General General ChemistryChemistryGas LawsGas Laws

CE 541CE 541

What Are Gas LawsWhat Are Gas Laws

The The gas lawsgas laws are a set of laws that are a set of laws that describe the relationship between describe the relationship between thermodynamic temperaturethermodynamic temperature ( (TT), ), pressurepressure ( (PP) and ) and volumevolume ( (VV) of ) of gasesgases

Boyle's LawBoyle's Law

Boyle's lawBoyle's law (sometimes referred to as (sometimes referred to as the the Boyle Mariotte lawBoyle Mariotte law) is one of the ) is one of the gas lawsgas laws. .

It states that “It states that “For a fixed mass of ideal For a fixed mass of ideal gas at fixed gas at fixed temperaturetemperature, the product , the product of of pressurepressure and and volumevolume is a constant”. is a constant”.

The mathematical expression for The mathematical expression for Boyle's law is:Boyle's law is:

where:where: PP is the is the pressurepressure of the gas of the gas VV is is volumevolume of the gas of the gas kk is a constant, and has units of force is a constant, and has units of force

times distance times distance

kPV

Value of Value of kk is computed from measurements of is computed from measurements of volume and pressure for a fixed quantity of gas. volume and pressure for a fixed quantity of gas.

The equation says that, after forcing the volume The equation says that, after forcing the volume VV of the fixed quantity of gas to increase, keeping the of the fixed quantity of gas to increase, keeping the gas at the initially measured temperature, the gas at the initially measured temperature, the pressure pressure PP must decrease proportionally. must decrease proportionally. Conversely, reducing the volume of the gas Conversely, reducing the volume of the gas increases the pressure. increases the pressure.

Boyle's law is commonly used to predict the result Boyle's law is commonly used to predict the result of introducing a change, in volume and pressure of introducing a change, in volume and pressure only, to the initial state of a fixed quantity of gas. only, to the initial state of a fixed quantity of gas. The "before" and "after" volumes and pressures of The "before" and "after" volumes and pressures of the fixed amount of gas, where the "before" and the fixed amount of gas, where the "before" and "after" temperatures are the same (heating or "after" temperatures are the same (heating or cooling will be required to meet this condition), are cooling will be required to meet this condition), are related by the equation:related by the equation: PPafterafter V Vafterafter = P = Pbeforebefore V Vbeforebefore

In practice, this equation is solved for one of the In practice, this equation is solved for one of the two "after" quantities to determine the effect that a two "after" quantities to determine the effect that a change in the other "after" quantity will have. For change in the other "after" quantity will have. For example:example: PPafterafter = P = Pbefore before V Vbeforebefore / V / Vafterafter

Charles's lawCharles's law

Charles's lawCharles's law is one of the is one of the gas lawsgas laws. .

It states that “It states that “At constant pressure, At constant pressure, the volume of a given mass of an ideal the volume of a given mass of an ideal gas increases or decreases by the gas increases or decreases by the same factor as its temperature (in same factor as its temperature (in kelvins) increases or decreases”kelvins) increases or decreases” . .

The mathematical expression for The mathematical expression for Charles's law is:Charles's law is:

where:where: VV is the is the volumevolume of the gas of the gas TT is the is the temperaturetemperature of the gas (measured in of the gas (measured in

kelvinskelvins) ) kk is a constant is a constant

kT

V

To maintain the constant, To maintain the constant, kk, during , during heating of a gas at fixed pressure, the heating of a gas at fixed pressure, the volume must increase. Conversely, volume must increase. Conversely, cooling the gas decreases the volume. cooling the gas decreases the volume. The exact value of the constant need The exact value of the constant need not be known to make use of the law in not be known to make use of the law in comparison between two volumes of comparison between two volumes of gas at equal pressure:gas at equal pressure:

In simpler form, as the temperature In simpler form, as the temperature increases the volume of the gas increases the volume of the gas increases.increases.

Gay-Lussac's lawGay-Lussac's law

Gay-Lussac's law, known as the Gay-Lussac's law, known as the law of law of combining volumescombining volumes..

It states that “ It states that “ At constant volume, the At constant volume, the pressure of a fixed mass of a given gas pressure of a fixed mass of a given gas is directly proportional to the Kelvin is directly proportional to the Kelvin temperature”temperature”. .

The mathematical expression for Gay-The mathematical expression for Gay-Lussac's law is:Lussac's law is:

where:where: PP is the is the pressurepressure of the gas. of the gas. TT is the is the temperaturetemperature of the gas of the gas

(measured in kelvins). (measured in kelvins). kk is a is a constantconstant. .

kT

P

This law holds true because This law holds true because temperature is a measure of the temperature is a measure of the average average kinetic energykinetic energy of a substance; of a substance; as the kinetic energy of a gas as the kinetic energy of a gas increases, its particles collide with the increases, its particles collide with the container walls more rapidly, thereby container walls more rapidly, thereby exerting increased pressure.exerting increased pressure.

