Chap 12.2
Stoichiometric mole-to-mole conversion.
How can you determine the number of moles of hydrogen produced when 0.0400 mole of
potassium is used?
Start by writing the balanced chemical equation
2K(s) + 2H2O(l) → 2KOH(aq) + H2(g)
The given substance is 0.0400 mol K the unknown is the number of moles of H.
The mole ratio of K to H is
Remember that when you use a conversion factor, the units must cancel.
If you put 0.0400 mol K into water, 0.0200 mol H2 will be produced.
Now suppose you know the number of moles of a reactant or product in a reaction and you
want to calculate the mass of another product or reactant.
Determine the mass of sodium chloride or table salt (NaCl) produced when 1.25 moles of
chlorine gas reacts vigorously with sodium.
Write the balanced equation
2Na(s) + Cl2(g) → 2NaCl(s)
Write the mole ratio that relates mol NaCl to mol Cl2
Multiply the number of moles of Cl2 by the mole ratio.
Multiply mol NaCl by the molar mass of NaCl (58.44g).
If you were preparing to carry out a chemical reaction in the laboratory, you would need to
know how much of each reactant to use in order to produce that mass of product you required.
Ammonium nitrate (NH4NO3), an important fertilizer, produces N2O gas and H2O when it
decomposes. Determine the mass of water produced from the decomposition of 25.0g of solid
ammonium nitrite.
Step one: Write the balanced equation for the reaction and identify the known and unknown
substances.
Step two: Convert grams of NH4NO3 to moles of NH4NO3
Step three: Determine from the equation the mole ratio of H2O to mol NH4NO3. The unknown
is the numerator.
Step four: Multiply mol NH4NO3 by the mole ratio.
Step five: Calculate the mass on H2O using the molar mass 18.02g as the conversion factor.
Chap 12.3
Limiting Reactants
Recall the steps in stoichiometric Calculations
1. Write a balanced chemical equation. Interpret the equation in terms of moles.
2. Determine the moles of the given substance using a mass-to-mole conversion. Use the
inverse of the molar mass as the conversion factor.
3. Determine the moles of the unknown substance from the moles of the given substance. Use
the appropriate mole ratio from the balanced chemical equation as the conversion factor.
4. From the moles of the unknown substance, determine the mass of the unknown substance
using a mole-to-mass conversion. Use the molar mass as the conversion factor.
Why do reactions stop?
Rarely in nature are reactants in a chemical reaction present in the exact ration specified by the
balanced equation.
Generally, one or more reactants are in excess, while one is limited.
As the name implies, the limiting reactant limits the extent of the reaction and, thereby,
determines the amount of product.
leftover reactants are called excess reactants.
Calculating the Product When a Reactant is Limited
Consider the formation of disulfur dichloride a chemical used to vulcanize rubber.
S8(l) + 4Cl2(g) → 4S2Cl2(l)
If 200.0g of sulfur reacts with 100.0g chlorine, what mass of disulfur dichloride is produced?
Next determine whether the two reactants are n the correct mole ration as given in the
balanced chemical equation.
Only 1.808 mol of chlorine is actually available for every 1 mol of sulfur in stead of the 4 mol of
chlorine required by the balanced chemical equation. Therefore, chlorine is the limiting
reactant.
Then, moles of S2Cl2 is converted to grams of S2Cl2 by multiplying by the conversion factor that
relates mass and moles, molar mass.
Both these equations can be combined thus.
Now you know that 190.0g S2Cl2 is produced when 1.410 mol Cl2 reacts with an excess of S8.
Determine the limiting reactant
The reaction between solid white phosphorus and oxygen prodeces solid tetraphosphorus
decoxide (P4O10). This compound is often called diphosphorus pentoxide because its empirical
formula is P2O5.
a. Determine the mass of tetraphosphorus decoxide formed if 25.0g of phosphorus (P4) and
50.0g of oxygen (O2) are combined.
b. How much of the excess reactant remains after the reaction stops?
Percent Yield
How Much Product?
The theoretical yield is the maximum amount of product that can be produced from a given
amount of reactant.
A chemical reaction rarely produces the theoretical yield of a product.
The actual yield is the amount of product actually produced when the chemical reaction is
carried out in an experiment.
Chemists need to know how efficient a reaction is in producing the desired product.
Percent yield of product is the ratio of the actual yield to the theoretical yield expressed as a
percent.
