Molecules and the Space Time Collide and Then the Mollecules Again
The Kinetic Molecular Theory
The Kinetic Molecular Theory Postulates
The experimental observations about the beliefs of gases discussed then far can exist explained with a elementary theoretical model known every bit the kinetic molecular theory. This theory is based on the following postulates, or assumptions.
- Gases are composed of a large number of particles that carry like hard, spherical objects in a land of constant, random move.
- These particles move in a direct line until they collide with another particle or the walls of the container.
- These particles are much smaller than the altitude between particles. Most of the volume of a gas is therefore empty space.
- There is no force of attraction between gas particles or betwixt the particles and the walls of the container.
- Collisions between gas particles or collisions with the walls of the container are perfectly rubberband. None of the energy of a gas particle is lost when information technology collides with some other particle or with the walls of the container.
- The average kinetic energy of a collection of gas particles depends on the temperature of the gas and nada else.
The assumptions backside the kinetic molecular theory can be illustrated with the apparatus shown in the figure below, which consists of a drinking glass plate surrounded by walls mounted on height of three vibrating motors. A handful of steel brawl bearings are placed on summit of the glass plate to represent the gas particles.
When the motors are turned on, the drinking glass plate vibrates, which makes the ball bearings move in a constant, random fashion (postulate 1). Each ball moves in a straight line until it collides with another ball or with the walls of the container (postulate 2). Although collisions are frequent, the average distance between the brawl bearings is much larger than the diameter of the balls (postulate 3). There is no force of attraction between the private brawl bearings or between the brawl bearings and the walls of the container (postulate four).
The collisions that occur in this apparatus are very different from those that occur when a safety ball is dropped on the flooring. Collisions between the rubber ball and the floor are inelastic, as shown in the effigy beneath. A portion of the energy of the brawl is lost each fourth dimension it hits the floor, until it eventually rolls to a stop. In this apparatus, the collisions are perfectly elastic. The balls have just as much energy after a standoff as before (postulate v).
Any object in move has a kinetic energy that is defined as half of the product of its mass times its velocity squared.
KE = i/two mv 2
At any time, some of the ball bearings on this apparatus are moving faster than others, only the system tin can be described by an average kinetic free energy. When we increase the "temperature" of the system by increasing the voltage to the motors, we find that the average kinetic energy of the ball bearings increases (postulate vi).
How the Kinetic Molecular Theory Explains the Gas Laws
The kinetic molecular theory can be used to explain each of the experimentally determined gas laws.
The Link Betwixt P and n
The pressure of a gas results from collisions between the gas particles and the walls of the container. Each time a gas particle hits the wall, it exerts a force on the wall. An increment in the number of gas particles in the container increases the frequency of collisions with the walls and therefore the pressure of the gas.
Amontons' Law (P
The concluding postulate of the kinetic molecular theory states that the average kinetic free energy of a gas particle depends merely on the temperature of the gas. Thus, the boilerplate kinetic energy of the gas particles increases as the gas becomes warmer. Because the mass of these particles is abiding, their kinetic energy tin only increase if the average velocity of the particles increases. The faster these particles are moving when they striking the wall, the greater the force they exert on the wall. Since the force per standoff becomes larger equally the temperature increases, the pressure of the gas must increase besides.
Boyle's Police force (P = 1/v)
Gases tin can be compressed because almost of the book of a gas is empty space. If nosotros compress a gas without changing its temperature, the average kinetic energy of the gas particles stays the same. There is no change in the speed with which the particles motion, but the container is smaller. Thus, the particles travel from one end of the container to the other in a shorter menses of fourth dimension. This ways that they hit the walls more often. Whatever increase in the frequency of collisions with the walls must pb to an increase in the pressure of the gas. Thus, the pressure level of a gas becomes larger as the volume of the gas becomes smaller.
Charles' Police force (V
The average kinetic energy of the particles in a gas is proportional to the temperature of the gas. Because the mass of these particles is abiding, the particles must movement faster every bit the gas becomes warmer. If they move faster, the particles will exert a greater force on the container each fourth dimension they hitting the walls, which leads to an increment in the pressure of the gas. If the walls of the container are flexible, it will aggrandize until the pressure level of the gas once again balances the force per unit area of the temper. The book of the gas therefore becomes larger every bit the temperature of the gas increases.
