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Gases, Liquids & Solids
Gases, Liquids & Solids
General Properties
• Gases • Have an indefinite volume
Expand to fill a container• Have an indefinite shape
Take the shape of a container• Have low densities
• Have high kinetic energies
2
air
H O
d 1.2 g / L at 25 C
d 1.0 g / mL
Going Nowhere Fast
• Molecules move quickly, but take a long time to get anywhere because of collisions with each other.
• Without collisions, a molecule would cross a room in a fraction of a second.
• Collisions can make the journey last several minutes.
What is Gas Pressure?
What is Pressure
ForcePressure =
Area
Pressure depends on the•Number of gas molecules•Temperature of the gas•Volume the gas occupies
SI unit for force is N = Newton = kg-m/s2
SI unit for pressure is P = Pascal = kg/s2 - m
What is Pressure?
ForcePressure =
AreaThe force divided by the area over which it is distributed
Pressure Conversions
Convert 675 mm Hg to atm. Note: 760 mm Hg = 1 atm
Convert 675 mm Hg to torr. Note: 760 mm Hg = 760 torr.
Atmospheric Pressure
• Atmospheric pressure is due to the mass of the atmospheric gases pressing down on the earth’s surface.
• Gravity makes the air density higher near the earth’s surface.
• Pressure decreases with elevation – air density decreases.
Mass of column of air extending intoupper atmosphere ~ 10,000 kg.
Force exerted = ma = mg = 10,000 kg*9.8 m/s2 = 1*105 kg-m/s2 = 1*105 N
Pressure = 1*105 kg-m/s2 / 1 m2 = 1*105 kg/s2 -m = 1*105 Pa
Measuring Pressure
Because it is difficult to measurethe total force exerted by gasmolecules, the pressure of a gas is usually measured indirectlyby comparing it with a liquid pressure.
Liquid pressure is directly proportionalto the liquid density and the height of the liquid column.
Open end manometer
Mathematical Description of a Gas
• We need four variables to define the “physical” state of a gas.– Temperature– Pressure– Volume– Amount of gas, n = mols
• Equations that express the relationships between these variables are known as the gas laws.
Dependence of Pressure on Number of MoleculesVolume & Temperature Constant
P is proportional to n (number of molecules) at Tc (constant T) and Vc (constant V).The increased pressure is due to more frequent collisions with walls of the container.
Volume is 22.4 Liters in each case shown
Dependence of Pressure on TemperatureVolume and Moles Constant
P is proportional to T at nc
(constant number of moles) and Vc.
The increased pressure is due to• more frequent collisions•higher energy collisions
Dependence of Pressure on VolumeTemperature & Moles Constant
P is inversely proportional to V at nc (constant number of moles) and Tc.
The increased pressure is due to• more frequent collisions
Some Gas Laws
• Boyle’s Law • Charles’s Law• Avogadro’s Law• The Ideal Gas Equation
Boyle’s Law (T & n constant)
What happens to V if you double P?•V decreases by half!
What happens to P if you double V?•P decreases by half!
•Mathematically we say P variesinversely with V (or V varies inverselywith P)
• Mathematically we write P α 1/V
• Mathematically P = constant * 1/V or V * P = constant.
• For two sets of conditions we may write V1* P1 = V2 * P2
Boyle’s Law – the volume of a fixed quantity of gas maintained at constant T is inversely proportional to the pressure.
Boyle’s Law (T & n constant)
A plot of P versus 1/V yields a straight line
Y = mx where m = slope = constant.
Boyle’s Law
• A sample of argon gas occupies 500.0 mL at 920. torr. Calculate the pressure of the gas if the volume is increased to 937 mL at constant temperature and constant # of mols.
1 12
2
PV
PV
1 1 2 2 PV PV
2
920. torr 500. mL = = 491 torr
937 mLP
Calculate
Set-Up
Charles’ Law – P and moles constant
• The volume of an ideal gas at absolute zero (-273°C) is zero.
• Real gases condense at their boiling point so it is not possible to have a gas with zero volume.
• The gas laws are based on Kelvin temperature.
• All gas law problems must be worked in Kelvin!
The volume of a fixed amount of gas at a constant pressure is directly proportional to its absolute temperature.
Mathematically we may write V α T and we say V varies directly with T
Mathematically we may write V = constant * T or V/T = constant
For two sets of conditions we have V1/T1 = V2 /T2
Charles’ Law
• A 2.0 L He balloon at 25°C is taken outside on a cold winter day at -15°C. What is the volume of the balloon if the pressure remains constant?