Percent yield is calculated thus
Chap 8
Ionic Compounds
Chemical bonds
The force that holds two atoms together is called a chemical bond.
Recall that an electron-dot structure is a type of diagram used to keep track of valence electrons
and is especially useful when illustrating the formation of chemical bonds.
Recall that ionization energy refers to how easily an atom loses an electron.
The term electron affinity indicates how much attraction an atom has for electrons.
Noble gases, having high ionization energies and low electron affinities, show a general lack of
chemical reactivity.
The presence of eight valence electrons in the outer energy level of noble gases, is chemically
stable and is called the stable octet.
Elements tend to react to acquire the stable electron structure of a noble gas.
Formation of Positive Ions
Recall that a positive ion forms when an atom loses one or more valence electrons in order to
attain a noble gas configuration.
A positively charged ion is called a cation.
Compare the electron configurations of the noble gas neon, atomic number 10, and the alkali
metal sodium, atomic number 11.
Neon
1s22s22p6
Sodium 1s22s22p63s1
The sodium atom has one s valence electron.
By losing an electron the sodium atom acquires the stable outer electron configuration of neon.
Reactivity of metals is based on the ease with which they lose valence electrons to achieve a
stable octet.
Group 1A elements, lose their one valence electron, forming an ion with a 1+ charge.
Group 2A elements loose two valence electrons and form ions with a 2+ charge.
Group 3A elements in general loose two electrons, but transition metals also have d sublevel
electrons.
Occasionally, transition metals loose d sublevel electrons thus transition elements commonly
form ions of 3+ or greater, depending on the number of d electrons in the electron structure.
Formation of Negative Ions
Non-metals, located on the right side of the periodic table, have a great attraction for electrons
and form a stable outer electron configuration by gaining electrons.
Consider the chlorine atom, a halogen from group 7A.
Chlorine
1s22s22p63s23p5
Chlorine gains one electron, forming a negative ion with a 1- charge; giving chlorine the electron
configuration of argon.
Argon 1s22s22p63s23p6
With the addition of one electron, chlorine becomes an anion, another name for a negative ion.
To designate an anion, the ending -ide is added to the root name of the element.
Thus chlorine becomes chloride, nitrogen becomes nitride, and oxygen becomes oxide.
Phosphorus, a group 5A element with the electron configuration of [Ne]3s23p3, has five valence
electrons.
Some nonmetals, such as phosphorus, can lose or gain other numbers of electrons to form an
octet.
Phosphorus can loose five electrons or gain three electrons.
Formation of an Ionic Bond
The electrostatic force that holds oppositely charged particles together in an ionic compound is
referred to as an ionic bond.
Compounds that contain ionic bonds are ionic compounds.
If ionic bonds occur between metals and the nonmetal oxygen, oxides form.
Most other ionic compounds are called salts.
Hundreds of compounds contain ionic bonds.
Consider the formation of the ionic compound calcium fluoride from calcium (Ca) and fluorine
(F).
Calcium has the electron configuration of [Ar]4s2 and fluorine has the electron configuration of
[He]2s22p5.
Because the number of electrons lost must equal the number of electrons gained, it will take
two fluorine atoms to gain the two electrons lost from one calcium atom.
Unprotected aluminum metal reacts with oxygen in air, forming the white coating you can
observe on aluminum objects such as lawn furniture. Explain the formation of an ionic
compound from the elements aluminum and oxygen.
Aluminum is a group 3A element with three valence electrons and oxygen is a group 6A element
with six valence electrons.
Each aluminum atom must lose three electrons and each oxygen atom must gain two electrons.
Remember the number of electrons lost must equal the number of electrons gained.
The smallest number divisible by both 2 and 3 is 6.
The overall charge on one unit of this compound is zero: 2Al3+ + 3O2-
Properties of Ionic Compounds
During the formation of an ionic compound, the positive and negative ions are packed into a
regular repeating pattern that balances the forces of attraction and repulsion between the ions.
This particle packing forms an ionic crystal.
Large numbers of positive ions and negative ions exist together in a ratio determined by the
number of electrons transferred from the metal to the nonmetal.
This strong attraction of positive and negative ions results in a crystal lattice.
A crystal lattice is a three-dimensional geometric arrangement of particles.
Melting point, boiling point, and hardness are physical properties that depend on how strongly
the particles are attracted to each other.
