Gas Laws

Avogadro

Boyle

Charles

Dalton

Gay Lussac

Graham

Avagadro's number is 6.022x10^23 [image]

Boyle's Law is P1v1=P2V2

P=pressure V=volume

At a fixed temperature, the volume of a gas is inversely proportional to the pressure exerted by the gas.

Charles Law is (V1/T1)=(V2/T2)

V=volume T=temperature

"At a fixed pressure, the volume of a gas is proportional to the temperature of the gas.

Dalton's Law is Ptotal=P1+P2....

P=pressure

Gay Lussac's Law is (P1/T1)=(P2/T2)

P=pressure T=temperature

Graham's Law is (Rate1/Rate2)=square root(mass2/mass1)

The effusion rate of a gas is inversely proportional to the square root of its molecular mass.

Postulates

1. Gases are composed of a large number of particles that behave like hard, spherical objects in a state of constant, random motion.
2. These particles move in a straight line until they collide with another particle or the walls of the container.
3. These particles are much smaller than the distance between particles. Most of the volume of a gas is therefore empty space.
4. There is no force of attraction between gas particles or between the particles and the walls of the container.
5. Collisions between gas particles or collisions with the walls of the container are perfectly elastic. None of the energy of a gas particle is lost when it collides with another particle or with the walls of the container.
6. The average kinetic energy of a collection of gas particles depends on the temperature of the gas and nothing else.

Partial Pressures

The pressure of a mixture of nitrogen, carbon dioxide, and oxygen is 150 kPa. What is the partial pressure of oxygen if the partial pressures of the nitrogen and carbon dioxide are 100 kPA and 24 kPa, respectively?

P = P_nitrogen + P_{carbon dioxide} + P_oxygen

150 kPa = 100 kPa + 24 kPa + P_oxygen

P_oxygen = 150 kPa - 100 kPa - 24 kPa

P_oxygen = 26 kPa

[P + (n2a/V2)](V - nb) = nRT

P=pressure

n=Number of moles

V=volume

T=temperature

R=ideal gas constant

a and b=constants, which are chosen to fit experiment as closely as possible to individual gas molecule.

Tables of values for a and b are found in reference books. Below are some values for a and b. The units for a are liters² atm. mole^-2 and the units of b are liters mole^-1.

Rate₁ / Rate₂ = square root of (Mass₂ / Mass ₁)

Graham's Law shows the relationship between the molar or molecular mass of a gas and the rate at which it will effuse. Effusion is the process of gas molecules escaping through tiny holes in their container.

Maxwell-Boltzman distribution

The Maxwell distribution describes the distribution of particle speeds in an ideal gas.

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• Average Speed

  The average speed is the sum of the speeds of all of the particles divided by the number of particles.

• Most Probable Speed

  The most probable speed is the speed associated with the highest point in the Maxwell distribution. Only a small fraction of particles might have this speed, but it is more likely than any other speed.

• Width of the Distribution

  The width of the distribution characterizes the most likely range of speeds for the particles. One measure of the width is the Full Width at Half Maximum (FWHM). To determine this value, find the height of the distribution at the most probable speed (this is the maximum height of the distribution). Divide the maximum height by two to obtain the half height, and locate the two speeds in the distribution that have this half-height value. On speed will be greater than the most probably speed and the other speed will be smaller. The full width is the difference between the two speeds at the half-maximum value.