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Chapter 6:The States of Matter

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PHYSICAL PROPERTIES OF MATTER• All three states of matter have certain properties that help

distinguish between the states. Four of these properties are density, shape, compressibility, and thermal expansion.

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DENSITY• Density is equal to the mass of a sample divided by the

volume of the same sample.

mass

densityvolume

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SHAPE• The shape matter takes depends upon the physical state

of the matter.

COMPRESSIBILITY• Compressibility is the change in volume of a sample of

matter that results from a pressure change acting on the sample.

THERMAL EXPANSION• Thermal expansion is the change in volume of a sample of

matter resulting from a change in the temperature of the sample.

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CHARACTERISTIC PROPERTIES OF THE THREE STATES OF MATTER

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THE KINETIC MOLECULAR THEORY OF MATTER• The kinetic molecular theory of matter is a useful tool for

explaining the observed properties of matter in the three different states of solid, liquid and gas.

POSTULATES OF THE THEORY• Postulate 1: Matter is made up of tiny particles called

molecules.• Postulate 2: The particles of matter are in constant motion

and therefore possess kinetic energy.• Postulate 3: The particles possess potential energy as a

result of repelling or attracting each other.• Postulate 4: The average particle speed increases as the

temperature increases.• Postulate 5: The particles transfer energy from one to

another during collisions in which no net energy is lost from the system.

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KINETIC ENERGY• Kinetic energy is the energy a particle has as a result of

being in motion.• Kinetic energy (KE) is calculated using the equation:

In this equation, m is the mass of a particle and v is its velocity.

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POTENTIAL ENERGY• Potential energy is the energy a particle has as a result of

being attracted to or repelled by other particles.

COHESIVE FORCE• A cohesive force is an attractive force between particles. It

is associated with potential energy.

DISRUPTIVE FORCE• A disruptive force results from particle motion. It is

associated with kinetic energy.

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THE SOLID STATE• The solid state is characterized by a high density, a

definite shape that is independent of its container, a small compressibility, and a very small thermal expansion.

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THE LIQUID STATE• The liquid state is characterized by a high density, an

indefinite shape that depends on the shape of its container, a small compressibility, and a small thermal expansion.

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THE GASEOUS STATE• The gaseous state is characterized by a low density, an

indefinite shape that depends on the shape of its container, a large compressibility, and a moderate thermal expansion.

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A KINETIC MOLECULAR VIEW OF SOLIDS, LIQUIDS, AND GASES

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THE GAS LAWS• The gas laws are mathematical equations that describe the

behavior of gases as they are mixed, subjected to pressure or temperature changes, or allowed to diffuse.

• The pressure exerted on or by a gas sample and the temperature of the sample are important quantities in gas law calculations.

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PRESSURE• Pressure is defined as a force pushing on a unit area of

surface on which the force acts.• In gas law calculations, pressure is often expressed in

units related to the measurement of atmospheric pressure.

STANDARD ATMOSPHERE OF PRESSURE• A pressure of one standard atmosphere is the pressure

needed to support a 760-mm (76.0-cm) column of mercury in a barometer.

ONE TORR OF PRESSURE• One torr of pressure is the pressure needed to support a

1-mm column of mercury in a barometer. A pressure of 760 torr is equal to one standard atmosphere.

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OFTEN-USED UNITS OF PRESSURE

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TEMPERATURE• The temperature of a gas sample is a measurement of the

average kinetic energy of the gas molecules in the sample.• The Kelvin temperature scale is used in all gas law

calculations.

ABSOLUTE ZERO• A temperature of 0 K

is called absolute zero.It is the temperature atwhich gas moleculeshave no kinetic energy because all motion stops. On the Celsiusscale, absolute zero isequal to -273°C.

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PRESSURE, TEMPERATURE AND VOLUME RELATIONSHIPS FOR GASES

• Mathematical equations relating the pressure, temperature and volume of gases are called gas laws.

• All of the gas laws are named after the scientists who first discovered them.

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BOYLE'S LAW• Boyle's law is a gas law that describes the pressure and

volume behavior of a gas sample that is maintained at constant temperature.