Energy and the Ionic Bond
During any chemical reaction, energy is either absorbed or released; it is endothermic or
exothermic respectively.
The formation of ionic compounds from positive and negative ions is always exothermic.
The energy required to separate one mole of the ions of an ionic compound is referred to as the
lattice energy.
The more negative the lattice energy, the stronger the force of attraction.
Lattice energy is directly related to the size of the ions bonded.
Smaller ions generally have a more negative value for lattice energy because the nucleus is
closer to and thus has more attraction for the valence electrons.
The ionic bond formed form the attraction of ions with larger positive or negative charges
generally has a more negative lattice energy.
Names and formulas for Ionic Compounds
Because no single particle of an ionic compound exists, ionic compounds are represented by a
formula that provides the simplest ratio of the ions involved.
The simplest ratio of the ions represented in an ionic compound is called a formula unit.
The formula KBr represents a formula unit for potassium bromide because potassium and
bromide ions are in a one-to-one ratio in the compound.
A monatomic ion is a one-atom ion, such as, Mg2+ or Br-.
The charge of a monatomic ion is its oxidation number.
Common Ions Based on Groups
Group
Atoms
Charge
1A
H, Li, Na, K, Rb, Cs
1+
2A
Be, Mg, Ca, Sr, Ba
2+
5A
N, P, As
3-
6A
O, S, Se, Te
2-
7A
F, Cl, Br, I
1-
Most transition metals and group 3A and 4A metals have more than one oxidation number.
Common Ions of Transition Metals and Groups 3A and 4A
Group
Common ions
3B
Sc3+, Y3+, La3+
4B
Ti2+, Ti3+
5B
V2+, V3+
6B
Cr2+, Cr3+
7B
Mn2+, Mn3+, Tc2+
8B
Fe2+, Fe3+
8B
Co2+, Co3+
8B
Ni2+, Pd2+, Pt2+, Pt4+
1B
Cu+,
2B
Zn2+, Cd2+, Hg22+, Hg2+
3A
Al3+, Ga2+, Ga3+, In+, In2+, In3+, Tl+, Tl3+
4A
Sn2+, Sn4+, Pb2+, Pb4+
Cu2+, Ag+, Au3+
The oxidation numbers of ions are used to determine the formulas for the ionic compounds they
form.
In the chemical formula, for any ionic compound, the symbol of the cation is always written first,
followed by the symbol of the anion.
Subscripts are used to represent the number of ions of each element in an ionic compound.
Polyatomic Ions
Polyatomic ions are ions made up of more than one atom.
The charge given to a polyatomic ion applies to the entire group of atoms.
Common Polyatomic ions
Ion
Name
NH4+
ammonium
NO2-
nitrite
NO3-
nitrate
HSO4-
hydrogen sulfate
OH-
hydroxide
CN-
cyanide
MnO4-
permanganate
HCO3-
hydrogen carbonate
ClO-
hypochlorite
ClO2-
chlorite
ClO3-
Chlorate
ClO4-
perchlorate
BrO3-
bromate
IO3-
iodate
IO4-
periodate
C2H3O2- acetate
H2PO4- dihydrogen phosphate
CO32-
carbonate
SO32-
sulfite
SO42-
sulfate
S2O32-
thiosulfate
O22-
peroxide
CrO42-
chromate
Cr2O72- dichromate
HPO42- hydrogen phosphate
PO43-
phosphate
AsO43-
arsenate
An oxyanion is a polyatomic ion composed of an element, usually a nonmetal, bonded to one or
more oxygen atoms.
These ions are easily named using the following conventions.
The ion with more oxygen atoms is named using the root of the nonmetal plus the suffix -ate.
The ion with fewer oxygen atoms is named using the root of the nonmetal plus the suffix -ite.
NO3-
NO2-
nitrate nitrite
SO42-
SO32-
sulfate sulfite
Chlorine in group 7A forms four oxyanions
ClO4-
ClO3-
ClO2-
ClO-
perchlorate
chlorate
chlorite hypochlorite
Use the following general rules in naming ionic compounds when their formulas are known.
1. Name the cation first and the anion second.
2. Monatomic cations use the element name.
3. Monatomic anions take their name from the root of the element name plus the suffix -ide
4. Group 1A and group 2A metals have only one oxidation number. Transition metals and
metals on the right side of the periodic table often have more than one oxidation number.
