Gases

Elements that exist as gases at 250C and 1 atmosphere

5.1

5.1

• Gases assume the _________ and the __________ of their containers.

• Gases are the most ____________ state of matter.

• Gases will mix __________ and completely when confined to the same container.

• Gases have much lower __________ than liquids and solids.

5.1

Physical Characteristics of Gases

Units of Pressure

5.2Barometer

Pressure = ForceArea

(force = mass x acceleration)

Sea level 1 atm

4 miles 0.5 atm

10 miles 0.2 atm

5.2

Boyle’s LawBoyle’s LawP P αα 1/V 1/VThis means Pressure and This means Pressure and

Volume are _________ if Volume are _________ if moles and temperature are moles and temperature are constant (do not change). constant (do not change). For example, P goes up as For example, P goes up as V goes down.V goes down.

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

Charles’s Charles’s LawLaw

If n and P are constant, If n and P are constant, then V then V αα T T

V and T are _____ V and T are _____ proportional.proportional.

• If one temperature goes up, the If one temperature goes up, the volume goes up!volume goes up!

Jacques Charles (1746-Jacques Charles (1746-1823). Isolated boron 1823). Isolated boron and studied gases. and studied gases. Balloonist.Balloonist.

Gay-Lussac’s LawGay-Lussac’s LawIf n and V are If n and V are

constant, constant, then P then P αα T T

P and T P and T are____proportional.are____proportional.

If one temperature goes up, If one temperature goes up,

the pressure goes up!the pressure goes up!

Joseph Louis Gay-Joseph Louis Gay-Lussac (1778-1850)Lussac (1778-1850)

Combined Gas Law• The good news is that you don’t

have to remember all three gas laws! Since they are all related to each other, we can combine them into a single equation. BE SURE YOU KNOW THIS EQUATION!

P1 V1 P2 V2

= T1 T2

No, it’s not related to R2D2

And now, we pause for this commercial message from STP

OK, so it’s really not THIS kind of STP…

STP in chemistry stands for Standard Temperature and

Pressure

Standard Pressure = 1 ___

(or an equivalent)

Standard Temperature = 0 deg C ____ K)

STP allows us to compare amounts of

gases between different pressures and temperatures

Avogadro’s Law

V number of moles (n)

V = constant x n

V1/n1=______

5.3

Constant temperatureConstant pressure

Ideal Gas Equation

5.4

Charles’ law: V T(at constant n and P)

Avogadro’s law: V n(at constant P and T)

Boyle’s law: V (at constant n and T)1P

V nTP

V = constant x = R nTP

nTP

R is the gas constant

PV =______

The conditions 0 0C and 1 atm are called standard temperature and pressure (STP).

PV = nRT

R = PVnT

=))

5.4

Experiments show that at STP, 1 mole of an ideal gas occupies 22.414 L.

Density (d) Calculations

d = mV = PM

RTm is the mass of the gas in gM is the molar mass of the gas

Molar Mass (M ) of a Gaseous Substance

dRTP

M = d is the density of the gas in g/L5.4

Solve for n, which = mass/molar mass

Or,

A 2.10-L vessel contains 4.65 g of a gas at 1.00 atm and 27.00C. What is the molar mass of the gas?

5.3

n =2.10 L X 1 atm

0.0821 x 300.15 KL•atmmol•K

M = 54.6 g/mol

PV = nRT

n = 0.0852 mol

g

Mn =

Gas Stoichiometry

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

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

V = 5.5

Dalton’s Law of Partial Pressures

V and T are

constant

P1 P2 Ptotal = ______

5.6

Consider a case in which two gases, A and B, are in a container of volume V.

PA = nARTV

PB = nBRTV

nA is the number of moles of A

nB is the number of moles of B

5.6

A sample of natural gas contains 8.24 moles of CH4, 0.421 moles of C2H6, and 0.116 moles of C3H8. If the total pressure of the gases is 1.37 atm, what is the partial pressure of propane (C3H8)?

