Topic 6: Thermodynamics

Thermodynamics studies how energy moves during chemical and physical changes, especially energy transferred as heat. In this unit you will measure heat with calorimetry and predict the enthalpy of a reaction using several complementary tools. The goal is to connect what happens at the particle level to the energy values you calculate.

Endothermic vs Exothermic and Energy Diagrams

Every reaction either absorbs or releases energy. An exothermic process releases energy to the surroundings, so the products sit lower in energy than the reactants and the enthalpy change (deltaH) is negative. An endothermic process absorbs energy from the surroundings, leaving the products higher in energy than the reactants, so deltaH is positive. A potential energy diagram plots energy on the vertical axis against the progress of the reaction. For an exothermic reaction the curve ends below where it started; for an endothermic reaction it ends above. The peak of the curve represents the activated complex, and the height from reactants to that peak is the activation energy. Remember that the sign of deltaH always describes the system: a negative value means the system lost energy and the surroundings warmed up.

Heat Transfer and Thermal Equilibrium

Heat (q) is energy that flows because of a temperature difference. Energy always moves spontaneously from the hotter object to the colder object, never the reverse. When two objects are placed in contact, heat keeps flowing until both reach the same temperature, a state called thermal equilibrium. At that point there is no net energy transfer even though particles are still colliding. A key bookkeeping rule follows from conservation of energy: in an isolated system the heat lost by the hot object equals the heat gained by the cold object, so q_lost + q_gained = 0. Temperature measures the average kinetic energy of particles, while heat measures the total energy transferred, so these two ideas are related but not identical.

Heat Capacity and Calorimetry

Specific heat capacity (c) is the energy needed to raise the temperature of one gram of a substance by one degree Celsius (or one kelvin). Substances with a high specific heat, such as water at about 4.18 J/(g C), resist temperature change. The central equation is q = m c deltaT, where m is mass, c is specific heat, and deltaT is the temperature change (final minus initial). Calorimetry uses this equation to measure heat released or absorbed by a reaction. The reaction happens in an insulated container, and the heat it exchanges shows up as a temperature change in the surrounding water, which we measure. Worked example: a 50.0 g sample of water absorbs heat and rises from 22.0 C to 30.0 C. The heat absorbed is q = (50.0 g)(4.18 J/(g C))(30.0 C - 22.0 C) = (50.0)(4.18)(8.0) = 1672 J, or about 1.67 kJ. If this heat came from a reaction, the reaction released that same amount, so its q would be -1672 J.

Energy of Phase Changes

Phase changes absorb or release energy without changing temperature. During melting, boiling, or sublimation the added energy goes into overcoming intermolecular forces rather than speeding up particles, so the temperature stays flat on a heating curve while a phase change occurs. Melting and vaporization are endothermic because the system must absorb energy to separate particles; freezing and condensation are exothermic because particles release energy as they come together. The energy per mole to melt a solid is the enthalpy of fusion, and the energy per mole to boil a liquid is the enthalpy of vaporization. Vaporization always requires more energy than fusion for the same substance because particles must be fully separated. On a heating curve, sloped segments use q = m c deltaT while flat segments use the phase-change enthalpy times the number of moles or grams.

Enthalpy of Reaction

Enthalpy (H) is the heat content of a system at constant pressure, and the enthalpy of reaction (deltaH_rxn) is the heat released or absorbed when a reaction occurs as written. Because enthalpy is a state function, deltaH depends only on the initial and final states, not on the path taken. This property is what makes Hess's law and formation calculations possible. Enthalpy is also extensive, so if you double the amounts of reactants you double deltaH, and if you reverse a reaction you flip the sign of deltaH. Standard enthalpy values are reported under standard conditions, usually 1 atm and a specified temperature such as 25 C, and are written as deltaH with a degree symbol that we will simply call standard.

Using Bond Enthalpies

Bonds store energy, and a reaction rearranges bonds. Breaking bonds requires energy (endothermic), while forming bonds releases energy (exothermic). Average bond enthalpy is the typical energy needed to break one mole of a particular bond in the gas phase. To estimate deltaH for a reaction, use deltaH = (sum of bonds broken) - (sum of bonds formed). In words, add up the energy to break all reactant bonds, then subtract the energy released when all product bonds form. If more energy is released forming bonds than was spent breaking them, the reaction is exothermic. Because these are average values that vary with molecular environment, bond enthalpy gives an approximate deltaH, not an exact one, and it strictly applies only to gas-phase species.

Enthalpy of Formation

The standard enthalpy of formation (deltaH_f) is the enthalpy change when one mole of a compound forms from its elements in their standard states. By definition, the standard enthalpy of formation of any element in its most stable form is zero, so substances like O2 gas, N2 gas, and solid carbon as graphite have deltaH_f equal to zero. Tabulated formation values let you calculate a reaction enthalpy with the equation deltaH_rxn = (sum of deltaH_f of products) - (sum of deltaH_f of reactants), each multiplied by its coefficient. This products-minus-reactants pattern appears repeatedly in thermodynamics. A common mistake is forgetting to multiply each formation value by the stoichiometric coefficient from the balanced equation.

Hess's Law

Hess's law states that if a reaction can be written as the sum of several steps, its enthalpy change is the sum of the enthalpy changes of those steps. This works because enthalpy is a state function, so the overall energy change is independent of the route. To apply it, manipulate known reactions until they add up to the target equation: reverse a reaction and flip the sign of its deltaH, or multiply a reaction by a factor and multiply its deltaH by the same factor. Then cancel species that appear on both sides and add the adjusted deltaH values. Hess's law is powerful because it lets you find enthalpy changes that are difficult or dangerous to measure directly, building them from reactions you can measure.