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General Chemistry Principles, Patterns, and Applications, 2011

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V = ( constant)(nTP)<br />

By convention, the proportionality constant in Equation 10.10 is called thegas constant, which is<br />

represented by the letter R. Inserting R into Equation 10.10gives<br />

Equation 10.11<br />

V = RnTP = nRTP<br />

Clearing the fractions by multiplying both sides of Equation 10.11 by P gives<br />

Equation 10.12<br />

PV = nRT<br />

This equation is known as the ideal gas law.<br />

An ideal gas is defined as a hypothetical gaseous substance whose behavior is independent of attractive<br />

<strong>and</strong> repulsive forces <strong>and</strong> can be completely described by the ideal gas law. In reality, there is no such thing<br />

as an ideal gas, but an ideal gas is a useful conceptual model that allows us to underst<strong>and</strong> how gases<br />

respond to changing conditions. As we shall see, under many conditions, most real gases exhibit behavior<br />

that closely approximates that of an ideal gas. The ideal gas law can therefore be used to predict the<br />

behavior of real gases under most conditions. As you will learn in Section 10.8 "The Behavior of Real<br />

Gases", the ideal gas law does not work well at very low temperatures or very high pressures, where<br />

deviations from ideal behavior are most commonly observed.<br />

Note the Pattern<br />

Significant deviations from ideal gas behavior commonly occur at low temperatures <strong>and</strong> very high<br />

pressures.<br />

Before we can use the ideal gas law, however, we need to know the value of the gas constant R. Its form<br />

depends on the units used for the other quantities in the expression. If V is expressed in liters (L), P in<br />

atmospheres (atm), T in kelvins (K), <strong>and</strong>n in moles (mol), then<br />

Equation 10.13<br />

R = 0.082057 (L·atm)/(K·mol)<br />

Because the product PV has the units of energy, as described in Chapter 5 "Energy Changes in Chemical<br />

Reactions", Section 5.1 "Energy <strong>and</strong> Work" <strong>and</strong> Essential Skills 4 (Chapter 5 "Energy Changes in Chemical<br />

Reactions", Section 5.6 "Essential Skills 4"),R can also have units of J/(K·mol) or cal/(K·mol):<br />

Equation 10.14<br />

R = 8.3145 J/(K·mol) = 1.9872 cal/(K·mol)<br />

Saylor URL: http://www.saylor.org/books<br />

Saylor.org<br />

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