5. If the compound contains a polyatomic ion, simply name the ion.
Metallic Bonds and Properties of Metals
The electron sea model proposes that all the metal atoms in a metallic solid contribute their
valence electrons to form a "sea" of electrons.
Because they are free to move, they are often referred to as delocalized electrons.
A metallic bond is the attraction of a metallic cation for delocalized electrons.
The melting points of metals vary greatly.
Mercury is a liquid at room temperature and the melting point of tungsten is 3422ºC
Metals are malleable, which means they can be hammered into sheets, and they are ductile,
which means they can be drawn into wire.
Metals are generally durable.
The mobile electrons in transition metals consist not only of the two outer s electrons but also
the inner d electrons.
As the number of delocalized electrons increases, so do the properties of hardness and strength.
An alloy is a mixture of elements that has metallic properties.
Some Commercially Important Alloys
Common name Composition
Uses
Alnico
Fe 50%, Al 20%, Ni 20%, Co 10% Magnets
Brass
Cu 67-90%, Zn 10-33%
Bronze
Plumbing,
hardware, lighting
Cu 70-95%, Zn 1-25%, Sn 1-18%
Bearings, bells,
medals
Cast iron
Fe 96-97%, C 3-4%
Casting
Dental amalgam
Hg 50%, Ag 35%, Sn 15%
Dental fillings
Gold, 10 carat Au 42%, Ag 12-20%, Cu 38-46%
Lead shot
Pewter
Pb 99.8%, As 0.2%
Sn 70-95%, Sb 5-15%, Pb, 0-15%
Stainless steel Fe 73-79%, Cr 14-18%, Ni 7-9%
Sterling silver
Jewelry
Shotgun shells
Tableware
Instruments, sinks
Ag 92.5%, Cu 7.5%
Tableware, jewelry
Two basic types of alloys exist, substitutional and interstitial.
Substitutional alloys have atoms of the original metallic solid replaced by other metal atoms of
similar size.
Sterling silver, brass, and pewter are all examples of substitutional alloys.
An interstitial alloy is formed when the small holes (interstices) in a metallic crystal are filled
with smaller atoms.
Think of this alloy as like pouring sand into a bucket of gravel.
The best known interstitial alloy is carbon steel.
Iron is relatively soft and malleable; however, the presence of carbon makes the solid harder,
stronger, and less ductile than pure iron.
Chem chap 13.2
Vocabulary
dispersion force
dipole-dipole force
hydrogen bond
Forces of Attraction
If all particles of matter at room temperature have the same average kinetic energy, why are
some materials gases while others are liquids or solids? The answer lies with the attractive
forces within and between particles. The attractive forces that hold particles together in ionic,
covalent, and metallic bonds ate called intramolecular forces.
Intermolecular forces
The three intermolecular forces that will be discussed are dispersion forces, dipole-dipole
forces, and hydrogen bonds.
Dispersion Forces
Dispersion forces are weak forces that result from temporary shifts in the density of electrons in
electron clouds.
Dispersion forces are sometimes called London forces after the German-American physicist who
first described them, Fritz London.
Recall that electrons in an electron cloud are in constant motion.
When nonpolar molecules are in close contact, especially when they collide, the electron cloud
of one molecule repels the electron cloud of the other molecule.
The electron density around each nucleus is, for a moment, greater in one region of each cloud.
Each molecule forms a temporary dipole.
Due to the temporary nature of the dipoles, dispersion forces are the weakest intermolecular
force.
Dispersion forces are the dominant forces of attraction between identical nonpolar molecules.
Recall that the number of nonvalence electrons increases from fluorine to chlorine to bromine
to iodine.
Because the larger halogen molecules have more electrons, there can be a greater difference
between the positive and negative regions of their temporary dipoles and, thus, stronger
dispersion forces.
This difference in dispersion forces explains why fluorine and chlorine are gases, bromine is a
liquid, and iodine is a solid at room temperature.
Dipole-dipole forces
Polar molecules contain permanent dipoles; that is, some regions of a polar molecule are always
partially negative and some regions of the molecule are always partially positive.
Attractions between oppositely charged regions of polar molecules are called dipole-dipole
forces.
Because dipoles are permanent, dipole-dipole forces are stronger than dispersion forces,
provided the molecules being compared have approximately the same mass.
Hydrogen Bonds
A hydrogen bond is a dipole-dipole attraction that occurs between molecules containing a
hydrogen atom bonded to a small, highly electronegative atom with at lease one lone electron
pair.