For comparing the same substance For comparing the same substance under two different sets of conditions, under two different sets of conditions, the law can be written as:the law can be written as:

Combined gas lawCombined gas law

The The combined gas lawcombined gas law is a is a gas lawgas law which which combines combines Charles's lawCharles's law, , Boyle's lawBoyle's law, and , and Gay-Gay-Lussac'sLussac's law law. In each of these laws, . In each of these laws, pressurepressure, , temperaturetemperature, and , and volumevolume, , respectively, must remain constant for the respectively, must remain constant for the law to be true. In the combined gas law, law to be true. In the combined gas law, any of these properties can be found any of these properties can be found mathematically.mathematically.

The law states that “The law states that “The product of the The product of the volume of a gas and its pressure over the volume of a gas and its pressure over the temperature is equal to a constant”.temperature is equal to a constant”.

The mathematical expression for the combined The mathematical expression for the combined law is:law is:

where:where:pp is the pressure. is the pressure. VV is the volume. is the volume. TT is the temperature (measured in is the temperature (measured in kelvinkelvin in in SISI units). units). kk is a constant is a constant

kT

PV

For comparing the same substance under For comparing the same substance under two different sets of conditions, the law can two different sets of conditions, the law can be written as:be written as:

We can however remove n (number of We can however remove n (number of moles of the gas) from the equation because moles of the gas) from the equation because it is constant when changing only the it is constant when changing only the conditions, to make:conditions, to make:

The addition of The addition of Avogadro's lawAvogadro's law to the to the combined gas law yields the combined gas law yields the ideal gas lawideal gas law..

Ideal Gas LawIdeal Gas LawThe The ideal gas lawideal gas law is the is the equation of stateequation of state of a hypothetical of a hypothetical ideal gasideal gas..

The The statestate of an amount of of an amount of gasgas is determined by its pressure, is determined by its pressure, volume, and temperature according to the equation:volume, and temperature according to the equation:

wherewhere P P is the is the pressurepressure [Pa], [Pa], V is the V is the volumevolume [m [m33], ], n is the n is the amount of substanceamount of substance of gas [mol], of gas [mol], R is the R is the gas constantgas constant 8.3143 m 8.3143 m33·Pa·K·Pa·K-1-1·mol·mol-1-1, and , and T is the T is the temperaturetemperature in in kelvinskelvins [K]. [K].

nRTPV

The The ideal gas constantideal gas constant ( (R)R) is dependent is dependent on what units are used in the formula. on what units are used in the formula. The value given above, 8.314472, is for The value given above, 8.314472, is for the SI units of pascal-cubic meters per the SI units of pascal-cubic meters per mole-Kelvin. Another value for mole-Kelvin. Another value for RR is is 0.082057 L atm per mol -Kelvin0.082057 L atm per mol -Kelvin

The ideal gas law is the most accurate for The ideal gas law is the most accurate for monatomic gases and is favored at high monatomic gases and is favored at high temperatures and low pressures. It does temperatures and low pressures. It does not factor in the size of each gas not factor in the size of each gas molecule or the effects of intermolecular molecule or the effects of intermolecular attraction.attraction.

A sample of chlorine gas weighs 1.31 g A sample of chlorine gas weighs 1.31 g at STP. Calculate the volume this at STP. Calculate the volume this sample of chlorine would occupy sample of chlorine would occupy under the following new conditions:under the following new conditions:

3.20 atm and 0.03.20 atm and 0.0 C C

ExampleExample

SolutionSolution Calculate the moles of ClCalculate the moles of Cl2 2 from 1.31 grams = 0.0184 from 1.31 grams = 0.0184

moles Clmoles Cl22

Check the temperature and convert to Kelvin if Check the temperature and convert to Kelvin if necessary: K = C + 273 = 0.00 + 273 = 273 K necessary: K = C + 273 = 0.00 + 273 = 273 K

Check the pressure given and convert to atmospheres Check the pressure given and convert to atmospheres unit. Pressure is already in atmospheres, 3.20 atm unit. Pressure is already in atmospheres, 3.20 atm

Use the value of R = 0.0821 liter-atm/mole-K Use the value of R = 0.0821 liter-atm/mole-K Using the PV = nRT plug in the moles, temperature, Using the PV = nRT plug in the moles, temperature,

pressure, and R and solve for the Volume in liters V = pressure, and R and solve for the Volume in liters V = nRT / P = (0.0184 moles) ( 0.0821 liter-atm / mol-K) nRT / P = (0.0184 moles) ( 0.0821 liter-atm / mol-K) (273 K) / 3.20 atm = 0.129 liters (273 K) / 3.20 atm = 0.129 liters

