**GAS LAWS & STUFF**

**Pressure**

Pressure is the force that an object applies to another object or its surroundings. Pressure can be measured in many ways:

PSI (Pounds per Square Inch)

Atm ( Atmosphere)

Torr

kPa (KiloPascal)

mmHg (millimeters of Mercury)

**Gas Laws**

**Effusion & Diffusion**

1Atm = 760 mmHG = 760 torr = 101.3 kPa = 14.7 PSI

Boyle's Law

Boyle's Law states that pressure and volume are inversely related. Assuming that temperature is constant. As shown by the equation below:

P V = P V

1 1 2 2

As you can see this would mean that as the volume increases, the pressure would decrease. Or as pressure increases, volume would decrease.

Charles's Law

Charels's Law states that the volume of a gas is directly proportional to its temperature. Assuming constant pressure. As you can see by the equation below:

V V

T T

___ ___

1 2

1 2

=

This equation shows that as volume increase the temperature would have to increase as well. Or vice versa, if temperature increases, volume increases. This happens to maintain the direct proportion.

Avogadro's Law

Avogadro's Law states that if a gas is at a constant pressure and temperature, then volume and the number of moles in the of gas are directly proportional. The following equation explains that:

V V

n n

___ ___

=

1 2

1 2

As you can see from the equation, when the number of moles increases, the volume must also increase in order to keep the same ratio. If one increases with out the other, then either the pressure or temperature is increasing.

Ideal Gas Law

The Ideal Gas law considers the relationship of volume, pressure, temperature and moles of a gas. The equation is as follows:

PV=nRT

Initial Volume

Initial Pressure

Final Pressure

Final Volume

Number of Moles

Temperature

Constant Gas Rate (depends on Pressure)

Pressure

Volume

The ideal gas law shows how pressure and volume are directly proportional to number of moles and temperature with a gas constant.

The Ideal Gas Law regards the behaviors that real gases approach at low pressures and high temperatures.

Wait....there's more!

Ideal Gas Law cont.

**Kinetic Molecular Theory of Gases**

**Real Gases**

Partial Pressure's & Dalton's Law

Dalton's Law states that for a mixture of gases in a container, the total pressure exerted is the sum of the pressures that each gas would exert if it were alone. The equation is as follows:

P = P + P + P ......

1 2 3

total

This is used in situations when you have more than one type of gas in a container, and need to find the individual pressures of each gas. Since you can find the total pressure, temperature and volume, then using the Ideal Gas Law, you can find individual pressures.

**All gases are real gases, no gas is truly an ideal gas. So, to account for the non-ideal behavior there are modifications to the ideal gas equation.**

**P =**

**nRT**

_____________

obs

**V - nb**

**- a( )**

n

___

V

2

Number of moles, gas constant, and temperature

Pressure correction factor

Volume correction factor

Observed pressure

Volume

**This equation uses correction factors in order to make up for discrepancies in volume and pressure since most gases aren't under ideal conditions.**

**Effusion**

**Diffusion**

Effusion is the process off the passage of a gas through a tiny opening into an evacuated chamber. The equation to determine the rate of effusion is as follows:

Diffusion is the process of mixing gases. A generalized equation used to describe the process of diffusion uses the distance traveled of the gasses relative to the velocities of the gas molecules.

Note that each partial pressure can be used to find the other parts of the ideal gas equation.

P =

n RT

V

________

1

1

√M

√M

2

1

_________

=

Rate of effusion for gas 1

Rate of effusion for gas 2

____________________________

*M = Molar mass

This equation is known as Graham's Law of Effusion. The Kinetic molecular theory does fit this Law, so it can be used.

Distance Traveled by gas

Distance Traveled by gas

______________________________

1

2

=

u for gas

u for gas

____________

rms

rms

1

2

=

√

M

M

___

1

2

However this is not an accurate representation of how diffusion actually works. In a tube filled with air, the gas molecules have many collisions with the air which cause a decrease in velocity that we cannot determine.

The Kinetic Molecular Theory (KMT) is a simple model that explains the properties of and ideal gas, and its particles. Here are the rules:

The particles are so small compared with the distances between them that the volume of the individual particles can be assumed to be negligible.

The particles are in constant motion. The collisions of the particles with the walls of the container are the cause of the pressure exerted by the gas.

The particles are assumed to exert no forces on each other; they are assumed neither to attract not to repel each other.

The average kinetic energy of a collection of gas particles is assumed to be directly proportional to the kelvin temperature of the gas.

Kinetic Energy & Temperature

Kelvin temperature is an index of the random motions of an object. Thus higher motion means a higher temperature. This can be used in the equation for the average kinetic energy of a molecule:

(KE) = RT

avg

3

___

2

Gas constant & Kelvin Temperature

Average Kinetic Energy

This shows that the higher the temperature the more energy it'll have.

Root Mean Square Velocity

The root mean square velocity (or u ) is the average of the square of the particle velocities. The steps shown below explain how to derive the equation for the root mean square velocity:

rms

The ideal gas law can be used with other measurements such as density and molar mass. You can use the current variables to "derive" the density and molar mass formulas.

Molar Mass & Density

Using the variable "n", which is the number of moles, you can derive the molar mass.

n = =

grams of gas

molar mass

________________

m

molar mass

_____________

P = = = =

nRT

______

V

( )

m

________

molar mass

RT

________

V

m(RT)

_________

V(molar mass)

dRT

________

molar mass

Ideal Gas Equation

substitute for "n"

Put molar mass underneath

Density =

m

V

_____

By manipulating these equations, you now have an equation that you can plug molar mass and density into. This is useful depending on what information you are given.

3

2

__

avg

√u

2

rms

=

Combine equations

u =

2

____

3RT

M

_____

u =

rms

(KE) = RT

√

_____

M

3RT

u

________

Root Mean

Square Velocity

Average of the square of the

particle velocities

Kinetic energy equation

Average of the square of the particle velocities

Kinetic equation

Molar mass of the gas

Root mean square velocity

Square root of the kinetic energy over the molar mass

The root mean square velocity can be used in various other equations and models that will be covered later.