For a hydrogen bond to form, hydrogen must be bonded to either a fluorine, oxygen,, or
nitrogen atom.
These atome are electronegative enough to cause a large partial positive charge on the
hydrogen atom, yet small enough that their lone pairs of electrons can come close to hydrogen
atoms.
Hydrogen bonds explain why water is a liquid at room temperaturewhile compounds of
comparable mass are gases.
The difference between methane and water is easy to explain; because, methane is nonpolar,
the only forces holding the molecules together are relatively weak dispersion forces.
The difference between ammonia and water is not as obvious.
Molecules of both compounds can form hydrogen bonds, yet ammonia is a gas at room
temperature and water is liquid.
Because oxygen atoms are more electronegative that nitrogen atoms, the O-H bonds in water
are more polar than the N-H bonds in ammonia.
As a result hydrogen bonds between water molecules are stronger than those between
ammonia molecules.
Chap 13.3
Vocabulary
viscosity
surface tension
surfactant
crystalline solid
unit cell
amorphus solid
Liquids and solids
Although the kinetic-molecular theory was developed to explain the behavior of gases, the
model can be applied to liquids and solids.
Liquids
Individual liquid molecules do not have fixed positions in the liquid.
However, forces of attraction between liquid particles limit their range of motion so that the
particles remain closely packed in a fixed volume.
Density and compression
At 25C and one atmosphere of air pressure liquids are much denser than gases.
Like gases, liquids can be compressed; but, the change in volume for liquids is much smaller
because liquid particles are already tightly packed together.
An enormous amount of pressure must be applied to reduce the volume of a liquid by even a
few percent.
Fluidity
Fluidity is the ability to flow.
Gases and liquids are classified as fluids because they can flow.
A liquid can diffuse through another liquid; however, more slowly than a gas at the same
temperature, because, intermolecular attractions interfere with the flow.
Thus, liquids are less fluid than gases.
Viscosity
Viscosity is a measure of the resistance of a liquid to flow.
The viscosity of a liquid is determined by the type of intermolecular forces involved, the shape
of the particles, and the temperature.
The stronger the attractive forces, the higher the viscosity.
Molecules with long chains have a higher viscosity than shorter, more compact molecules.
Viscosity and Temperature
Viscosity decreases with temperature.
With an increase in temperature there is an increase in the average kinetic energy of the
molecules composing the liquid.
Surface Tension
Particles in the middle of a liquid can be attracted to particles above them, below them, and to
either side.
For particles at the surface of the liquid, there are no attractions from above to balance the
attractions from below.
Thus, there is a net attractive force pulling down on particles at the surface.
The energy required to increase the surface area of a liquid by a given amount is called surface
tension.
Surface tension is a measure of the inward pull by particles in the interior.
Compounds that lower the surface tension of water are called surface active agents or
surfactants.
Capillary Action
When water is placed in a narrow container such as graduated cylinder the surface forms a
concave meniscus.
What is happening to the water at the molecular level is a combination of two forces; cohesion
and adhesion.
Choesion describes the force of attraction between identical molecules.
Adhesion describes the force of attraction between molecules that are different.
Because the the adhesive forces between water molecules and silicon dioxide in glass are
greater than the cohesive forces between water molecules, the water rises along the inner walls
of the cylinder.
If the cylinder is extremely narrow, a tin film of water will be drawn upward.
This movement of a liquid such as water is called capillary action, or capillarity.
Solids
According to the kinetic-molecular theory, a mole of solid particles has as much kinetic energy
as a mole of liquid particles at the same temperature.
For a substance to be a solid rather than a liquid at a given temperature, there must be strong
attractive forces acting between particles in the solid.
Thus, there is more order in a solid than in a liquid.
Because of this order, solids are musch less fluid that liquids and gases.
In fact, solids are not classified as fluids.
Density of Solids
Most solids are more dense than most liquids.
Water is an exception because the molecules are less closely packed together than in liquid
water.
Crystalline solids
A crystalline solid is a solid whose atoms, ions, of molecules are arranged in an orderly,
geometric, three-dimensional structure.
A unit cell is the smallest arrangement of connected points that can be repeated in three
directions to form the lattice.
The relationship of a unit cell to a crystal lattice is similar to that of a formula unit to an ionic
compound.
The shape of a crystalline solid is determined by the type of unit cell from which its lattice is
built.
