CP8: Calorimetry and Hess’s Law

Hess’s law follows because enthalpy change depends on initial and final states. A useful calorimetric context compares anhydrous and hydrated forms of a salt dissolving to the same final solution composition. Let A be dissolution of the anhydrous salt and B dissolution of the hydrated salt; the desired hydration process plus route B must equal route A when water amounts and states are consistently balanced.

For the schematic cycle, ΔH(hydration) = ΔH(A) − ΔH(B). This sign follows from the balanced routes, not a rule that every Hess question uses subtraction in the same order. State waters of crystallisation and the specified common final state. Different final concentrations or unbalanced water terms weaken the direct cycle interpretation.

For a copper sulfate example, the target is CuSO₄(s) + 5H₂O(l) → CuSO₄·5H₂O(s). Dissolving the anhydrous salt directly gives route A; first forming the hydrate and then dissolving it gives hydration plus route B. Route B needs five fewer additional waters to produce the same final solution composition. Adding the two steps cancels the intermediate hydrate and recovers the direct route.

Use measured reactant masses, solution quantities, initial temperatures and temperature changes in an insulated calorimeter with appropriate stirring. Calculate q for the measured surroundings using the stated combined mass and heat capacity; include apparatus heat capacity if supplied. The reaction energy has the opposite sign. Divide by the moles for the reaction equation actually written.

Take a temperature time series where appropriate and use a justified correction for transfer to the room. Exothermic dissolution warms the solution; endothermic dissolution cools it. A cooling measurement can gain heat from the room, so its measured temperature fall may be too small. Keep final-state assumptions and apparatus conditions comparable, rather than assuming identical-looking cups remove every error.

For a difference of two enthalpies, conservative absolute uncertainties add under a worst-case model. If the desired difference is small compared with the two individual values, its percentage uncertainty can be large. Random scatter can be assessed through repeated independent runs, while systematic heat exchange or an incorrect hydrate formula can bias the cycle.

A sample labelled hydrated salt may have the wrong water content if stored poorly. Partial dissolution, splashing, temperature lag and a water-like heat-capacity assumption also matter. Improve a named limitation and explain how it affects the measured route. Do not promise that heat losses cancel merely because the same equipment was used for both experiments.

Attempt these problems on paper before opening the worked reasoning. Explain your steps as well as giving a final answer.