5.6

Chemistry in Action:Scuba Diving and the Gas Laws

P V

Depth (ft) Pressure (atm)

0 1

33 2

66 3

5.6

Kinetic Molecular Theory of Gases

1. The molecules can be considered to be points; that is, they possess mass but have negligible ________.

2. Collisions among molecules are perfectly _________.

3. Gas molecules exert neither ________ forces on one another.

4. The average kinetic energy of the molecules is proportional to the temperature of the gas in ____. Any two gases at the same temperature will have the same average kinetic energy

5.7

Kinetic theory of gases and …

• Compressibility of Gases

• Boyle’s LawP collision rate with wallCollision rate number densityNumber density 1/VP 1/V

• Charles’ LawP collision rate with wallCollision rate average kinetic energy of gas moleculesAverage kinetic energy TP T

5.7

Kinetic theory of gases and …

• Avogadro’s LawP collision rate with wallCollision rate number densityNumber density nP n

• Dalton’s Law of Partial PressuresMolecules do not attract or repel one anotherP exerted by one type of molecule is unaffected by the

presence of another gasPtotal = Pi

5.7

Deviations from Ideal Behavior

1 mole of ideal gas

PV = nRT

n = PVRT = 1.0

5.8

Repulsive Forces

Attractive Forces

Effect of intermolecular forces on the pressure exerted by a gas.

5.8

5.8

Van der Waals equationnonideal gas

P + (V – nb) = nRTan2

V2( )}

correctedpressure

}

correctedvolume

The distribution of speedsfor nitrogen gas molecules

at three different temperatures

The distribution of speedsof three different gases

at the same temperature

5.7

Velocity of a Gas

_________________is the gradual mixing of molecules of one gas with molecules of another by virtue of their kinetic properties.

5.7

NH3

17 g/molHCl

36 g/mol

NH4Cl

Gas DiffusionGas Diffusionrelation of mass to rate of diffusionrelation of mass to rate of diffusion

• HCl and NH3 diffuse from opposite ends of tube.

• Gases meet to form ?• ? heavier than ?• Therefore, NH4Cl

forms closer to HCl end of tube.

GAS DIFFUSION AND GAS DIFFUSION AND EFFUSIONEFFUSION

• ____________ is the gradual is the gradual mixing of molecules mixing of molecules of different gases.of different gases.

• ____________ is the movement is the movement of molecules through a of molecules through a small hole into an empty small hole into an empty container.container.

GAS DIFFUSION AND GAS DIFFUSION AND EFFUSIONEFFUSION

Graham’s law governs Graham’s law governs effusion and diffusion of effusion and diffusion of gas molecules. gas molecules. KE=1/2 mv2

Thomas Graham, 1805-1869. Thomas Graham, 1805-1869. Professor in Glasgow and London.Professor in Glasgow and London.

Rate of effusion is Rate of effusion is ________ proportional ________ proportional to ________________to ________________

GAS DIFFUSION AND GAS DIFFUSION AND EFFUSIONEFFUSION

Molecules effuse thru holes in a rubber Molecules effuse thru holes in a rubber balloon, for example, at a rate (= balloon, for example, at a rate (= moles/time) that ismoles/time) that is

• proportional to Tproportional to T• inversely proportional to M.inversely proportional to M.Therefore, ____ effuses more rapidly Therefore, ____ effuses more rapidly

than ______ at same T.than ______ at same T.

HeHe

Graham’s Law Problem 1

1 mole of oxygen gas and 2 moles of ammonia are placed in a container and allowed to react at 850 degrees celsius according to the equation:

4 NH3(g) + 5 O2(g) --> 4 NO(g) + 6 H2O(g)

Using Graham's Law, what is the ratio of the effusion rates of NH3(g) to O2(g)?

Graham’s Law Problem 2

What is the rate of effusion for H2 if 15.00 ml of CO2 takes 4.55 sec to effuse out of a container?

Graham’s Law Problem 3

What is the molar mass of gas X if it effuses 0.876 times as rapidly as N2(g)?