Gas Laws Lec

GASES

The Nature of GasesGas particles can be monatomic (Ne), diatomic (N2), or polyatomic (CH4) – but they all have these characteristics in common: 1) Gases have mass.

2) Gases are compressible. 3) Gases fill their containers. 4) Gases diffuse 5) Gases exert pressure. 6) Pressure is dependent on

Temp.

Kinetic Molecular Theory

The theory states that the tiny particles in all forms of matter in all forms of matter are in constant motion.This theory is used to explain the behaviors common among gasesThere are 3 basic assumptions of the KMT as it applies to gases.

KMT Assumption #1A gas is composed of small hard particles.The particles have an insignificant volume and are relatively far apart from one another. There is empty space between particles.No attractive or repulsive forces between particles.

KMT Assumption #2The particles in a gas move in constant random motion.Particles move in straight paths and are completely independent of each of otherParticles path is only changed by colliding with another particle or the sides of its container.

KMT Assumption #3All collisions a gas particle undergoes are perfectly elastic.No energy is lost from one particle to another, and the total kinetic energy remains constant.

Gas variablesIn order to describe a gas sample completely and then make predictions about its behavior under changed conditions, it is important to deal with the values of: 1) amount of gas

2) volume 3) temperature 4) pressure

Amount (n)

The quantity of gas in a given sample expressed in terms of moles of gas.This of course is in terms of 6.02 x 1023 molecules of the gas. Don’t forget to convert mass to moles you just divide by the molar mass of the gas.

Volume (V)

The volume of the gas is simply the volume of the container it is contained in.The metric unit of volume is the liter (L)There might also be problems that use cubic meters as the unit for volume.- 1 L = 1 dm3

Temperature (T)

the average kinetic energy of the particles that make up an object All calculations involving gases should be made after converting the Celsius to Kelvin temperature.Kelvin = C° +

273

Pressure (Pressure (PP))The pressure of a gas is the force exerted on the wall of the container a gas is trapped in.There are several units for pressure depending on the instrument used to measure it including: 1) atmospheres

(atm) 2) Millimeters of Mercury (mmHg) 3) torr

S T PS T PThe behavior of a gas depends very strongly on the temperature and the pressure at which the gas is held.To make it easier to discuss the behavior of a gas, it is convenient to designate standard conditions, called STP. - Temperature = 0°C or 273K

- Pressure = 1atm or 760mmHg or 101.3kPa

Gas LawsGas LawsStudies of the behavior of gases played a major role in the development of physical sciences in the 7th and 8th centuries.The Kinetic Molecular theory marked a significant achievement in understanding the behavior of gases.Observations have become mathematical laws which we can use to predict quantitative outcomes.

Boyle’s Law

At constant temperature, the volume of a given quantity of gas is inversely proportional to its pressure : V a 1/P

Robert Boyle Robert Boyle (1627-1691). (1627-1691). Son of Earl of Son of Earl of Cork, Ireland.Cork, Ireland.

As the pressure increases

Volumedecreases

How does Pressure and Volume of gases relate

graphically?Vo

lum

e Vo

lum

e

PressurePressure

PV = kPV = kTemperature, # of particlesremain constant

Boyle’s Mathematical Law:

since PV = kP1V1 = P2V2

What if we had a change in conditions?

Boyle’s Law:Examples:

An inflated balloon has a volume of 0.55 L at sea level (1.0 atm) and is allowed to rise to a height of 6.5 km, where the pressure is about 0.40 atm. Assuming that the temperature remains constant, what is the final volume of the balloon?

A sample of chlorine gas occupies a volume of 946 mL at a pressure of 726 mmHg. Calculate the pressure of the gas (in mmHg) if the volume is reduced at constant temperature to 154 mL.

Charles’ Law

At constant pressure, the volume of a given quantity of gas is directly proportional to the absolute temperature :

V T (in Kelvin)Jacques Charles (1746-Jacques Charles (1746-1823). Isolated boron 1823). Isolated boron and studied gases. and studied gases. Balloonist.Balloonist.

Volume of balloon at

room temperature

Volume of balloon at 5°C

Temp

How does Temperature and Volume of gases relate

graphically?Vo

lum

e

V/T = kPressure, # of particlesremain constant

Charles’ Mathematical Law:

since V/T = k

V1 V2

T1 T2=

What if we had a change in conditions?

Charles’ Law:Examples:A 452-mL sample of fluorine gas is heated from 22C to 187C at constant pressure. What is its final volume?

A sample of carbon monoxide gas occupies 3.20 L at 125C. Calculate the temperature at which the gas will occupy 1.54 L if the pressure remains constant.

Gay Lussac’s LawOld man Lussac determined the relationship between temperature and pressure of a gas.He measured the temperature of air at different pressures, and observed a pattern of behavior which led to his mathematical law.During his experiments volume of the system and amount of gas were held constant.

Pressure Gauge

Car before a trip

Think of a tire...

Let’s get onthe road

Dude!

Car after a long tripCar after a long trip

Think of a tire...

WHEW!

Pressure Gauge

Temp

Pres

sure

How does Pressure and Temperature of gases relate

graphically?

P/T = kVolume, # of particlesremain constant

Lussac’s Mathematical Law:What if we had a change in conditions?

since P/T = k

P1 P2

T1 T2=

Eg: A gas has a pressure of 3.0 atm at 127º C. What is its pressure at 227º C?

