much mass as a mole of Carbon-12.

The mass per mole of a substance is called its molar mass. When measured in grams

(or, to be precise, g/mol) the molar mass of a particular substance has the same

numerical value as the atomic mass of the substance. Why? The atomic mass of an

atom of carbon-12 is 12 u by definition, and a mole of carbon-12 atoms is exactly 12

grams, by the definition of Avogadro’s number.

Consider a substance with an atomic mass of 36 u. Each particle will be three times as

massive as an atom of carbon-12. One mole of the substance has the same number of

particles as one mole of carbon-12. This means a mole of this substance would have a

mass that is three times the mass of a mole of carbon-12, or 36 grams. In physics, the

molar mass is usually stated in kg/mol instead of g/mol.

How many helium atoms are in

the balloon?

(0.43 moles)(6.022×10^23 atoms/mol)

2.6×10^23 helium atoms

19.5 - Ideal gas law

Ideal gas law: The product of a gas’s pressure

and volume is proportional to the amount of gas

and its temperature.

The ideal gas law shown in Equation 1 is an empirical law that describes the

relationship of pressure, volume, amount of gas, and temperature in an ideal gas. It

states that the pressure of an amount of an ideal gas times its volume is proportional to

the amount of gas times its temperature. The pressure is the absolute, not gauge,

pressure. (Absolute pressure equals gauge pressure plus atmospheric pressure.) The

small n in the equation is the number of molecules, measured in moles. The

temperature is measured in kelvins. R is a constant called the universal gas constant.

Its value is 8.314 51 J/mol·K.

Everyday observations confirm the main precepts of the ideal gas law. When you inflate

a bicycle tire, you increase the amount of gas in the tire, which increases both its

pressure and volume. Once it is inflated and its volume is held nearly constant by the

tire, an increase in temperature increases the pressure of the gas within. A hot day or

the rolling friction from riding increases its temperature. You are told to check the

pressure of a tire when it is “cold” since the correct pressure for a tire is established for

20°C or so. Checking tire pressure when the tire is hot may cause you to deflate the

tire unnecessarily.

Sometimes, it is useful to be able to apply the ideal gas law when the number of

particles N is known, rather than the number of moles. Since the number of particles is

the number of moles times Avogadro’s number, we can rewrite the ideal gas law as

shown in Equation 2. The constant k here is called Boltzmann’s constant, which equals

the gas constant R divided by Avogadro’s number NA. Its value is 1.380 66×10í^23 J/K.

While the first statement of the ideal gas law relates P,V and T to the macroscopic

properties R and n of a gas, the second relates them to the microscopic properties k

and N.

If this is the ideal gas law, are there non-ideal gases? Yes, there are. For instance,

water vapor (steam) is a non-ideal gas. The ideal gas law provides accurate results

when gas molecules bounce into each other with perfectly elastic collisions. If the

molecules also interact in other ways, as they do with steam, the law becomes a less

accurate predictor of the relationship between pressure, volume, temperature, and the

amount of gas. In the case of water vapor, steam tables are used to relate these values.

In Example 1, the volume of one mole of gas at standard pressure and temperature is

calculated. The volume is 2.25×10í^2 m^3 (22.5 liters, or about six gallons). One mole of

any ideal gas occupies this same volume under these conditions. In 1811, Avogadro

first proposed that equal volumes of all gases at the same pressure and temperature

contained the same number of molecules.

Ideal gas law

Pressure times volume proportional to:

·molar quantity of gas

·Kelvin temperature of gas

Ideal gas law, number of moles

PV = nRT

P = absolute pressure (Pa)

V = volume, n = moles

R = universal gas constant

R = 8.31 J/mol·K

T = Kelvin temperature

Ideal gas law, number of

particles

PV = NkT

N = number of particles

k = R/NA = Boltzmann's constant

k = 1.38×10í^23 J/K

(^364) Copyright 2000-2007 Kinetic Books Co. Chapter 19