Gas Laws

Elements that exist as gases at 250C and 1 atmosphere

5.1

5.1

• Gases assume the volume and shape of their containers.

• Gases are the most compressible state of matter.

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

• Gases have much lower densities than liquids and solids.

5.1

Physical Characteristics of Gases

Units of Pressure

1 pascal (Pa) = 1 N/m2

1 atm = 760 mm Hg = 760 torr

= 101,325 Pa = 14.7 psi = 29.92 in. Hg

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 INVERSELY Volume are INVERSELY PROPORTIONAL if moles PROPORTIONAL if moles and temperature are 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.

PP11VV11 = P = P22 V V22

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 TV and T are directly V and T are directly

proportional.proportional.VV11 V V22

==

TT11 T T22

• 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 are directly P and T are directly proportional.proportional.

PP11 P P22

==

TT11 T T22

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 atm

(or an equivalent)

Standard Temperature = 0 deg C (273 K)

STP allows us to compare amounts of

gases between different pressures and temperatures

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 = V2/n2

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 nT

P

V = constant x = RnT

P

nT

PR is the gas constant

PV = nRT

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

PV = nRT

R = PVnT

=(1 atm)(22.414L)

(1 mol)(273.15 K)

R = 0.082057 L • atm / (mol • K)

5.4

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

Density (d) Calculations

d = mV =

PMRT

m is the mass of the gas in g

M 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)

g C6H12O6 mol C6H12O6 mol CO2 V CO2

5.60 g C6H12O6

1 mol C6H12O6

180 g C6H12O6

x6 mol CO2

1 mol C6H12O6

x = 0.187 mol CO2

V = nRT

P

0.187 mol x 0.0821 x 310.15 KL•atmmol•K

1.00 atm= = 4.76 L

5.5

Dalton’s Law of Partial Pressures

V and T are

constant

P1 P2 Ptotal = P1 + P2

5.6

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

PA = nART

V

PB = nBRT

V

nA is the number of moles of A

nB is the number of moles of B

PT = PA + PB XA = nA

nA + nB

XB = nB

nA + nB

PA = XA PT PB = XB PT

Pi = Xi PT

5.6

mole fraction (Xi) = ni

nT

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)?

Pi = Xi PT

Xpropane = 0.116

8.24 + 0.421 + 0.116

PT = 1.37 atm

= 0.0132

Ppropane = 0.0132 x 1.37 atm = 0.0181 atm

5.6

2KClO3 (s) 2KCl (s) + 3O2 (g)

Bottle full of oxygen gas and water vapor

PT = PO + PH O2 2 5.6

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. A gas is composed of molecules that are separated from each other by distances far greater than their own dimensions. The molecules can be considered to be points; that is, they possess mass but have negligible volume.

2. Gas molecules are in constant motion in random directions. Collisions among molecules are perfectly elastic.

3. Gas molecules exert neither attractive nor repulsive forces on one another.

4. The average kinetic energy of the molecules is proportional to the temperature of the gas in kelvins. 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 Law

P collision rate with wall

Collision rate number densityNumber density 1/VP 1/V

• Charles’ LawP collision rate with wall

Collision rate average kinetic energy of gas molecules

Average kinetic energy T

P T

5.7

Kinetic theory of gases and …

• Avogadro’s Law

P collision rate with wall

Collision rate number densityNumber density nP n

• Dalton’s Law of Partial Pressures

Molecules do not attract or repel one another

P exerted by one type of molecule is unaffected by the presence of another gas

Ptotal = 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

urms = 3RTM

Velocity of a Gas

Gas diffusion 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 DIFFUSION AND GAS DIFFUSION AND EFFUSIONEFFUSION

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

• effusioneffusion is the is the movement of molecules movement of molecules through a small hole through a small hole into an empty container.into an empty 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 inversely proportional inversely proportional to its molar mass.to its molar mass.

Rate of effusion is Rate of effusion is inversely proportional inversely proportional to its molar mass.to its molar mass.

M of AM of B

Rate for B

Rate for A

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, He effuses more rapidly Therefore, He effuses more rapidly than Othan O22 at same T. at same T.

HeHe

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

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 NH4Cl

• HCl heavier than NH3

• Therefore, NH4Cl forms closer to HCl end of tube.

• HCl and NH3 diffuse from opposite ends of tube.

• Gases meet to form NH4Cl

• HCl heavier than NH3

• Therefore, NH4Cl forms closer to HCl end of tube.

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)?