Thermochemistry and Energetics of Chemical Reactions notes

Thermochemistry and Heat Changes

Thermochemistry is the study of heat changes during chemical reactions and physical changes. Heat is energy transferred between a system and its surroundings because of a temperature difference. It is represented by q and is commonly measured in joules or kilojoules.

A reaction may release heat to the surroundings or absorb heat from them. The sign of q or ΔH tells whether heat is released or absorbed by the system.

• Exothermic reactions release heat to the surroundings. Their ΔH is negative.
• Endothermic reactions absorb heat from the surroundings. Their ΔH is positive.
• Combustion of fuels, acid-base neutralization and respiration are examples of exothermic processes.
• Photosynthesis, thermal decomposition of calcium carbonate and melting of ice are examples of endothermic processes.
• In an exothermic process, the temperature of the surroundings usually increases.
• In an endothermic process, the temperature of the surroundings usually decreases.
• Heat required to raise the temperature of unit mass of a substance by 1 K is called specific heat capacity.
• The relation for heat change is q = mcΔT, where m is mass, c is specific heat capacity and ΔT is change in temperature.

System, Surroundings and Spontaneous Processes

The part of the universe selected for study is called the system. Everything outside the system that can interact with it is called the surroundings. The system and surroundings together make the universe.

A spontaneous process occurs naturally under specified conditions without continuous external assistance. Spontaneity does not mean that a process is fast. Some spontaneous processes are very slow.

Open systems exchange both matter and energy with the surroundings. Closed systems exchange energy but not matter. An isolated system exchanges neither matter nor energy.

A refrigerator transfers heat from a colder region to a warmer surrounding. This process is not spontaneous by itself and requires external electrical work. Heat naturally flows from a hot body to a cold body.

• System: the part of the universe under observation.
• Surroundings: everything outside the system that can exchange energy or matter with it.
• Open system: exchanges matter and energy with surroundings.
• Closed system: exchanges energy but not matter with surroundings.
• Isolated system: exchanges neither matter nor energy with surroundings.
• A spontaneous process can occur naturally under given conditions.
• Synthesis of glucose by plants is non-spontaneous without energy input from sunlight.
• Spontaneity and rate are different concepts. A spontaneous process may be slow.

State Functions and Path Functions

A state function is a macroscopic property whose value depends only on the initial and final states of a system. It does not depend on the route or path used to reach the final state. State functions describe the state of the system at a particular condition.

Heat and work are path functions. Their values depend on how a process takes place. For example, the same change in internal energy can occur through different combinations of heat transfer and work.

State functions are useful because changes in them can be calculated for a convenient route, even when the actual route is difficult to observe.

• A state function depends only on the initial and final states.
• Internal energy, enthalpy, temperature, pressure, volume and entropy are state functions.
• Heat q and work w are path functions.
• The change in a state function is independent of the path followed.
• For a complete cycle, the net change in any state function is zero.
• Enthalpy is a state function.
• The value of a state function is a macroscopic property of the system.
• Hess's law is based on the state function nature of enthalpy.

Internal Energy

The total energy possessed by a system is called its internal energy, represented by E or U. It is the sum of the microscopic kinetic and potential energies of the particles in the system.

Kinetic energy is associated with the motion of atoms, ions and molecules. Potential energy is associated with the forces and positions of particles, including chemical bonds and intermolecular attractions. Internal energy does not include the energy of the system as a whole due to its position in a gravitational field or its overall motion.

The absolute value of internal energy cannot normally be measured directly. The change in internal energy, ΔE, can be measured or calculated.

• Internal energy is the sum of microscopic kinetic and potential energies.
• It includes molecular translation, rotation, vibration and chemical bonding energies.
• It does not include energy due to the overall gravitational position of the system.
• It does not include the overall kinetic energy of the complete system as a whole.
• Internal energy is a state function.
• For a change, ΔE = Efinal - Einitial.
• If energy enters the system, ΔE is positive.
• If energy leaves the system, ΔE is negative.

First Law of Thermodynamics

The first law of thermodynamics is the law of conservation of energy. Energy can neither be created nor destroyed, although it can be converted from one form to another. For a chemical system, energy is transferred mainly as heat and work.

Using the chemistry sign convention, q is positive when heat is supplied to the system and negative when heat leaves the system. Work w is positive when work is done on the system and negative when work is done by the system.

For expansion against a constant external pressure, work is represented by w = -PextΔV. Therefore, the first law is written as ΔE = q + w. For pressure-volume work only, ΔE = q - PextΔV.

