10.2. Mass, Volume, and the Mole http://www.ck12.org
Because different gases have different molar masses, the mass contained in a set volume of gaswilldepend on the
identity of the gas. For example, at a certain temperature and pressure, one liter of hydrogen gas has a mass of
0.0899 grams, while a liter of oxygen gas has a mass of 1.43 grams. This ratio is approximately equal to 1:16, which
is the ratio of the molar masses for these two elements. TheFigure10.2 shows the amount of mass contained in a
given volume of various gases.
FIGURE 10.2
Relative masses of various gases.The implications of Avogadro’s work were extensive and helped in developing the kinetic theory of gases in the
last half of the 19thcentury. They also were useful as practical guidelines for how to run reactions with gases.
For example, water has a formula of H 2 O, which means that for each mole of oxygen atoms, there are two moles of
hydrogen atoms. A complete reaction can occur with no leftover hydrogen or oxygen only if the volume of hydrogen
used is twice the volume of oxygen used. Because the volume of a gas is easier to measure than its mass, this is a
useful experimental tool.
Example 10.9
Let’s say you have three balloons. One is filled with hydrogen gas, one with oxygen gas, and one with nitrogen gas.
The molar masses of these gases are 2 g/mol for H 2 , 32 g/mol for O 2 , and 28 g/mol for N 2. If all three balloons are
the same volume, which contains the most mass, and which contains the least?
Answer:
Based on their molar masses, hydrogen is the lightest molecule, and oxygen is the heaviest. Because all three
volumes are the same, each balloon contains the same number of gas molecules. Therefore, the hydrogen balloon
will have the lowest mass, and the oxygen balloon will have the highest.
Calculations Involving Gases
Because the volume of a gas is dependent on the pressure and temperature, scientists found it useful to collect
data at fixed pressures and temperatures so that they could be compared between different gases. A pressure of
one atmosphere and a temperature of 0°C is known asstandard temperature and pressure (STP). Under these
conditions, one mole of any gas takes up a volume of 22.4 liters. This information allows us to convert between
liters and moles for gases at STP.
Example 10.10
At STP, we have 46.2 liters of helium. How many moles of helium do we have?
( 46 .2 L He)( 22 1 mol He.4 L He) = 2 .06 mol He
Example 10.11
What volume does 4.96 moles of O 2 occupy at STP?
( 4 .96 mol O 2 )(^22 1 mol O.4 L O 22 ) =111 L O 2