You try this:You try this:

A sample of chlorine gas weighs 1.31 g at STP. A sample of chlorine gas weighs 1.31 g at STP. Calculate the volume this sample of chlorine Calculate the volume this sample of chlorine would occupy under the following new would occupy under the following new conditions:conditions:

760 torr and -23.0760 torr and -23.0 C C

SolutionSolutionCalculate the moles of ClCalculate the moles of Cl22 from 1.31 grams = 0.0184 moles Cl from 1.31 grams = 0.0184 moles Cl22

Check the temperature and convert to Kelvin if necessary: K = C Check the temperature and convert to Kelvin if necessary: K = C + 273 = -23.0 + 273 = 250 K + 273 = -23.0 + 273 = 250 K

Check the pressure given and convert to atmospheres Check the pressure given and convert to atmospheres unit .Pressure is in torr units and 1 atm = 760 torr units so 760 unit .Pressure is in torr units and 1 atm = 760 torr units so 760 torr torr 1 atm / 760 torr = 1 atm 1 atm / 760 torr = 1 atm

Use the value of R = 0.0821 liter-atm/mole-K Use the value of R = 0.0821 liter-atm/mole-K

Using the PV = nRT plug in the moles, temperature, pressure, Using the PV = nRT plug in the moles, temperature, pressure, and R and solve for the Volume in liters V = nRT / P = (0.0184 and R and solve for the Volume in liters V = nRT / P = (0.0184 moles) ( 0.0821 liter-atm / mol-K) (250 K) / 1 atm = 0.378 liters moles) ( 0.0821 liter-atm / mol-K) (250 K) / 1 atm = 0.378 liters

Dalton's LawDalton's Law

In In chemistrychemistry and and physicsphysics, Dalton's , Dalton's law (also called Dalton's law of law (also called Dalton's law of partial pressures) states that the partial pressures) states that the total pressure exerted by a total pressure exerted by a gaseous mixture is equal to the gaseous mixture is equal to the sum of the partial pressures of sum of the partial pressures of each individual component in a each individual component in a gas mixture.gas mixture.

Mathematically, the pressure of a Mathematically, the pressure of a mixture of gases can be defined as the mixture of gases can be defined as the summation:summation:

Where PWhere P11, P, P22, and P, and P33 represent the partial represent the partial pressure of each component. It is pressure of each component. It is assumed that the gases do not react with assumed that the gases do not react with each other.each other.

Add partial pressures:Add partial pressures:

P=P=11nn11RT/V RT/V

P= P= 22nn22RT/V RT/V

P = (PP = (P11+ P+ P22 = ((n = ((n11+ n + n 22)()( RT/V)RT/V)

Add moles of each substance:Add moles of each substance:

n = n+ n = n+ 11nn22

P = (nRT/V = ((nP = (nRT/V = ((n11+n+n22)) )RT/V()RT/V(

Henry’s LawHenry’s LawIn chemistry, In chemistry, Henry's lawHenry's law is one of the gas is one of the gas laws. It states that:laws. It states that:““At a constant temperature, the amount of a given At a constant temperature, the amount of a given gas dissolved in a given type and volume of liquid gas dissolved in a given type and volume of liquid is directly proportional to the partial pressure of is directly proportional to the partial pressure of that gas in equilibrium with that liquid”. that gas in equilibrium with that liquid”.

OROR

““The Solubility of a Gas in a Liquid is Directly The Solubility of a Gas in a Liquid is Directly Proportional to the Partial Pressure of the Gas Proportional to the Partial Pressure of the Gas above the Liquid”.above the Liquid”.

The Law can be represented by:The Law can be represented by:

WhereWhere

CCequalequal = concentration of gas dissolved = concentration of gas dissolved in the liquid at equilibriumin the liquid at equilibrium

PPgasgas = partial pressure of the gas above = partial pressure of the gas above the liquidthe liquid

KKHH = Henry’s law constant for the gas = Henry’s law constant for the gas at the given temperatureat the given temperature

gasHequil PKC

Graham’s LawGraham’s Law

The Law states that:The Law states that:

““The rate of diffusion of a The rate of diffusion of a gas is inversely proportional gas is inversely proportional to the square root of its to the square root of its molecular weightmolecular weight””

The Law can be represented by:The Law can be represented by:

WhereWhere

t = time required for diffusiont = time required for diffusion

MW = Molecular WeightMW = Molecular Weight

SoSo

A and B are gas A and gas B, A and B are gas A and gas B, respectivelyrespectively

MWt

B

A

B

A

MW

MW

t

t