Gas LawsGas Laws

Gas LawsGas Laws

What are gas laws???What are gas laws??? Study of the relationships between Study of the relationships between

pressure, volume, temperature, and pressure, volume, temperature, and amount of gases in a systemamount of gases in a system

Boyle’s LawBoyle’s Law

If the pressure If the pressure of a gas is of a gas is increased, the increased, the volume is volume is decreaseddecreased

This is an This is an inverseinverse relationshiprelationship

PP11VV11 = P = P22VV22

Boyle’s LawBoyle’s LawPP11VV11 = P = P22VV22

Example: 16.0 L of hydrogen gas Example: 16.0 L of hydrogen gas exerts a pressure of 740.0 mm Hg at exerts a pressure of 740.0 mm Hg at standard temperature. At what standard temperature. At what volume will the gas exert a pressure volume will the gas exert a pressure of 550.0 mm Hg? (Be sure your of 550.0 mm Hg? (Be sure your units of volume and pressure agree!)units of volume and pressure agree!)

(740.0)(16.0) = (550.0)(V2)

V2 = 21.5 L

Charles’ LawCharles’ Law

If the temperature of a gas increases, If the temperature of a gas increases, the volume of a gas increasesthe volume of a gas increases

This shows a direct relationship This shows a direct relationship between V and Tbetween V and T

Temperature must be in Kelvin! Temperature must be in Kelvin! (Celsius + 273)(Celsius + 273)

VV11 = = VV22 T T11 T T22

Charles’ LawCharles’ LawVV11 = = VV22

TT11 T T22 Example: 16.0 L of oxygen gas Example: 16.0 L of oxygen gas

occupies a gas cylinder at 0.00ºC. occupies a gas cylinder at 0.00ºC. What will be the volume of the gas What will be the volume of the gas if the temperature is increased to if the temperature is increased to 35.0ºC? (Hint: Celsius 35.0ºC? (Hint: Celsius Kelvin) Kelvin)

_16.0_

273

_V2_308

=

V2 = 18.1 L

Gay-Lussac’s LawGay-Lussac’s Law

If the temperature of a gas If the temperature of a gas increases, the pressure also increases, the pressure also increasesincreases

This is a This is a directdirect relationship relationship between T and Pbetween T and P

PP11 = = PP22 T T11 T T22

Gay-Lussac’s LawGay-Lussac’s LawPP11 = = PP22

T T11 T T22

Example: If a gas at 25.0ºC and 1.00 atm Example: If a gas at 25.0ºC and 1.00 atm is heated to 45.0ºC, then what is the new is heated to 45.0ºC, then what is the new pressure? Assume constant volume pressure? Assume constant volume

__1.00__

298

_P2_

318=

P2 = 1.10 atm

Combined Gas LawCombined Gas Law

Puts Boyle, Charles, and Gay-Puts Boyle, Charles, and Gay-Lussac’s Laws togetherLussac’s Laws together

PP11VV11 = = PP22VV22

TT11 T T22

Ideal Gas LawIdeal Gas Law

PV = nRTPV = nRT P = pressureP = pressure V = volume (use only L)V = volume (use only L) n = number of moles of gasn = number of moles of gas R = constant (.0821 atm-L/mol-K R = constant (.0821 atm-L/mol-K

or 62.4 mmHg-L/mol-K)or 62.4 mmHg-L/mol-K) T = temperature in KelvinT = temperature in Kelvin

Dalton’s Law of Partial Dalton’s Law of Partial PressuresPressures

The sum of the pressures of all gases The sum of the pressures of all gases present in a system equals the total present in a system equals the total pressure of the systempressure of the system

PP11 + P + P22 + P + P33 + … = P + … = Ptt

Graham’s LawGraham’s Law

The rates of diffusion of gases at the The rates of diffusion of gases at the same temperature and pressure are same temperature and pressure are inversely proportional to the square inversely proportional to the square roots of their molar massesroots of their molar masses

Normal languageNormal language: lighter gases move : lighter gases move through the air faster than heavier through the air faster than heavier gasesgases

ExampleExample: helium moves faster than : helium moves faster than radonradon