1 2
1 2
V V
T T
1 22
1
rearranged gives VT
VT
2
(2.0 L)(258 K) = = 1.7 L
298 KVCalculate
Set-Up 1 2
1 2
V V
T T
Avogadro’s Law - V α n
Avogadro’s Law
Avogadro’s Law
Example #: A cylinder with a movable piston contains 2.00 g of helium, He, at room temperature. More helium was added to the cylinder and the volume was adjusted so that the gas pressure remained the same. How many grams of helium were added to the cylinder if the volume was changed from 2.00 L to 2.70 L? (The temperature was held constant.)
For a given mass of an ideal gas, the volume and amount (moles) of the gas are directly proportional if the temperature and pressure are constant.
Mathematically V α n or V = constant * n or V/n = constant
For two different sets of conditions we have:
Combined Gas Laws
= constant
= constantFor a fixed # of molsof gas
Combined Gas Law
• A sample of oxygen gas occupies 500.0 mL at 722 torr and –25°C. Calculate the temperature in °C if the gas has a volume of 2.53 L at 491 mmHg.
1 2 22
1 1
T PVT
PV
1 1 2 2
1 2
PV PV
T T
2
491 torr 2530 ml 248K= =853K 580 C
722 torr 500.0 mlT
Set-Up
Calculate
Practice Problems
The Ideal Gas Equation
= constant
P V ∙ = constant = Rn T∙
P V = n R T∙ ∙ ∙
PV =nRT
Ideal Gas Law
Always Kelvin!
Units for gas constant, R = Liter atm/mol K∙ ∙
R= 0.08206 L atm/mol K∙ ∙
Remember moles = n = grams/ molar mass = g/M
Another useful form of the ideal gas law: PV = gRT M
Copyright © 2011 Pearson Canada Inc. Slide 30 of 41General Chemistry: Chapter 6
Using the Gas Laws
Applying the ideal gas equation
Copyright © 2011 Pearson Canada Inc. Slide 31 of 41General Chemistry: Chapter 6
Useful Forms of the Ideal Gas Law
Remember moles = n = grams/ molar mass = g/M
Substituting g/M yields another useful form of the ideal gas law:
1) PV = gRT MAlso, we may rearrange the ideal gas law as follows: n = P
V RT
Multiplying both sides of the equation by Molar Mass, M yields:
n M = P M where n/V * M = density, d in g/L yielding: V RT
2) d = density = PM RT
Ideal Gas Law
• How many moles of Ar are contained in 1.3L at 24°C and 745 mm Hg?
Knowns V = 1.3 L T = 24°C = 297 K P = 745 mm Hg = 0.980 atm
Set-Up
Calculate
PV
nRT
(0.980 atm)(1.3 L) = =0.052 mol
L atm(0.0821 )(297 K)
mol K
n
PV nRT R
L atm where = 0.0821
mol K
Ideal Gas Law
• Calculate the molar mass (M) of an unknown gas, if 4.12 g occupy a volume of 943mL at 23°C and 751 torr.
Set-Up
Calculate
g g = so =
M Mn PV RT
L atm(4.12 g)(0.0821 )(296 K)
mol KM = =107 g/mol(0.988 atm)(0.943 L)
R T
P V
g M =
Practice Problems
Guy-Lussac and the Law of Combining Volumes
• Guy-Lussac carried out experiments on the properties of gases.• He observed that at a given T and P, the volumes of gases that
react with one another are in the ratios of small whole numbers.
This led to Avogadro’s hypothesis: equal volumes of gases at the same T & P, containequal numbers of molecules.
Volumes of Gases in Chemical RX’s – Guy Lussac’s Law
The ratio of the volumes of gases (at constant T & P) consumed or produced in a chemical reaction is equal to the ratio of simple whole numbers (coefficients in the balanced equation).
This is the molar volume – the volume that 1 mole of gas occupies at STP
Molar Volume at Standard Temperature and Pressure
Standard Temperature and Pressure, STP = 1 atm and 0°C or 273.15K
Gas Stoichiometry
Gas Stoichiometry
Dalton’s Law of Partial Pressures
• The total pressure of a mixture of gases equals the sum of the pressures that each would exert if it were present alone.
• In other words,
Ptotal = P1 + P2 + P3 + …
Dalton’s Law of Partial Pressures
T & V constant
Dalton’s Law of Partial Pressures
Collecting a gas over waterFigure 6-13
Ptot = Pbar = Pgas + PH2O
Partial PressurePtot = P1 + P2 +…
P1 = n1(RT/V) P2= n2(RT/V) P3 = n3(RT/V)……etc.