There is seven common crystalline solids: cubic, tetragonal, orthorhombic, triclinic, hexagonal,
rhombohedral, and monoclinic.
Crystalline solids can be classified into five categories based on the types of particles they
contain: atomic solids, molecular solids, covalent network solids, ionic solids, and metallic solids.
Type
Unit Particles
atomic atoms
Characteristics of Solid Phase
Examples
soft to very soft; very low melting
points; poor conductivity
group 8A
elements
molecular
molecules
fairly sofe; low to moderately high
melting points; poor conductivity
I2, H2O, NH3,
CO2
C12H22O11
covalent
network
atoms connected
by covalent bonds
very hard; bery high melting points;
often poor conductivity
ionic
ions
hard; brittle; high melting points; poor
diamond(C) and quartz
(SiO2)
conductivity
NaCl, KBr,
CaCO3
metallic atoms surrounded
by mobile valence
electrons
soft to hard; low to very high
melting points; malleable and
ductile; excellent conductivity all metallic elements
Molecular solids
In molecular solids, the molecules are held together by dispersion forces, dipole-dipole forces,
or hydrogen bonds.
Most molecular compounds are not solids at room temperature.
Covalent network solids
Atoms such as carbon and silicon, which can form multiple covalent bonds, are able to form
covalent network solids.
Ionic solids
Ionic crystals are strong, but brittle.
The type of ions and the ratio of ions determine the structure of the lattice and the shape of the
crystal.
The network of attractions that extends throughout an ionic crystal gives thses compounds their
high melting points and hardness.
Metallic solids
The strength fo the metallic bonds between cations and electrons varies among metals and
accounts for their wide range of physical properties.
The mobile electrons make metals malleable – easly mammered into shapes – and ductile –
easily drawn into wires.
Mobile electrons make metals good conductors of heat and electricity.
Amorphous solids
An amorphous solid is one in which the partticles are not arranged in a regular, repeating
pattern.
Glass, rubber, and many plastics are amorphous solids.
Chap 14.
Vocabulary
Boyle's law
Charles's law
Gay-Lussac's law
Gases
The Three Gas Laws
Kinetic Theory
The kinetic theory assumes the following concepts about gases are true.
Gas particles do not attract or repel each other.
Gas particles are much smaller than the distances between them.
Gas particles are in constant, random motion.
No kinetic energy is lost when gas particles collide with each other or with the walls of their
container.
All gases have the same average kinetic energy at a given temperature.
The Nature of Gases
Actual gases don't obey all the assumptions made by the kinetic theory.
But for many gases, their behavior approximates the behavior assumed by the kinetic theory.
All the assumptions of the kinetic theory are based on four factors; the number of gas particles
present, the temperature, the pressure, and the volume of the gas sample.
What happens to a gas in a balloon if you squeeze it?
Because the balloon is closed, the amount of gas is constant.
Assume the temperature is held constant.
Decreasing the volume pushes the gas particles closer together.
Pushing the gas particles closer together increases the number of collisions between particles
with particles and particles with its container.
As the number of collisions per unit time increases, so does the observed pressure.
The interdependence of the variables of volume, pressure, temperature, and amount of gas is
the basis for the following gas laws.
Boyle's Law
Boyle's Law states that the volume of a given amount of gas held at a constant temperature
varies inversely with the pressure.
The products of pressure times volume for any two sets of conditions are equal, so Boyle's law
can be expressed mathematically as follows.
P1V1 = P2V2
P1 and V1 represent a set of initial conditions for a gas and P2 and V2 represent a set of new
conditions.
Charles Law
The French physicist Jacques Charles (1746-1823) studied the relationship between volume and
temperature.
In his experiments, he observed that as temperature increases, so does the volume of a gas
sample when the pressure is held constant.
Graph of volume versus temperature for a gas sample kept at a constant pressure.
The temperature at which the volume will reach a value of zero liters by extrapolating the line at
temperatures below which values were actually measured.
The temperature on this graph corresponding to zero volume is zero Kelvin, or -273.15C.
Charles's law states that the volume of a given mass of gas is directly proportional to its kelvin
temperature at constant pressure.
Charle's law can be expressed as:
Here V1 and T1 represent any initial pair of conditions, while V2 and T2 are any new set of
conditions.
The temperature must be expresed in kelvin units when using the equation for Charles's
law.
