The Gas Laws• You can predict how pressure, volume,

temperature, and number of gas particles are related to each other based on the molecular model of a gas.

The Gas Laws• The Kinetic Molecular Theory• 1.) Gas particles are in constant motion and move in

a straight line until they hit another gas particle or the side of the container.

• 2.) There are not attractive or repulsive forces between the gas particles.

• 3.) The volume of the actual gas particle is assumed to be zero, since it is insignificant to the volume of the whole sample of gas.

The Gas Laws• The Kinetic Molecular Theory (cont.)• 4.) The temperature is an indirect measure the

average kinetic energy of all the gas particles in the sample.

Kinetic Energy = ½ (mass) x (velocity)2

• 5.) There is no exchange of energy when 2 gas particles collide, the collision is totally elastic.

(Just like when two billiard balls collide.)

The Gas Laws• Pressure

• Pressure = Force Applied / Area (P = F / A)

• When the gas molecules collide with the inside wall of the container, it exerts a force over an area. Therefore there is always an internal pressure on a gas.

The Gas Laws• Measuring Pressure• Pressure can be measured using a device

called a manometer.

The Gas Laws• Measuring Pressure• Atmospheric Pressure can be measured using

a device called a barometer.

The Gas Laws• Units for Measuring Pressure• Pascal (Pa) – Metric System unit for pressure• Atmosphere (atm)• Pounds per square inch (psi)• Torricelli (torr)• Millimeter of Mercury (mm Hg)

1 atm = 101,300 Pa = 101.3 kPa = 14.7 psi = 760 torr = 760 mm Hg

The Gas Laws• Pressure Conversions

1 atm = 101,300 Pa = 101.3 kPa = 14.7 psi = 760 torr = 760 mm Hg

• Convert 0.75 atm into mm Hg.

• Convert 32.0 psi into kPa.

The Gas Laws• Robert Boyle (1627 – 1691)• An English scientist whose work revolved around

trying to discover the relationship between the pressure and volume of a gas.

The Gas Laws• Boyle’s Law• If the pressure exerted on a gas increases, the

volume of the gas will proportionally decrease.

• What is the relationshipbetween the pressure exerted ona gas and its volume?

The Gas Laws• Boyle’s Law• The product of the pressure and volume of a gas

must always be a constant as long as the temperature and # of moles of gas remain constant.

Pressure x Volume = constant

Pressure(initial) x Volume(initial) = Pressure(final) x Volume (final)

P1V1 = P2V2

The Gas Laws• Boyle’s Law• Initially, a 3.0 L expandable tank of gas is under a

pressure of 13 atm. What would be the volume of the tank if the pressure inside the tank is reduced to 5.0 atm. The temperature and # of moles of gas remain constant.

The Gas Laws• Jacques Charles (1746 – 1823)• A French scientist, inventor, and avid balloonist.• He was interested in discovering the affect that the

temperature had on the volume of a gas.

The Gas Laws• Charles’ Law

• The volume of a gas divided by its Kelvin temperature must remain constant. As long as the pressure and # moles of gas does not change.

Volume = constant Temperature

Volume(initial) = Volume(final)

Temperature(initial) Temperature(final)

V1 = V2

T1 T2

Temperature must be in Kelvins!

The Gas Laws• Charles’ Law

• This is how absolute zero was determined. Is it possible?

The Gas Laws• Charles’ Law Problem• A balloon has a volume of 1.0 L at 23.0°C. What is

the volume of the balloon if the temperature decreases to -10.0°C? Assume that the pressure and # of moles of gas particles remains constant.

The Gas Laws• Combined Gas Law (Boyle’s and Charles’ Law)

P1.V1 = P2.V2

T1 T2

• The number of moles of gas must remain constant.

The Gas Laws• Combined Gas Law (Boyle’s and Charles’ Law)

• A 2.0 L balloon initially at Standard Temperature and Pressure (STP) is heated to 100.0 °C and pressurized to 1.5 atmospheres. Calculate the new volume of the balloon.

The Gas Laws• Joseph Louis Gay-Lussac (1778 – 1850)• French Chemist and Physicist who discovered th

relationship between the pressure and the temperature of a gas.

The Gas Laws• Joseph Louis Gay-Lussac (1778 – 1850)• Gay-Lussac’s Law

P1 = P2

T1 T2

• The volume and number of moles of gas must remain constant.

The Gas Laws• Gay-Lussac’s Law

• Initially, a sample of gas has a temperature of 10.0°C. It is then pressurized from 740. mm Hg to 800. mm Hg. What will be the new temperature of the gas if the volume and number of moles of gas remain constant?

The Gas Laws• The Ideal Gas Law

• The only gas law that incorporates moles into it.

PV = nRTP = Pressure (atm or kPa)V = Volume (L)n = # of moles of gas particlesR = The Gas Law Constant (0.0821 L.atm)

mol.KT = Temperature (K)

The Gas Laws• The Ideal Gas Law

• What volume would 44.01 grams of CO2 occupy at 0.00°C and 1.00 atmosphere?

The Gas Laws• The Ideal Gas Law

• What is pressure of 10.0 grams of NH3 in a 5.0 L tank at 50.0°C?

The Gas Laws• John Dalton (1766-1844)• What did he not do?

The Gas Laws• Dalton’s Law of Partial Pressures

• The partial pressure (pgas X) of a gas is the pressure that the gas exerts when it is part of a mixture of gases.

• Right now, the room that we are sitting in contains nitrogen gas, oxygen gas, water vapor, and trace amount of other gases.

0.21 atm O2 + 0.78 atm N2 + 0.05 atm CO2 +

0.05atm trace gases = 1.0 atm (atmospheric pressure)

The Gas Laws• Dalton’s Law of Partial Pressures

• The total pressure of a mixture of gases is equal to the sum of all of the partial pressures of the gases that make up the gas mixture.

p gas 1 + p gas 2 + p gas 3 + ……… = P total

The Gas Laws• Graham’s Law of Effusion

• Effusion – The movement of a gas molecule through a small hole so its velocity may be measured.

• Diffusion – The movement of gas particles from an area of high concentration to an area of low concentration.

• What causes a gas particle to diffuse?

The Gas Laws• Graham’s Law of Effusion

• What is diffusion?

The Gas Laws• Graham’s Law of Effusion

• A heavier gas particle will travel slower than a lighter gas particle.

• KE = ½ mass x velocity2

• If the kinetic energy is the same for a heavy and a light gas particle, then the velocity of the heavier one will be less than the velocity of the lighter one.

The Gas Laws• Graham’s Law of Effusion

• The rate at which a ligher gas will travel faster than a heavier gas is equal to the inverse square root of the molar mass of the gases.

Rate of light gas = √ (molar mass of heavy gas)Rate of heavy gas √ (molar mass of light gas)

The Gas Laws• Graham’s Law of Effusion

• Which molecule will diffuse faster, H2 or O2? How many times faster will the ‘faster’ molecule diffuse compared to the slower one?