Avogadro'southward Hypothesis (V
Every bit the number of gas particles increases, the frequency of collisions with the walls of the container must increase. This, in plough, leads to an increment in the pressure of the gas. Flexible containers, such as a balloon, volition aggrandize until the pressure of the gas within the balloon once again balances the pressure of the gas outside. Thus, the book of the gas is proportional to the number of gas particles.
Dalton's Law of Partial Pressures (P t = P i + P ii + P 3 + ...)
Imagine what would happen if half-dozen brawl bearings of a unlike size were added to the molecular dynamics simulator. The total pressure level would increase because in that location would be more than collisions with the walls of the container. But the pressure level due to the collisions between the original brawl bearings and the walls of the container would remain the same. There is so much empty space in the container that each blazon of brawl bearing hits the walls of the container every bit oftentimes in the mixture every bit it did when there was only i kind of brawl begetting on the drinking glass plate. The full number of collisions with the wall in this mixture is therefore equal to the sum of the collisions that would occur when each size of ball bearing is present past itself. In other words, the full pressure of a mixture of gases is equal to the sum of the partial pressures of the individual gases.
Graham'south Laws of Diffusion and Effusion
A few of the concrete properties of gases depend on the identity of the gas. Ane of these physical properties can be seen when the movement of gases is studied.
In 1829 Thomas Graham used an appliance like to the one shown in the figure below to study the diffusion of gases 
Graham found that the rates at which gases lengthened is inversely proportional to the square root of their densities.
This relationship eventually became known as Graham'due south law of diffusion.
To empathize the importance of this discovery nosotros have to remember that equal volumes of different gases contain the aforementioned number of particles. Every bit a result, the number of moles of gas per liter at a given temperature and force per unit area is abiding, which means that the density of a gas is directly proportional to its molecular weight. Graham's law of improvidence tin therefore also be written as follows.
Like results were obtained when Graham studied the rate of effusion of a gas, which is the rate at which the gas escapes through a pinhole into a vacuum. The charge per unit of effusion of a gas is as well inversely proportional to the square root of either the density or the molecular weight of the gas.
Graham'due south law of effusion can be demonstrated with the apparatus in the effigy beneath. A thick-walled filter flask is evacuated with a vacuum pump. A syringe is filled with 25 mL of gas and the time required for the gas to escape through the syringe needle into the evacuated filter flask is measured with a stop watch.
As we tin can see when data obtained in this experiment are graphed in the figure below, the time required for 25-mL samples of different gases to escape into a vacuum is proportional to the square root of the molecular weight of the gas. The charge per unit at which the gases effuse is therefore inversely proportional to the square root of the molecular weight. Graham's observations about the rate at which gases diffuse (mix) or effuse (escape through a pinhole) advise that relatively low-cal gas particles such every bit H2 molecules or He atoms move faster than relatively heavy gas particles such as CO2 or SOii molecules.
The Kinetic Molecular Theory and Graham'south Laws
The kinetic molecular theory tin can be used to explicate the results Graham obtained when he studied the improvidence and effusion of gases. The central to this explanation is the last postulate of the kinetic theory, which assumes that the temperature of a organization is proportional to the boilerplate kinetic energy of its particles and zippo else. In other words, the temperature of a organisation increases if and only if there is an increase in the average kinetic free energy of its particles.
Two gases, such equally Hii and Otwo, at the same temperature, therefore must have the aforementioned average kinetic energy. This can exist represented by the following equation.
This equation can be simplified by multiplying both sides past two.
Information technology can and so exist rearranged to give the following.
Taking the square root of both sides of this equation gives a relationship between the ratio of the velocities at which the two gases movement and the square root of the ratio of their molecular weights.
This equation is a modified course of Graham'southward law. Information technology suggests that the velocity (or charge per unit) at which gas molecules motility is inversely proportional to the foursquare root of their molecular weights.
Source: http://chemed.chem.purdue.edu/genchem/topicreview/bp/ch4/kinetic4.html