Chemistry - A Molecular Science

THE IDEAL GAS LAW In Chapter 1, we discussed

Avogadro’s law

,

Equal volumes of gases measured under the sa

me conditions of temperature and pressure

contain equal numbers of molecules; or the vo

lume of a gas at cons

tant temperature and

pressure is directly proportional to the number of moles of gas.

V = k(P,T)n

Eq. 7.5

n is the number of moles of gas, and k(P,T)

is a proportionality cons

tant that depends upon

the pressure and the temperature of the gas.

We have three equations that relate the volume of a gas to the pressure, temperature,

and number of moles of the gas. Boyle's,

Charles', and Avogadro's Laws can all be

combined into one

ideal gas law

.

The volume of a gas is proportional to the

number of moles of t

he gas and its absolute

temperature and inversely proportional to its pressure.

PV = nRT

Eq. 7.6

R is the proportionality constant, known as the ideal gas law constant (R = 0.0820578 L⋅

atm

⋅mol

-1⋅K

-1). The use of the ideal gas law is revi

ewed in detail in Appendix B, but we

present one example of its use here. Example 7.2

A weather balloon with a volume of 1.0

x

10

3 L will collect data at a height of 10 km,

where the temperature is -50

oC and the pressure is 120 torr. How many grams of

helium should be pl

aced in the balloon to completely

fill it under these conditions?

The pressure in atmospheres is

120 torr760 torr/atm

= 0.158 atm

The temperature in kelvins is T = -50

+ 273 = 223 K, and the volume is 1.0x10

3 L. We are

asked for the amount of gas, represented by n

in the ideal gas law, so we solve Equation

7.6 for n and substitute the given values of P, V and T to obtain the number of moles of helium needed.

n =

PVRT

=

(0.158 atm)(1.0

×^10

3 L)

(0.0821 L

⋅atm

⋅K

-1⋅

mol

-1)(223 K)

= 8.6 mol

The molar mass of helium is 4.0 g/mol, so the mass of helium required is

8.6 mol

4.0 g×

mol

= 34 g He

Chapter 7 States of Matter and Changes in State

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North

Carolina

State

University