Chemistry 112

## Thermodynamics

Thermodynamics is the study of energy and its changes when physical or chemical processes occur.

The energy changes that occur during a chemical reaction are the underlying reasons for all reactivity and determine the position of equilibria in chemical reactions: all processes are driven to the lowest possible energy.

The study of thermodynamics is broken into three laws:

1. Energy is conserved. (There is a price to pay for everything.)

2. Entropy increases. (All processes increase the distribution of energy.)

3. Entropy is statistical. (A single distribution of energy can only be attained at absolute zero.)

## The First Law of Thermodynamics (Review)

The total energy (from all sources) of a system plus surroundings remains constant.

U = internal energy; this is composed of the kinetic and potential energies from all sources.

U is a state function, i.e., it is evaluated solely by the variables that define the state and not by the path by which that state is arrived.

In chemical systems, temperature, pressure, and composition normally define the state of a system.

U is nearly impossible to measure, but measuring the change in internal energy during a process can be done. Thus, we are normally interested in

 U = Ufinal – Uinitial

Internal energy changes by changes in heat or work.

Heat is an energy quantity associated with a temperature change. Heat is given the symbol q. When heat flows from the system to the surroundings, q is given a negative sign (the system is losing heat).

Work is an energy quantity associated with changes in position of a mass. Work is given the symbol w. When work is done by the system on the surroundings, w is given a negative sign (the system is losing work).

Since any internal energy change in a process must be distributed as either heat or work, the mathematical statement of the First Law is:

 U = q + w

q and w are not state functions. Changing how a process is run can change the distribution of heat and work!

Under normal laboratory conditions, chemical reactions are run at constant external pressure,

~ 1atm. Under these conditions, work is found as

 w = –PV

where P is the external pressure and V is the change in volume that occurs during a process;

 V = Vfinal – Vinitial

Thus, at constant pressure, the First Law becomes

 U =qp – PV

where qp is the heat at constant pressure.

V is tedious to measure for chemical systems (except where gases are involved), so U is rarely used.

Since the internal energy, U, is a poor thermodynamic function for most chemical processes. A better thermodynamic function is the enthalpy, H, defined as

H = U + PV

Enthalpy is also a state function.

At constant pressure,

H = U + (PV)

H = U + (P)V + P(V)

P = 0 (constant pressure), so

H = U + PV

Substituting the constant pressure form of the first law:

H = [qp – PV] + PV

H = qp

qp is easy to measure so H becomes a useful quantity to know.

Enthalpies of reaction have been measured for many reactions. Tabulation of all of this information would be unwieldy. Rather, a single type of reaction is chosen, and enthalpies are found for this standard reaction. The reaction chosen is one where a substance is formed from elements in their natural state at standard conditions (st, 25 °C, 1.0 atm, 1 mole of product, 1.0 M solution):

aA(st) + bB(st) + ... product (st)

A, B, etc. are elements. The enthalpy of this reaction is called the enthalpy of formation, called Hfo. Enthalpies of Formation are tabulated.

Enthalpies of formation can be used to find the standard enthalpy for any reaction.

aA(st) + bB(st) + ... cC(st) + dD(st) + ...

The enthalpy of the reaction is given by:

Ho = [cHfo(C) + dHfo(D) + ...] – [aHfo(A) + bHfo(B) + ...]

In general, this is written as:

mi and mj are the stoichiometric coefficients from the balanced reaction.

#### Example

Find the standard enthalpy of reaction between solid aluminum sulfate and aqueous sodium hydroxide.