Combined Gas Law:

P1V1 P2V2 T1 T2

=

Combined Gas Law:Examples:

A small bubble rises from the bottom of a lake, where the temperature and pressure are 80C and 6.4 atm, to the water’s surface, where the temperature is 250C and pressure is 1.0 atm. Calculate the final volume (in mL) of the bubble if its initial volume was 2.1 mL.A gas initially at 4.0 L, 1.2 atm, and 660C undergoes a change so that its final volume and temperature become 1.7 L and 420C. What is its final pressure? Assume the number of moles remains unchanged.

Ideal Gas Law:

P V = n R TP V = n R TP = PressureP = PressureV = VolumeV = VolumeT = TemperatureT = Temperaturen = number of molesn = number of molesR is a constant, called the R is a constant, called the Ideal Gas Ideal Gas

ConstantConstant

R = 0.08205 L atm / mol KR = 0.08205 L atm / mol K

Ideal Gas Law:Examples:

Sulfur hexafluoride (SF6) is a colorless, odorless, very unreactive gas. Calculate the pressure (in atm) exerted by 1.82 moles of the gas in a steel vessel of volume 5.43 L at 69.50C.

Calculate the volume (in liters) occupied by 2.12 moles of nitric oxide (NO) at 6.54 atm and 760C.

Ideal Gas Law and Density of a GAs:

Examples:

Calculate the density of ammonia (NH3) in grams per liter (g/L) at 752 mmHg and 550C.

What is the density (in g/L) of uranium hexafluoride (UF6) at 779 mmHg and 620C?

Ideal Gas Law and Molar Mass of a GAs:

Examples:A chemist has synthesized a greenish-yellow gaseous compound of chlorine and oxygen and finds that its density is 7.71 g/L at 360C and 2.88 atm. Calculate the molar mass of the compound and determine its molecular formula.

Chemical analysis of a gaseous compound showed that it contained 33.0 percent silicon and 67.0 percent fluorine by mass. At 350C, 0.210 L of the compound exerted a pressure of 1.70 atm. If the mass of 0.210 L of the compound was 2.38 g, calculate the molecular formula of the compound.

Avogadro’s Law:Equal volumes of gases at the Equal volumes of gases at the

same T and P have the same T and P have the same number of same number of molecules.molecules.

V = n (RT/P) = knV = n (RT/P) = knV and n are directly related.V and n are directly related.

twice as many twice as many moleculesmolecules

Avogadro’s Law and Gas Stoichiometry

1 Mole of an ideal gas = 22.4 L 1 Mole of an ideal gas = 22.4 L at STPat STPCalculate the volume of O2 (in liters) at STP

required for the complete combustion of 2.64 L of acetylene (C2H2) at STP:

2C2H2(g) + 5O2(g) 4CO2(g) + 2H2O(l)

Calculate the volume of O2 (in liters) at STP required for the complete combustion of 14.9 L of butane (C4H10) at STP:

2C4H10(g) + 13O2(g) 8CO2(g) + 10H2O(l)


Sodium azide (NaN3) is used in some automobile air bags. The impact of a collision triggers the decomposition of NaN3 as follows:

2NaN3(s) 2Na(s) + 3N2(g)The nitrogen gas produced quickly inflates the bag between the driver and the windshield. Calculate the volume of N2 generated at 210C and 823 mmHg by the decomposition of 60.0 g of NaN3.


The equation for the metabolic breakdown of glucose (C6H12O6) is the same as the equation for the combustion of glucose in air:

C6H12O6(s) + 6O2(g) 6CO2(g) + 6H2O(l)

Calculate the volume of CO2 produced at 370C and 1.00 atm when 5.60 g of glucose are used up in the reaction.

Dalton’s Law of Partial Pressures

What is the total pressure in the What is the total pressure in the flask?flask?

PPtotaltotal in gas mixture = P in gas mixture = PAA + P + PBB + ...+ ...

Therefore, Therefore, PPtotaltotal = P = PHH22OO + P + POO22 = 0.48 atm = 0.48 atm

Dalton’s Law: total P is sum Dalton’s Law: total P is sum ofof PARTIALPARTIAL pressures.pressures.

2 H2 H22OO2 2 (l) ---> 2 H(l) ---> 2 H22O (g) + OO (g) + O2 2 (g)(g)

0.32 atm 0.32 atm 0.16 0.16 atmatm

Deviation from Ideal Behavior

Plot of PV/RT versus P of 1 mole of a gas at 0C. For 1 mole of an ideal gas,PV/RT is equal to 1, no matter what the pressure of the gas is.For real gases, we observe various deviations from ideality at high pressures. At very low pressures, all gases exhibit ideal behavior; that is, their PV/RT values all converge to 1 as P approaches zero.


Real molecules have volume

The ideal gas consumes the entire amount of available volume. It does not account for the volume of the molecules themselves.


There are intermolecular forces.

An ideal gas assumes there are no attractions between molecules. Attractions slow down the molecules and reduce the amount of collisions.

Otherwise a gas could not condense to become a liquid.

Effect of intermolecularforces on the pressureexerted by a gas.

Van der Waals Equation for Real Gases

Gas Laws Lec

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