The Foundations of Chemistry

SUMMARY OF GAS LAWS: THE IDEAL GAS EQUATION

Let us summarize what we have learned about gases. Any sample of gas can be described

in terms of its pressure, temperature (in kelvins), volume, and the number of moles, n,

present. Any three of these variables determine the fourth. The gas laws we have studied

give several relationships among these variables. An ideal gasis one that exactly obeys

these gas laws. Many real gases show slight deviations from ideality, but at normal temper-

atures and pressures the deviations are usually small enough to be ignored. We will do so

for the present and discuss deviations later.

We can summarize the behavior of ideal gases as follows.

Boyle’s Law V  (at constant Tand n)

Charles’s Law V T (at constant Pand n)

Avogadro’s Law V n (at constant Tand P)

Summarizing V  (no restrictions)

As before, a proportionality can be written as an equality by introducing a proportion-

ality constant, for which we’ll use the symbol R. This gives

VR
or, rearranging, PVnRT

This relationship is called the ideal gas equationor the ideal gas law.The numerical value

of R,the universal gas constant,depends on the choices of the units for P, V,and T.One

mole of an ideal gas occupies 22.414 liters at 1.0000 atmosphere and 273.15 K (STP).

Solving the ideal gas law for Rgives

R0.082057

In working problems, we often round Rto 0.0821 Latm/molK. We can express Rin

other units, as shown inside the back cover of this text.

EXAMPLE 12-7 Units of R

Rcan have any energyunits per mole per kelvin. Calculate Rin terms of joules per mole per

kelvin and in SI units of kPadm^3 /molK.

Plan

We apply dimensional analysis to convert to the required units.

Solution

Appendix C shows that 1 Latm101.325 joules.

R8.3144 J/molK

Now evaluate Rin SI units. One atmosphere pressure is 101.325 kilopascals, and the molar

volume at STP is 22.414 dm^3.

101.325 J



1 Latm

0.082057 Latm



molK

Latm



molK

(1.0000 atm)(22.414 L)



(1.0000 mol)(273.15 K)

PV



nT

nT



P

nT



P

1



P

12-9

This equation takes into account the
values of n, T, P,and V. Restrictions
that apply to the individual gas laws
are therefore not needed for the ideal
gas equation.

450 CHAPTER 12: Gases and the Kinetic–Molecular Theory

Recall that 1 dm^3 1 L.

See the Saunders Interactive
General Chemistry CD-ROM,
Screen 12.4, The Ideal Gas Law.