Gas Law Variables

In order to describe gases, mathematically, it is essential to be familiar with the variables that are used. There are four commonly accepted gas law variables Temperature Pressure Volume Moles

Temperature The temperature variable is always symbolized as T. It is critical to remember that all temperature values used for describing gases must be in terms of absolute kinetic energy content for the system. Consequently, T values must be converted to the Kelvin Scale. To do so when having temperatures given in the Celsius Scale remember the conversion factor Kelvin = Celsius + 273 According to the Kinetic Molecular Theory, every particle in a gas phase system can have its own kinetic energy. Therefore, when measuring the temperature of the system, the average kinetic energy of all the particles in the system is used. The temperature variable is representing the position of the average kinetic energy as expressed on the Boltzmann Distribution.

Pressure The pressure variable is represented by the symbol P. The pressure variable refers to the pressure that the gas phase system produces on the walls of the container that it occupies. If the gas is not in a container, then the pressure variable refers to the pressure it could produce on the walls of a container if it were in one. The phenomenon of pressure is really a force applied over a surface area. It can best be expressed by the equation Consider the Pressure equation and the impact of variables on it. The force that is exerted is dependent upon the kinetic energy of the particles in the system. If the kinetic energy of the particles increases, for example, then the force of the collisions with a given surface area will increase. This would cause the pressure to increase. Since the kinetic energy of the particles is increased by raising the temperature, then an increase in temperature will cause an increase in pressure. If the walls of the container were reduced in total surface area, there would be a change in the pressure of the system. By allowing a given quantity of gas to occupy a container with a smaller surface area, the pressure of the system would increase.

As this container of gas is heated, the temperature increases. As a result, the average kinetic energy of the particles in the system increases. With the increase in kinetic energy, the force on the available amount of surface area increases. As a result, the pressure of the system increases. Eventually,..........................Ka-Boom

Volume The Volume variable is represented by the symbol V. It seems like this variable should either be very easy to work with or nonexistent. Remember, according to the Kinetic Molecular Theory, the volume of the gas particles is set at zero. Therefore, the volume term V seems like it should be zero. In this case, that is not true. The volume being referred to here is the volume of the container, not the volume of the gas particles. The actual variable used to describe a gas should be the amount of volume available for the particles to move around in. In other words Since the Kinetic Molecular Theory states that the volume of the gas particles is zero, then the equation simplifies. As a result, the amount of available space for the gas particles to move around in is approximately equal to the size of the container. Thus, as stated before, the variable V is the volume of the container.

Moles The final gas law variable is the quantity of gas. This is always expressed in terms of moles. The symbol that represents the moles of gas is n. Notice that, unlike the other variables, it is in lower case. Under most circumstances in chemistry, the quantity of a substance is usually expressed in grams or some other unit of mass. The mass units will not work in gas law mathematics. Experience has shown that the number of objects in a system is more descriptive than the mass of the objects. Since each different gas will have its own unique mass for the gas particles, this would create major difficulties when working with gas law mathematics. The whole concept of the Ideal Gas says that all gases can be approximated has being the same. Considering the large difference in mass of the many different gases available, using mass as a measurement of quantity would cause major errors in the Kinetic Molecular Theory. Therefore, the mole will standardize the mathematics for all gases and minimize the chances for errors.

Conclusions There are four variables used mathematically for describing a gas phase system. While the units used for the variables may differ from problem to problem, the conceptual aspects of the variables remain unchanged. T, or Temperature, is a measure of the average kinetic energy of the particles in the system and MUST be expressed in the Kelvin Scale. P, or Pressure, is the measure of the amount of force per unit of surface area. If the gas is not in a container, then P represents the pressure it could exert if it were in a container. V, or Volume, is a measure of the volume of the container that the gas could occupy. It represents the amount of space available for the gas particles to move around in. n, or Moles, is the measure of the quantity of gas. This expresses the number of objects in the system and does not directly indicate their masses.

The Ideal Gas Law and Gas Law Problems

Real Gases A complete introduction to the Kinetic Molecular Theory and Ideal Gases must also mention Real Gases. Generally, chemists try to ignore real gas behavior. Since there are uncountable numbers of different real gases and each needs its own mathematical description, the task of describing real gases is very intimidating. What is meant by the term Real Gas? Scientists describe a real gas as any gas that significantly disobeys any part of the Kinetic Molecular Theory. As long as a gas has sufficiently high kinetic energy and has the particles spaced far enough apart, then that gas will usually behave like the Ideal Gas. There are two sections of Kinetic Molecular Theory that will always cause problems for chemists. The ideas that the particles are volumeless and that they do not interact with each other are common potential sources of error.

Under what circumstances will the concept of the Ideal Gas and Kinetic Molecular Theory breakdown most significantly?

Very large volume gas molecules will deviate significantly from Ideal behavior. Since the Ideal Gas is able to move anywhere in the container, if the particles are of large volume, then they will be restricted from parts of the container that are occupied by the other gas particles. Remember that the V variable is the volume of the container and also the volume available to the particles. If the two ideas differ significantly, then Ideal behavior falls apart. Conversely, the most Ideal gas based on volume will be a gas with a very small volume. Theoretically, Helium is the smallest volume gas commonly found in our environment. Helium is the most Ideal. Note that Hydrogen could be smaller except for the fact that it is most commonly found as a diatomic molecule. Gas particles that exhibit nonpolar qualities are going to be more Ideal. Any gas that is highly polar, such as water, will experience significant attractions for the other particles in the system This will create problems with the concept of Ideal gases not interacting with each other. The Noble Gases, with their nonpolar character, will be the closest to Ideal in behavior. Overall, for all gases, when the system is at high pressure or low temperature, the deviation from Ideal behavior will be substantial. These circumstances cause the particles to be close together and improve chances for interactions. Conversely, when gases are at low pressures and high temperatures, then they will be more Ideal. These circumstances will allow gases to move around with less attraction for one another and have less volume taken up on a percentage basis by the particles themselves. There is an equation that will allow for the mathematical description of all real gases. As one would imagine, this equation becomes complex and difficult to work with. In addition, it establishes two more variables.

These variables are a, which represents the finite interactions of the gas particles b, which represents the finite volumes of the gas particles. If calculations ever need to be done very precisely for a specific gas, then this equation would work. Every individual gas has its own specific values for a and b. This must be readily available in order to do a problem with a specific gas. Without access to them , the equation can not be used. Even if the values are available, the math associated with the equation is very challenging. Notice what happens to the values of the variables when applied to the Ideal Gas. Because the Ideal gas particles have a volume of zero, the value of "b" is zero. Because the Ideal gas particles do not interact with each other, the value of "a" is zero. Consequently, the variables drop out of the real gas equation and the mathematics is greatly simplified.

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