Conversion of a temperature in Celcius to kelvin is easy just use the following equation:
Tk = 273 + Tc
Gay-Lussac's Law
Joseph Gay-Lussac explored the relationship between temperature and pressure of a contained
gas at a fixed volume.
He found that a direct proportion exists between the kelvin temperature and the pressure.
Gay-Lussac's law states that the pressure of a given mass of gas varies directly with the kelvin
temperature when the volume remains constant.
It can be expressed mathematically thus:
Chap 14.2
Vocabulary
combined gas law
Avogadro's principle
molar volume
The Combined Gas Law, Avogadro's Principle and the Ideal Gas Law
The Combined Gas Law
Boyle's, Charles's, Gay-Lussac's laws can be combined into a single law.
This Combined Gas Law states the relationship b\among pressure, volume, and temperatire of a
fixed amount of gas.
The equation for the combined gas law can be expressed as:
Avogadro's Principle
The particles making up different gases can vary greatly in size.
However, according to the kinetic-molecular theory, the particles in a gas sample are usually far
enough apart that size has a negilible influence on the volume occupied by a fixed number of
particles.
For example, 1000 relatively large krypton gas particles occupy the same volume as 1000 much
smaller helium gas particles at the same temperature and pressure.
Avogadro first proposed , in 1811, the idea known today as Avogadro's principle.
Avogadro's principle states that equal volumes of gases at the same temperature and pressure
contain equal numbers of particles.
23
Recall one mole contains 6.02 X 10 particles.
The molar volume for a gas is the volume that one mole occupies at 0.00C and 1.00atm
pressure.
These conditions of temperature and pressure are known as standard temperature and pressure
(STP).
Avogadro showed experimentally that one mole of any gas will occupy a volume of 22.4L at STP.
Use the following equation to convert from moles to volume:
Chap 14.3
Vocabulary
ideal gas constant(R)
ideal gas law
The Ideal Gas Law
The laws of Avogadro, Boyle, Charles, and Gay-Lussac can be combined into a single
mathematical statement that describes the relationship among pressure, volume, temperature,
and number of moles of a gas.
This formula is called the ideal gas law.
Recall that the combined gas law relates volume, temperature, and pressure of a sample of gas.
The relationship of pressure,volume, and temperature is always the same. Thus:
where k is a constant based on the amount of gas present, n.
Experiments using known values of P, T, V, and n show that:
k = nR
where R represents an experimentally determined constant that is referred to as the ideal gas
constant.
Therefore, the ideal gas law
PV = nRT
In the ideal gas equation, the value of R depends on the units used for pressure.
Numerical Values of the Gas Constant, R
Units of R
Numerical values of R
Units of P
Units of V
Units of T
Units of n
L•atm
0.0821
atm
L
K
mol
8.31
kPa
L
K
mol
62.4
mmHg
L
K
mol
mol•K
L•kPa
mol•K
L•mmHg
mol•K
Real vs. ideal gases
An ideal gas is one whose particles take up no space and have no intermolecular attractive
forces.
An ideal gas follows the gas laws under all conditions of temperature and pressure.
In the real world, no gas is truly ideal.
All gas particles have some volume, however small it may be, because of the sizes of their atoms
and the lengths of their bonds.
All gas particles also aree subject to intermolecular interactions.
Despite that, most gases will behave like ideal gases at many temperature and pressure levels.
Real gases deviate most from ideal gas behavior at extremely high pressures and low
temperatures.
The nature of the particles making up a gas also affects how ideally the gas behaves.
Polar gas molecules such as water vapor have larger attractive forces between their particles
than nonpolar molecules.
Therefore, polar gases do not behave as ideal gases.
Also, particles of gases composed of larger molecules like butane (C4H10) occupy more actual
volume than an equal number of gas particles of smaller molecules such as helium (He).
Therefore, larger gas molecules tend to cause a greater departure from ideal behavior than do
smaller gas molecules.
Applying the Ideal Gas Law
To find the molar mass of a gas sample, the mass, temperature, pressure, and volume of the gas
must be known.
Recall that the number of moles of a gas (n) is equal to the mass (m) divided by the molar mass
(M).
Therefore the n in the ideal gas law (PV = nRT) can be replaced with;
Thus:
Recall density (D) is defined as mass (m) per unit volume (V).
Rearrange the ideal gas equation to solve for molar mass, D can be substituded for
Thus becomes
or
Rearrange this equation to solve for density of a gas