Worksheet: Thermodynamics

In thermodynamics, a system is defined as a specific part of the universe that we focus on for analysis, whereas everything else is termed as the surroundings. An open system allows both energy and matter to exchange with surroundings, like a pot of boiling water. A closed system can exchange energy but not matter, like a sealed container of gas. An isolated system cannot exchange either energy or matter, such as thermos flasks. The universe is the sum of the system and surroundings.

Internal energy (U) is the total energy contained in a system, including kinetic and potential energy of the molecules. It changes when heat is added or removed (q) and when work is done on or by the system (w). According to the first law of thermodynamics, the change in internal energy is given by ΔU = q + w. This equation emphasizes that internal energy is a state function, depending only on initial and final states, not on the path taken.

Extensive properties depend on the amount of substance present, such as mass and volume. Intensive properties do not depend on the quantity, like temperature and pressure. For example, mass and volume are extensive because they change when you have more or less of the material, whereas temperature and pressure remain the same regardless of the amount of substance. This distinction is crucial in thermodynamic processes.

The first law of thermodynamics states that the total energy of an isolated system is constant. Mathematically, it is expressed as ΔU = q + w, where ΔU is the change in internal energy, q is the heat added to the system, and w is the work done on the system. This law signifies the principle of conservation of energy; energy can neither be created nor destroyed, only transformed from one form to another.

Enthalpy (H) is a thermodynamic quantity defined as H = U + pV, where U is the internal energy, p is pressure, and V is volume of the system. The change in enthalpy (ΔH) during a process is related to heat transfer at constant pressure. Enthalpy takes into account not only internal energy but also the work done by or on the system during expansion or compression.

Hess's Law states that the total enthalpy change in a chemical reaction is the same, no matter how many steps the reaction takes. This law is based on the fact that enthalpy is a state function. For example, if we know the enthalpy changes for a series of reactions leading to the same products, we can sum them to find the overall enthalpy change. An example is finding the enthalpy change for the formation of CO from its elements through intermediate reactions like C + O2 → CO2 and CO2 + C → 2CO.

Entropy (S) is a measure of the disorder or randomness in a system. It quantifies how much energy in a system is not available for doing work. The second law of thermodynamics states that for spontaneous processes, the total entropy change (system + surroundings) must be greater than zero (ΔS_total > 0). This means that spontaneous processes lead to an increase in disorder in the universe.

Gibbs free energy (G) is a thermodynamic potential that measures the maximum reversible work obtainable from a thermodynamic system at constant temperature and pressure. It is defined as G = H - TS, where H is enthalpy, T is temperature, and S is entropy. A reaction is spontaneous if the change in Gibbs free energy (ΔG) is negative (ΔG < 0). This means that the reaction can occur without the input of work.

The spontaneity of a reaction depends both on enthalpy change (ΔH) and entropy change (ΔS), as incorporated in the Gibbs free energy equation (ΔG = ΔH - TΔS). If ΔG is negative, the reaction is spontaneous. For example, exothermic reactions (negative ΔH) tend to be spontaneous at all temperatures. In contrast, endothermic reactions (positive ΔH) can become spontaneous at high temperatures if the entropy change is positive and large enough to outweigh the enthalpy term.

The first law of thermodynamics states that the energy of an isolated system is constant. It can be expressed mathematically as ΔU = q + w, where ΔU is the change in internal energy, q is the heat added to the system, and w is the work done on the system. For example, in a closed container where heat is added (q > 0) and work is done on the system (w > 0), both contribute to an increase in internal energy (ΔU > 0).

Internal energy (U) is the total energy of a system, encompassing kinetic and potential energies of molecules, while enthalpy (H = U + pV) incorporates the pressure-volume work that can be done. They are equivalent when processes occur at constant volume and are considered in situations where pressure changes, such as at constant atmospheric pressure. For reactions happening at constant pressure, H is preferred for calculations involving heat transfer.

Hess’s law states that the total enthalpy change for a reaction is the sum of the enthalpy changes for individual steps leading to the same final state. For example, to calculate the enthalpy change for the combustion of carbon, we can use the enthalpy changes of the combustion of related compounds. If the combustion of CO2 gives -393.5 kJ/mol, factored with the combustion of C and O2 can yield the overall reaction enthalpy.

Entropy (S) is a measure of disorder or randomness in a system. It quantifies the number of microscopic configurations that correspond to a macroscopic state. The second law of thermodynamics states that in an isolated system, the total entropy always increases over time, indicating that natural processes tend to move toward a state of maximum disorder. For instance, the melting of ice (solid to liquid) is accompanied by an increase in entropy.

Gibbs free energy (G) is defined by the equation G = H - TS. It combines the concepts of enthalpy and entropy to predict the spontaneity of reactions at constant temperature and pressure. If ΔG is negative, the process is spontaneous; if positive, it is non-spontaneous. For example, a reaction with ΔH < 0 and ΔS > 0 will always be spontaneous.

The enthalpy change (ΔH) in an endothermic reaction that absorbs q amount of heat at constant pressure can be directly related to the internal energy change as ΔU = ΔH - pΔV. For a process involving specific heat capacity (C), where C = q/ΔT, we can calculate ΔH = C * ΔT. For instance, if 100 J of heat is absorbed at a constant pressure with C = 4.18 J/g°C and ΔT is 25°C, ΔH = C * ΔT = 4.18 * 25 = 104.5 J.

Spontaneous processes, such as the rusting of iron or combustion of fuels, occur naturally without continuous external input, typically indicating a negative Gibbs free energy change. Non-spontaneous processes, like the conversion of diamond to graphite, require energy input. In spontaneous reactions, enthalpy often decreases while entropy increases; they can be quantified with ΔG calculations to establish their feasibility.

The relationship given by ΔG° = -RT ln(K) allows the calculation of equilibrium constant K from Gibbs free energy change ΔG°, where R is the universal gas constant (8.314 J/K∙mol) and T is in Kelvin. For example, if ΔG° is -40 kJ/mol, converting to J gives K = e^(-ΔG°/RT). Substituting these values helps find K.

Discuss how energy conservation is maintained in the reaction and provide examples of possible work done and changes in internal energy.

Explain the relationship between enthalpy, temperature, and the irreversibility of the process using specific heat capacities.

Provide examples of reactions where Hess's law can be applied and demonstrate calculations involving multiple steps.

Analyze various scenarios with different signs of Gibbs free energy and relate them to spontaneous and non-spontaneous processes.

Apply the Gibbs energy equation to explain such conditions and provide contextual examples.

Illustrate your points with examples of substances in their standard states and calculations of their enthalpy changes.

Discuss how changes in entropy can drive processes where energy conservation does not alone dictate the outcome.

Provide derivations for work done in different types of expansion (isothermal, adiabatic) and relate them to energy conservation.

Create a comprehensive overview outlining how Gibbs free energy varies with temperature changes.

Delve into the interpretation of energy profiles for reactions, including transition states and their Gibbs energy implications.