• First law: ΔE = q + w.
• For expansion work, w = -PextΔV.
• Therefore, ΔE = q - PextΔV.
• During expansion, ΔV is positive and expansion work is negative.
• During compression, ΔV is negative and work done on the system is positive.
• At constant volume, ΔV = 0, so qv = ΔE.
• If a reaction occurs with no change in gaseous volume, q may equal ΔE.
• Energy supplied as heat may increase internal energy, perform work, or do both.

Enthalpy and Enthalpy Changes

Enthalpy is a thermodynamic state function represented by H. It is defined as H = E + PV. The change in enthalpy is ΔH = ΔE + Δ(PV). For reactions occurring at constant pressure, the heat absorbed or released is equal to the enthalpy change, qp = ΔH.

In many chemical reactions, especially those occurring in open containers, pressure is approximately constant. Therefore, enthalpy change is commonly used to describe heat changes in chemical reactions.

For reactions involving gases, the relation ΔH = ΔE + ΔngRT is used when gases behave ideally. Here, Δng is the change in moles of gaseous substances, and R is the gas constant. For reactions involving no change in gaseous moles, ΔH = ΔE.

• Enthalpy is defined as H = E + PV.
• At constant pressure, qp = ΔH.
• For gaseous reactions, ΔH = ΔE + ΔngRT.
• If Δng = 0, then ΔH = ΔE.
• For 2NH3(g) → N2(g) + 3H2(g), gaseous moles change from 2 to 4, so ΔH is not generally equal to ΔE.
• For reactions involving only solids and liquids, PV work is usually small, so ΔH and ΔE are close.
• For melting or fusion, the system expands slightly because the liquid occupies more volume than the solid, so ΔH is greater than ΔE.
• Enthalpy change may be positive or negative.

Important Enthalpy Changes

The standard enthalpy change is measured when substances are in their standard states under standard conditions. The standard state of an element is its most stable form at the specified temperature and pressure. The standard enthalpy of formation of a free element in its standard state is zero.

The standard enthalpy of formation, ΔHf°, is the enthalpy change when one mole of a compound is formed from its elements in their standard states. Some enthalpies of formation cannot be measured directly, so they are calculated by applying Hess's law.

The standard enthalpy of combustion is the enthalpy change when one mole of a substance is completely burned in oxygen under standard conditions. It is usually negative.

The standard enthalpy of neutralization is the enthalpy change when an acid and a base react to form one mole of water in dilute aqueous solution. For a strong acid and a strong alkali, it is approximately -57.0 kJ mol-1 at 25 °C because the net ionic reaction is H+(aq) + OH-(aq) → H2O(l).

• Standard enthalpy of formation: enthalpy change when one mole of compound forms from its elements in standard states.
• The standard enthalpy of formation of an element in its standard state is zero.
• Standard enthalpy of combustion: heat change when one mole of substance burns completely in oxygen.
• Standard enthalpy of atomization: enthalpy change when one mole of gaseous atoms forms from an element in its standard state.
• For Na(s) → Na(g), ΔH = +107 kJ mol-1, and this is an enthalpy of atomization.
• For 1/2 H2(g) → H(g), the enthalpy change is an enthalpy of atomization.
• Standard enthalpy of neutralization for a strong acid and strong alkali is approximately -57.0 kJ mol-1 of water formed.
• The neutralization value is independent of the particular strong acid or strong alkali because the net reaction is H+(aq) + OH-(aq) → H2O(l).

Hess's Law and Calculation of Enthalpy

Hess's law states that the total enthalpy change of a reaction is the same whether the reaction occurs in one step or several steps. This follows because enthalpy is a state function and depends only on the initial and final states.

To use Hess's law, chemical equations may be reversed or multiplied. If an equation is reversed, the sign of ΔH is changed. If an equation is multiplied by a number, its ΔH is multiplied by the same number. The equations are then added and unwanted substances are cancelled.

For example, the combustion enthalpies of graphite and diamond can be compared because both produce CO2. Using the given values, ΔHcomb(graphite) = -393.51 kJ mol-1 and ΔHcomb(diamond) = -395.41 kJ mol-1. The conversion graphite to diamond has ΔH = (-393.51) - (-395.41) = +1.90 kJ mol-1. The reverse conversion, diamond to graphite, has ΔH = -1.90 kJ mol-1. The sign depends on the direction of the conversion.

• Hess's law: total enthalpy change is independent of the route.
• A reversed chemical equation has the opposite sign of ΔH.
• Multiplying an equation by a factor multiplies ΔH by the same factor.
• Dividing an equation by a factor divides ΔH by the same factor.
• Equations can be added after cancelling common substances.
• Indirect enthalpy changes can be calculated even when direct measurement is difficult.
• For graphite and diamond, the combustion data give graphite to diamond as approximately +1.90 kJ mol-1.
• The sign of an enthalpy change must match the direction written in the equation.