Physical Chemistry , 1st ed.

and similarly:

pf2.71 atm

To calculate (pV), multiply the final pressure and volume together, then

subtract the product of the initial pressure and volume:

(pV) (2.71 atm)(0.375 L) (20.3 atm)(0.0500 L)  0

as expected for what is basically a Boyle’s-law expansion of an ideal gas.

Therefore HUand so

H0 J

Although the changes in the two state functions are equal (and zero) in this

example, this is not always the case.

Because His a common state function, we base the definitions of some

terms on enthalpy, not internal energy. The term exothermicis applied to any

process where Hfor the process is negative. In such cases, energy is being

given off by the system into the surroundings. The term endothermicrefers to

any process where His positive. In these cases, energy is being absorbed by

the system from the surroundings.

2.6 Changes in State Functions

Although we stated that we can know only the changein internal energy or

enthalpy, so far we have mostly dealt with the overall change of a complete

process. We have not considered infinitesimal changes in Hor Uin much

detail.

Both the internal energy and the enthalpy of a given system are determined

by the state variables of the system. For a gas, this means the amount, the pres-

sure, the volume, and the temperature of the gas. We will initially assume an

unchanging amount of gas (although this will change when we get to chemi-

cal reactions). So,Uand Hare determined by p,V, and Talone. But p,V, and

Tare related by the ideal gas law (for an ideal gas), so knowing any two you

can determine the third. There are therefore only two independent state vari-

ables for a given amount of gas in a system. If we want to understand the in-

finitesimal change in a state function, we need only understand how it varies

with respect to two of the three state variables ofp,V, and T. The third one

can be calculated from the other two.

Which two do we pick for internal energy and enthalpy? Although we can

pick any two, in the mathematics that follow there will be advantages to pick-

ing a certain pair for each state function. For internal energy, we will use tem-

perature and volume. For enthalpy, we will use temperature and pressure.

The total differential of a state function is written as the sum of the deriv-

ative of the function with respect to each of its variables. For example,dUis

equal to the change in Uwith respect to temperature at constant volume plus

the change in Uwith respect to volume at constant temperature. For the

change in Uwritten as U(T,V) →U(T+ dT,V+ dV), the infinitesimal change

in internal energy is

dU

U

T



V

dT+ 

U

V



T

dV (2.21)

(0.0400 mol)(0.08205 mLoaltmK)(310 K)



0.375 L

38 CHAPTER 2 The First Law of Thermodynamics