P1
Ptot
n1RT/VntotRT/V= =
n1
ntot
P1 =n1
ntot
Pt = (n1 + n2 + n3 +……..) RT/V = nt (RT/V)
= X1= mole fraction of gas 1
dimensionless
∙ Ptot = X1 ∙ Ptot
Practice Problems
Practice Problems
Practice Problems
Kinetic-Molecular Theory
This is a model that aids in our understanding of what happens to gas particles as environmental conditions change.
Main Tenets of Kinetic-Molecular Theory
Gases consist of large numbers of molecules that are in continuous, random motion.
The combined volume of all the molecules of the gas is negligible relative to the total volume in which the gas is contained.
The average kinetic energy of a particle is proportional to the temperature in kelvins.
The collision of one particle with another is completely elastic. When two particles collide they may exchange energy but there is no overall loss of energy.
Main Tenets of Kinetic-Molecular Theory
Attractive and repulsive forces between gas molecules are negligible.
Main Tenets of Kinetic-Molecular Theory
Energy can be transferred between molecules during collisions, but the average kinetic energy of the molecules does not change with time, as long as the temperature of the gas remains constant.
u = root-mean-square speed (rms) which is the speed of a molecule possessingaverage kinetic energy.
Molar Mass
Main Tenets of Kinetic-Molecular Theory
The average kinetic energy of the molecules is proportional to the absolute temperature.
Main Tenets of Kinetic-Molecular Theory
Practice Problems
Practice Problems
Practice Problem
For this type of problem use R = 8.314 J/mol-K and convert molar mass to kg/mol
Effusion
Effusion is the escape of gas molecules through a tiny hole into an evacuated space.
Effusion
The difference in the rates of effusion for helium and nitrogen, for example, explains a helium balloon would deflate faster.
Graham’s Law of Effusion
The rate of effusion of a gas is inversely proportional to the square root of the mass of its particles.
Molar mass
Stated another way, the relative rates of effusion of two gases at the same temperature and pressure are given by the inverse ratio of the square roots of the masses of the gas particles
Graham’s Law of Effusion
• Only for gases at low pressure (natural escape, not a jet).• Tiny orifice (no collisions)• Does not apply to diffusion.
Ratio used can be:· Rate of effusion (as above)· Molecular speeds· Effusion times
· Distances traveled by molecules· Amounts of gas effused.
Practice Problem
Calculate the ratio of the effusion rates of H2 and uranium hexafluoride, UF6, a gas used in the enrichment processto produce fuels for nuclear reactors.
Freon-12 is used as a refrigerant in central home air conditioners.The rate of effusion of Freon-12 to Freon-11 (molar mass = 137.4 g/mol)is 1.07:1. The formula of Freon is one of the following: CF4, CF3Cl,CF2Cl2, CFCl3, or CCl4. Which formula is correct for Freon-12?
Diffusion
Diffusion is the spread of one substance throughout a space or throughout a second substance.
Effusion & Diffusion
Diffusion - The spread of particles through random motion from regions of higher concentration to regions of lower concentration.
Effusion - The process in which individual molecules flow, through a hole without collisions between molecules, into a vacuum.
Diffusion
• diffusion of a gas – YouTube• Gaseous Diffusion Demonstration
, Jesse Miller, Chemist Corner, 9/3/2008 - YouTube
• Diffusion of Bromine vapor - YouTube
Practice Problem
HW Problem - 10.98
HW Problem - 10.34
Kinetic Molecular Theory (KMT)Assumptions of the KMT and ideal gases include:1. Gas molecules have tiny volumes compared with the collective
volume they occupy. Their individual volumes are so small as to be considered negligible, allowing particles in a gas to be treated as point masses; masses with essentially no volume.
2. Gases are separated by large distances, hence a gas is mostly empty space.
3. Gas molecules move constantly and randomly throughout the volume they collectively occupy.
4. The motion of these gas particles is associated with an average kinetic energy that is proportional to the absolute temperature of the gas. All populations of gas molecules at the same temperature have the same average kinetic energy. K.E. α TThese gases are at the
same T and have the same kinetic energy
Kinetic Molecular Theory
Assumptions of the KMT (continued):5. Gas molecules continually collide with one another and with their
container walls. These collisions are elastic; that is, they result in no net transfer of energy to the walls. Therefore, the average kinetic energy of gas particles is not affected by these collisions and remains constant as long as there is no change in temperature.
6. Each gas molecule acts independently of all other molecules in a sample. We assume there are no forces of attraction or repulsion between the molecules.
