1Sanity check: 21.1 J/K is small next to the 209 J/K of each water portion and falls in the 5 to 150 J/°C range expected for these cups.
Key terms
- Enthalpy
- A state function defined as internal energy plus pressure times volume; its change equals the heat absorbed by a system held at constant pressure.
- Specific heat capacity
- The heat needed to raise one gram of a substance by one kelvin; for water the course uses 4.18 J/g·K in every calorimetry calculation.
- Calorimeter heat capacity
- The heat absorbed by the cups, stir bar and thermometer per degree of temperature rise, measured once by calibration and then reused for every reaction run.
- Adiabatic process
- A process with zero heat flow across the boundary, the assumption that lets all heat terms inside an insulated calorimeter add up to zero.
- Hess's law
- The rule that a reaction's enthalpy change is the same whether it happens in one step or several, so known reaction enthalpies can be added and reversed to reach an unknown one.
- State function
- A property such as enthalpy or internal energy whose change depends only on the starting and ending states, never on the path taken between them.
Calorimetry, Enthalpy and Hess's Law FAQ
Why can't I just use the highest temperature the thermometer showed as the final temperature?
The cup starts losing heat before the water is fully mixed, so the true peak is never displayed. Extending the straight cooling section back to the instant of mixing recovers a higher, loss-corrected value, and using the lower raw maximum makes the calorimeter constant come out too large.
How do I know which reaction to reverse when combining the magnesium equations?
Compare each equation with the target, Mg plus half an oxygen giving MgO. Magnesium must be a reactant, so the metal-acid reaction stays as written, while MgO must be a product, so the oxide-acid reaction is flipped and its enthalpy changes sign before adding the water-formation step.
Is the heat from the reaction the same as the heat absorbed by the water and cup?
Equal in size but opposite in sign. If the solution and calorimeter together absorb 370 J, the reaction released 370 J, so its enthalpy is negative; dividing by the moles of limiting reagent then gives the molar value.
Exam move
Rework the calibration from scratch with your own numbers until you can set up the three-term balance without notes, then repeat with a reaction term divided by moles. Sketch one temperature-time plot by hand and practise drawing the extrapolation line through only the linear tail. Write the four magnesium equations on a card, mark which one gets reversed and why, and check that intermediates cancel.
Finish by computing a percent error against the accepted MgO value and listing two physical reasons your result might be off.
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