# Gases

Skills to Develop

• Explain the characteristics of a gas.
• Identify the variables or parameters associated with a gas (pressure, volume, temperature, and amounts in mass or in mole).
• Evaluate volume, pressure, temperature, and amount of a gas in problem solving.

## Gases

A material that fills the entire space or volume of its container regardless of the container size is called a gas. Gas is a state of a material, and as such, it should be considered together with other states: liquid and solid. There are many common properties for the gaseous state of any material, and this and the following modules will point out some of these common properties for you to consider as you experience, observe and study the gaseous state of materials.

Molecules in a gas have little attraction for each other, because the molecules are far apart from each other. In fact, most of the volume occupied by air is empty space. When condensed into a liquid or solid, the gas molecules occupy a very small volume. Due to the huge empty space between molecules in a gas, the compressibility of a gas is much larger than that of a liquid or solid state.

Many substances, for example water, transform between solid, liquid and gas states when driven by energy. A gas, when cooled or compressed, becomes a liquid. Both gas and liquid are fluid in that they have no definite shape. A liquid does not fill the entire space or volume of its container, and there is a visible boundary between the gas and the liquid phases when both are present. On cooling, a liquid will solidify forming a solid. A solid has not only a definite volume, but also a rigid shape. There are many kinds of solids: glass, crystal, polycrystal, composite, amorphous powder, etc. The same substance may exist in two or more different crystal types. Thus, the study of solids is much more complicated than that of gas.

Do you know how large a volume is occupied by one mole of water vapor at its boiling point, 373 K? If you know some of the theories regarding gases, you will have no difficulty in giving an estimate.

Water exists in three phases (ice, water, and vapor). When 18 mL (1 mol) of water evaporates to become a gas at 373 K, the vapor occupies 30,000 mL, at 1.0 atmosphere of pressure. The volume of 18 mL is insignificant compared to 30,000 mL. The volume occupied by molecules in a gas at low pressure is insignificant.

### Air

The common properties of various gases led early (about 300B.C.) philosophers such as Plato to consider air a primal or basic substance, because they had no way of telling the various gases apart. Humans learned air as a mixture in the 17th century. Nevertheless, many laws about gases were discovered before the 17th century.

Components of Air

Percent % Substance
78 nitrogen ($$\ce{N2}$$)
21 oxygen ($$\ce{O2}$$)
1 argon ($$\ce{Ar}$$)
Variable water, $$\ce{CO2}$$
Variable

You know very well today that air is a mixture, but humans living before the 17th century did not know.

Air is required for combustion. Investigation of combustion during the 17th century led to the discovery that only about 21% of air is consumed in combustion, and the left over air from combustion is different from ordinary air. This observation led to the discovery of oxygen as a component of air. The left over gas after combustion is mostly nitrogen. The inert gas argon ($$\ce{Ar}$$) as a component of air was discovered much later than nitrogen. The amount of carbon dioxide, $$\ce{CO2}$$, and water, $$\ce{H2O}$$, in the air vary with temperature, weather, altitude, and other factors.

The variation of $$\ce{CO2}$$ concentration over a long period of time is affected by populations of animals and plants. For long range considerations, how human activities affect the climate is a concern.

Other gases including $$\ce{NO}$$, $$\ce{NO2}$$, $$\ce{NH3}$$, $$\ce{SO2}$$, $$\ce{SO3}$$, $$\ce{HCl}$$, $$\ce{Cl2}$$, $$\ce{CO}$$, $$\ce{H2S}$$, $$\ce{O3}$$, $$\ce{CH4}$$, $$\ce{CF2H2}$$, and $$\ce{Ne}$$ are also present in air at measurable concentrations.

The atmosphere exerts a pressure due to gravitational attraction of the planet Earth.

### Atmospheric Pressure

Evangelista Torricelli (1608-1647) discovered atmospheric pressure. When he inverted a tube of mercury ($$\ce{Hg}$$) and placed the tube mouth into a pool of mercury, he saw an empty space developed at the top end of the tube. The space is due to the weight of the column of mercury in the tube. He measured the net height of the mercury column, 760 mm. This discovery has been used to measure atmosphere pressure ever since. New methods are now used, but a 76 cm mercury column is considered 1.0 atmosphere (pressure) or atm, normally observed at sea level.