• Mathematically, Boyle's law is written as follows:

or

In these equations, P is the pressure, V is the volume, and k is an experimentally determined constant.

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CHARLES'S LAW• Charles's law is a gas law that describes the temperature

and volume behavior of a gas sample that is maintained at constant pressure.

• Mathematically, Charles's law is written as follows:

or

In these equations, V is the volume, T is the temperature in Kelvin, and k' is an experimentally determined constant.

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THE COMBINED GAS LAW• Boyle's law and Charles's law can be combined to give the

combined gas law that is written mathematically as follows:

In this equation, P, V and T have the same meaning as before and k'' is another experimentally determined constant.

• The combined gas law can be expressed in another useful form where the subscript i refers to an initial set of conditions and the subscript f refers to a final set of conditions for the same gas sample.

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• Example: A gas sample has a volume of 2.50 liters when it is at a temperature of 30.0°C and a pressure of 1.80 atm. What volume in liters will the sample have if the pressure is increased to 3.00 atm, and the temperature is increased to 100°C?

• Solution: The problem can be solved:• using the combined gas law.• by identifying the initial and final conditions.• making sure all like quantities are in the same units.• expressing the temperatures in Kelvin.

• Thus, we see that the combined gas law must be solved for Vf.

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•The result is:

•Substitution of appropriate values gives:

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AVOGADRO’S LAW• Equal volumes of gases measured at the same temperature

and pressure contain equal numbers of molecules.

STANDARD CONDITIONS• STP = standard temperature and pressure

• 0°C (273 K)

• 1.00 atm

MOLAR VOLUME AT STP• 1 mole of any gas molecules

has a volume of 22.4 L at STP.

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THE IDEAL GAS LAW• The ideal gas law allows calculations to be done in which

the amount of gas varies as well as the temperature, pressure, and volume.

• Mathematically, the ideal gas law is written as follows:

PV= nRT

In this equation, P is the pressure of a gas sample, V is the sample volume, T is the sample temperature in Kelvin, n is the number of moles of gas in the sample, and R is a constant called the universal gas constant. A commonly- used value for R is:

• In calculations, the quantities V, P, and T must be expressed in units that match the units of R, liters (L), atm, and Kelvin, respectively.

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EXAMPLES OF IDEAL GAS LAW CALCULATIONS• Example 1: A 2.50 mole sample of gas is confined in a

6.17 liter tank at a temperature of 28.0°C. What is the pressure of the gas in atm?

• Solution: The ideal gas equation is first solved for P:

• The known quantities are then substituted into the equation, making sure the units cancel properly to give units of atm in the answer:

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• Example 2: A 4.00 g sample of gas is found to exert a pressure of 1.71 atm when confined in a 3.60 L container at a temperature of 27°C. What is the molecular weight of the gas in grams per mole?

• Solution: • The molecular weight is equal to the sample mass in

grams divided by the number of moles in the sample.

• Because the sample mass is known, the molecular weight can be determined by calculating the number of moles in the sample.

• The ideal gas equation is first solved for n:

• The known quantities are then substituted into the equation, making sure units cancel properly to give the units of mol for the answer.

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• The units are seen to cancel properly to give the number of moles as the answer. The molecular weight is calculated by dividing the number of grams in the sample by the number of moles in the sample:

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IDEAL GASES vs. REAL GASES• No ideal gases actually exist.• If they did exist, they would behave exactly as predicted by

the gas laws at all temperatures and pressures.• Real gases deviate from the behavior predicted by the gas

laws, but under normally encountered temperatures and pressures, the deviations are small.

• Consequently, the gas laws can be used for real gases.• Interparticle attractions make gases behave less ideally.• The gases laws work best for gases made up of single

atoms or nonpolar molecules.

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DALTON'S LAW OF PARTIAL PRESSURES• According to Dalton's law, the total pressure exerted by a

mixture of gases is equal to the sum of the partial pressures of the gases in the mixture.

total individual gasesP P

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PARTIAL PRESSURE• The partial pressure of an individual gas of a mixture is the

pressure the gas would exert if it were alone in the container at the same temperature as the mixture as shown in the following illustration: