The Theories and Behavior of Gas
Upon completion of this lesson, the students should be able to:
- become familiar with the basic characteristics of gases
- understand the postulates of the Kinetic Molecular Theory as applied to gases
- explain how the Kinetic Molecular Theory accounts for the properties of gases
- apply the relations of volume, temperature, pressure, and mass to solve problems on gases
What makes a gas different from liquid and a solid?
Gas is one of the three forms of matter. Every known substance is either a solid, liquid or a gas. These forms differ in the way they fill space and change shape. A gas, such as air has neither a fixed shape nor a fixed volume and has weight.
Properties of Gases
- Most gases exist as molecules (in case of inert gases as individual atoms).
- The molecules of gases are randomly distributed and are far apart.
- Gases can be easily compressed, the molecules can be forced to be closed together resulting to lesser space between them.
- The volume or space occupied by the molecules themselves is negligible as compared to the total volume of the container so that the volume of the container can be taken as the volume of the gas.
- Gases have lower densities than solids and liquids.
- The attractive forces between molecules (intermolecular) are negligible.
3. Most substances that are gaseous at normal conditions have low molecular mass.
Measurable Properties of Gases
torr, mm Hg, cm Hg, atm
ml, i, cm, m
Amount of gas
1 atm = 1 atmosphere = 760 torr = 760 mm = 76 m Hg
Temperature is always in Kelvin. At absolute zero (0K) molecules stop moving entirely, the gas is as cold as anything can get.
Standard Temperature and Pressure (STP) or Standard Conditions (SC):
T = 0 0C = 273 0K
P = 1 atm or its equivalents
Postulates of the Kinetic Molecular Theory
The behavior of gases is explained by what scientists call the Kinetic Molecular Theory. According to this theory, all matter is made of constantly moving atoms or molecules. Because of their mass and velocity, they possess kinetic energy, (K.E. = 1/2mv). The molecules collide with one another and with the sides of the container. There is no kinetic energy lost during collisions inspite of the transfer of energy from one molecule to another. At any given instant, the molecule do not have the same kinetic energy. The average kinetic energy of the molecule is directly proportional to the absolute temperature. At any given temperature, the average kinetic energy is the same for the molecules of all gases.
There are several laws that explain appropriately how the pressure, temperature, volume and the number of particles in the container of gas are related.
In 1662, Robert Boyle, an Irish chemist explained the relationship between the volume and pressure of a sample of a gas. According to him, if, at a given temperature, a gas is compressed, the volume of the gas will decrease and through careful experiments he found that at a given temperature, the volume occupied by a gas is inversely proportional to the pressure. This is known as Boyle’s Law.
P = k 1/v
P = pressure of a gas sample
V = volume of a gas sample
K = a constant
Therefore: PV = k
At a given temperature, the product of the pressure and volume of a gas must be constant. If the pressure is increased, the volume must decrease to maintain the constant product. For a given gas sample to be studied under different pressures, the following expressions must hold:
P1V1 = P2V2
P1 = original pressure of a gas sample
V1 = original volume of the sample
P2 = new pressure of a gas sample
V2 = new volume of the sample
A sample of a gas entrapped in a cylinder with a movable piston occupies a volume of 720 ml under a pressure of 0.375 atm. What volume will the gas occupy under a pressure of 1.000 atm when the temperature remains constant?
V1 = 720 ml P1 = 0.375 atm
V2 = ? P2 = 1.000 atm
V2 = 360 ml x 0.375 atm/1.000 atm
V = 0.27 ml
The French chemist Jacques Alexandre Cesar Charles, in studying the relationship between the volume of a gas and its temperature, discovered that the volume of a gas increases by 1/273 for its degree centigrade its temperature is increased. From this he reasoned that a temperature of -273 degrees Celsius, was the lowest possible attainable temperature. He called this temperature absolute temperature, and established the absolute temperature scale which is related to the centigrade scale as:
A = 0C + 273
A = 0F + 273
These expressions are used in finding the absolute temperature when the centigrade or Fahrenheit temperatures are known. Charle’s Law states that at a given pressure, the volume occupied by a gas is directly proportional to the absolute temperature of the gas.
V = K T
V = volume of the gas sample
T = absolute temperature of the gas sample
K = a constant
V/T = k
For a given sample, if the temperature is changed, this ratio must remain constant, so the volume must change in order to maintain the constant ratio. The ratio at a new temperature must be the same as the ratio at the original temperature, so:
V1 = V2 /T1 = T2
V1T2 = V2T1
V1 = original volume of sample of gas
T1 = original absolute temperature
V2 = new volume of the sample
T2 = new absolute temperature of the sample
A given mass of gas has a volume of 150 ml at 25 0C. What volume will the sample of gas occupy at 45 0C, when the pressure is held constant?
V1 = 150 ml T1 = 25 + 273 = 298 0K
V2 = ? T2= 45 + 273 = 318 0K
V2 = 150 ml x 318 0K/2980K
V2 = 160 ml
Gay-Lussac’s Law states that the pressure of a certain mass of gas is directly proportional to its absolute temperature at constant volume.
P1 /T1 = P2/T2
An LPG tank registers a pressure of 120 atm at a temperature of 27 0C. If the tank is placed in an air conditioned compartment and cooled to 10 0C, what will be the new pressure inside the tank?
P1 = 120 atm T1 = 27 + 273 = 300 0K
P2 = ? T2 = 10 + 273 = 283 0K
P2 = 120 atm x 283 0K /2990K
P2 = 113.6 atm
Combined Gas Law
The Combined Gas Law (Combination of Boyle’s Law and Charles Law) states that the volume of a certain mass of gas is inversely proportional to its pressure and directly proportional to its absolute temperature.
A gas sample occupies 250mm at 27 0C, and 780 mm pressure. Find its volume at 0 0C and 760mm pressure.
T1 = 270C + 273 = 300 0A
T2 = 00C + 273 = 273 0A
V2 = 250 mm x 2730A/3000A x 780 mm/760 mm = 234 mm
Ideal Gas Law
An ideal gas is one which follows the gas law perfectly. Such a gas is non-existent, for no known gas obeys the gas laws at all possible temperatures. There are two principal reasons why real gases do not behave as ideal gases;
* The molecules of a real gas has mass, or weight, and the matter thus contained in them cannot be destroyed.
* The molecules of a real gas occupy space, and thus can be compressed only so far. Once the limit of compression has been reached, neither increased pressure nor cooling can further reduce the volume of gas.
In other words, a gas would behave as an ideal gas only if its molecules were true mathematical points, if they possessed neither weight nor dimensions. However, at the ordinary temperatures and pressures used in industry or in the laboratory, molecules of real gases are so small, weigh so little, and are so widely separated by empty space, they follow the gas laws so closely that any deviations from these laws are insignificant. Nevertheless, we have to consider that the gas laws are not strictly accurate, and results obtained from them are really close approximations.
Graham's Law of Diffusion
In 1881, Thomas Graham, a Scottish scientist discovered the Graham’s Law of Diffusion. A gas that has a high density diffuses more slowly than a gas with a lower density. Graham’s Law of Diffusion states that the rates of diffusion of two gases are inversely proportional to the square roots of their densities, providing the temperature and pressure are the same for the two gases.
Solve the following:
- The volume of a sample hydrogen is 1.63 liters at -10 0C. Find the volume at 150 0C, assuming constant pressure.
- The pressure of air in a sealed flask is 760 mm at 27 0C. Find the increase in pressure if the gas is heated to 177 0C.
- A gas has a volume of 500 milliliters when a pressure equivalent to 760 millimeters of mercury is exerted upon it. Calculate the volume if the pressure is reduced to 730 millimeters.
- The volume and pressure of a gas are 850 milliliters and 70.0 mm respectively. Find the increase in pressure required to compress the gas to 720 milliliters.
- Compute the volume of oxygen at STP if the volume of the gas is 450 milliliters when the temperature is 23 0C and the pressure is 730 milliliters.