What is the pressure expressed in SI units? Pressure is the force applied to a unit area on a surface, and the pressure of a 76 cm $$\ce{Hg}$$ column is converted in the following way. The density of mercury is 13.6 g/mL or 13600 kg per cubic meter. The force exerted on a square meter is

$$\mathrm{13600\: kg/m^3\times\dfrac{9.80\: N}{1\: kg}\times 0.76 = 101293\: N/m^2}$$

Thus, air sustains a pressure of 101293 Newtons per square meter. A N/m2 is defined as a Pascal (Pa); 1 atmosphere is then 101293 Pa or 101.3 kPa (kilopascal). In today's standard,

\begin{align} \mathrm{1\: atm} &=\mathrm{101.325\: kPa\: (also\: called\: bar)}\\ &= \mathrm{760\: mm\: Hg\: (also\: called\: torr)}\\ &= \mathrm{14.696\: lb\: per\: square\: inch} \end{align}

For convenience, a temperature of 273 K and a pressure of 1 atm are called the standard temperature and pressure (STP). Today, an instrument used to measure pressure is called a manometer. The barometer reading in the atmosphere is the talk of the town at times, and Jack gives a treasure in this topic.

What is the height of a water column sustained by 1.0 atm?

Since mercury is 13.6 times more dense than water, the height of the water column sustained by 1 atm is therefore

\begin{align} \mathrm{13.6\: (water/Hg) \times 76\: cm\: (Hg)} &= \mathrm{1033.6\: cm\: water}\\ &= \mathrm{10.3\: m\: water} \end{align}

The implication is that water cannot be pumped up a distance more than 10 m by vacuum suction. However, a water pump which delivers more than one atmosphere will send water up a high rise building more than 100 m in height.

### Measurable Quantities of Gases

For a gas, pressure (P), temperature (T), volume (V), and amount (n) are basic, inter-related, measurable quantities. Other properties such as density are related to these quantities.

The measurement of gas pressures and their units have been briefly described above. The volume of a gas is usually measured in cubic meters (m3), liters (L), and mL.

The gas mass per unit volume is the density $$\rho$$. The density of air at STP is 1.293 g/L.

The amount in number of moles, (n), of a gas is also a quantity, and the mole concept has been discussed in Amounts of substances.

In summary, pressure (P), temperature (T), volume (V), and amount (n) are inter-related variables for a gas. The relationship will be discussed in Ideal gas and Physical properties of gases. U.S. Material Safety Data Sheets are available for hundreds of gases and gas mixtures. Take a look of one of these from this link to appreciate the need of studying gases.

## Confidence Building Questions

1. Both gas and liquid are fluid. What is the unique feature of a gas compared to a liquid?

Hint: A gas fills the entire container!

Skill:
Describe difference between gas and liquid if both are fluid.

2. Pressure is the force exerted per unit area. Calculate the pressure of your feet, assuming the contact area of your feet with the surface to be 100 cm2, and your mass (weight) to be 60 kg.

Hint: 58800 N/m2

Skill:
Formulate pressure calculation.

$$\mathrm{\dfrac{60\: kg \times 9.8\: m/s^2}{0.01\: m^2} =\: ??\: N/m^2}$$

3. A skater weighing 50 kg experiences a force of 1.5 times the gravitational force at a turn. The contact area between the skate and the ice is 1.0 cm2. What is the pressure the skate applied to the ice?

Hint: 7.35e6 N per square meter

Skill:
Formulation of pressure calculation:

$$\mathrm{\dfrac{50\: kg \times 1.5 \times 9.8\: m/s^2}{0.0001\: m^2} =\: ??\: Pa}$$

4. Assume the contact area of a tire with the surface to be 50 cm2. The weight of an automobile weighing 1000 kg is equally distributed on 4 tires. What is the pressure the tire applies to the surface?

Hint: 490000 Pa

Consideration:
Does the air pressure in the tire have to be the same?

5. If you are diving 100 m below the surface of water, what is the pressure (in atm) surrounding you?

Hint: 11 atm

Consideration:
At this depth, the amount of $$\ce{N2}$$ and $$\ce{O2}$$ dissolved in the blood is approximately 10 times that at 1 atm.

6. Assume every deep breath you take, 1 L air flows in and out of your lungs. What is the oxygen consumption (mL) in each deep breath, if the exhaled air contains 18% oxygen whereas normal air contains 21% by volume of oxygen?

Hint: 30 mL

Skill:
Find a simple way to solve a problem.

7. Assume that we take an average of 4 complete breaths every minute, and every breath consumes 30 mL of oxygen. If oxygen has a density of 1.4 g/L under the condition, what mass of oxygen in grams do we breathe a day?

Hint: $$\mathrm{4\times\dfrac{30}{1000}\times24\times60\times1.4\: g/day}$$

Consideration:
How many moles and how many molecules are there in this amount?