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## PowerPoint Slideshow about 'Gases' - mariko

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The official way to describe the differences in the phases of matter comes from the Kinetic Molecular Theory (or Model). The Kinetic Molecular Theory defines matter in the following two ways:

- All matter is made up of particles. These can be separate atoms or compounds/molecules. This is the “molecular” part of the theory.
- The particles in matter are constantly moving. This is the “kinetic” part of the theory.

Gases have enough translational energy that they also flow, like liquids (fluid), and gases are also assumed to:

- have particles in rapid, continuous, and random motion (Brownian Motion)
- have collisions that are perfectly elastic (do not chemically react) with each other and the walls of the container
- have densities significantly less (about 1/1000) than the solid or liquid form of the same substance

There are intermolecular forces between a substances molecules (hydrogen bonding, dipole-dipole, etc) that are trying to pull the molecules closer together.

At the same time the kinetic energy of the molecules is trying to spread the molecules farther apart as they bump and collide into each other.

The amount of kinetic energy is directly proportional to the heat energy of a system, and the heat energy of a system is comparatively measured by temperature

Pressure

One of the most important properties of gases is the pressure the gas applies.

The pressure of a gas comes from the collisions of the gas particles on the wall of the container or the interface of the liquid that is being used to when the pressure of the gas is measured.

As the gas particles hit the walls, some of the kinetic energy is passed onto the wall. Even though these collisions are elastic (no chemical reactions occur) the transfer of kinetic energy still happens.

The overall transfer of kinetic energy from the millions of molecules that hit each second is added up to one big force that is the pressure of the gas.

Historically the pressure of a gas has been measured using a liquid trapped in a tube. Evangelista Torricelli (1608-1647) is credited with making the first barometer in 1643 in an attempt to measure the weight of air (now more accurately called pressure).

He filled a glass tube that was closed at one end and about 3 feet in length with mercury. Covering the open end, he inverted the open end down inside a tray of mercury. Due to the force of gravity upon the mercury in the tube, some of the mercury flowed out of the tube and into the tray, leaving a vacuum at the top of the tube.

As the atmospheric pressure changes, so does the height of the mercury inside the tube. Thus a lower amount of mercury means lower atmospheric pressure and a higher atmospheric pressure would force more mercury up inside the tube making the level rise.

The level is measured in millimeters, and one of the ways that pressure is measured is in mm Hg (millimeters of mercury). Standard atmospheric pressure at sea level is considered to be 760 mm Hg, and is sometimes called a torr after Torricelli (760 mm Hg = 760 torr).

Comparing all the different measurements for the standard atmospheric pressure at sea level:

760 mm Hg = 760torr = 101,325 Pa = 14.7 psi = 1atm

Modern Barometer →

A barometer works well enough for measuring the atmospheric pressure, but typically pneumatic chemistry is concerned with the pressure of a confined gas, not the atmosphere.

A manometer measures the pressure of a trapped gas in relationship to the pressure of the atmosphere. A typical manometer needs to two parts, a gas container area for the trapped gas, and a U-bend of glass that is open to the container on one end and the atmosphere on the other. This U-bend is also filled to a moderate level with mercury. The sides of the U-bend are then marked in millimeters.

Boyle’s Law

In mathematical terms, P × V = k (a constant).

A more convenient form simply sets the same gas at one pressure and volume equal to a different pressure and volume. Usually this takes the form

P1 × V1 = P2 × V2

This must be for the same gas and kept at the same temperature

Charles’ Law

Charles’ Law shows a direct relationship between the volume of a gas and the temperature of the gas.

As with most things, as the temperature of a gas increases so does the volume. This law is represented as:

V1 = V2

T1 T2

Keep in mind that this mathematical relationship only works for the same gas at two different temperatures and volumes.

Kelvin Scale!!!!!

For Charles’s Law (and all other gas laws involving a temperature change) it is necessary to use the Kelvin temperature scale.

The simplest reason for using the Kelvin scale for temperature is that there are no negative numbers on the Kelvin scale so there will no negative volumes when calculations are performed. Absolute zero, the lowest point on the Kelvin scale has actually been determined from an extrapolation of Charles’ Law (in part).

0 °C = 273.15 K, and one degree Celsius is equal in size to one unit of Kelvin

This is considered to be Standard Temperature

Gay-Lussac’s Law

Joseph Gay-Lussac is given credit for the relationship between pressure and temperature.

The law worked out similarly in that the pressure of a gas is also proportional to the Kelvin temperature of the gas. This law can also be used for a determination of absolute zero.

P1 = P2

T1 T2

Once again this law is used to determine the new pressure or new temperature of just one gas. It will not work to compare two different gases.

Combined Gas Law

P1 × V1 = P2 × V2

T1 T2

The result of the combined gas law shows that neither the pressure, nor the volume, nor the temperature needs to be held constant (for the same gas). However, to use the formula five of the six variables need to be measurable. So the combined gas law has an advantage only if five different measurements can be made.

Dalton’s Law (of Partial Pressures)

An important law needs to be provided, as it can have an effect on all the laws previously stated.

Dalton’s Law says that the total pressure of a confined gas is equal to the sum of the individual partial pressures of the components of the gas.

Ptotal = Pgas1 + Pgas2 + …

If a gas is collected over water, as the gas is collected some of the water is evaporated and joins the gas. Thus the pressure in the collection container is the sum of the gas and the water. To find the pressure of just the gas, the partial pressure of the water needs to be subtracted. Use a chart of vapor pressure of water for this.

Ideal Gas Law

Values of RUnits

0.0820574587 L · atm · K-1 · mol-1

62.3637 L · mmHg · K-1 · mol-1

8.314472 J · K-1 · mol-1

8.20574587x10-5 m³ · atm · K-1 · mol-1

8.314472 cm3 · MPa · K-1 · mol-1

8.314472 L · kPa · K-1 · mol-1

8.314472 m3 · Pa · K-1 · mol-1

83.14472 L · mbar · K-1 · mol-1

1.987 cal · K-1 · mol-1

This works for one gas at one condition of pressure, volume, mole amount (n), and temperature.

Usually it is written as PV = nRT

Ideal Gas Law (continued)

Often in chemistry work, the number of moles is not known for an element, but the weight is.

We know that the molecular mass (M) is equal to the weight (w) divided by the number of moles (n):

If this is substituted into the ideal gas equation for n, then

PVM= wRT, for when the grams are known, but not the moles

(M is found using the P.T.)

Graham’s Law

Graham’s Law relates the relative velocities of two gases in terms of the square root of the inverse of their masses ( the square root of mass of gas B to gas A).

Usually the heavier gas is assigned as gas B. The heavier gas will move slower than the lighter one at the same temperature.

Diffusion – gradual mixing of gases due to Brownian motion

Effusion – gradual movement of a gas through a small opening

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