Gases
Mar 19, 2016
Gases
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
Sea level 1 atm
4 miles 0.5 atm
10 miles 0.2 atm
5.2
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)
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 T
V 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 constant, If n and V are constant,
then P then P αα T TP and T are directly P and T are directly
proportional.proportional.PP11 P P22
==
TT11 T T22 If one temperature goes up, the If one temperature goes up, the
pressure goes up!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
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 nTP
V = constant x = R nTP
nTP
R 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 = PM
RTm is the mass of the gas in gM is the molar mass of the gas
Molar Mass (M ) of a Gaseous Substance
dRTPM = d is the density of the gas in g/L
5.4
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
dRTPM = d = m
V4.65 g2.10 L
= = 2.21 gL
M =2.21 g
L
1 atm
x 0.0821 x 300.15 KL•atmmol•K
M = 54.6 g/mol
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 = nARTV
PB = nBRTV
nA is the number of moles of A
nB is the number of moles of B
PT = PA + PB XA = nA
nA + nBXB =
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 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
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 of mixing of molecules of different gases.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.
M of AM of B
Rate for BRate 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 than Therefore, He effuses more rapidly than
OO22 at same T. at same T.
HeHe
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.
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)?