16. Chapter A Macroscopic Description of Matter
Macroscopic systems are characterized as being either solid, liquid, or gas (water). These are called the phases of matter. In this chapter we'll be interested in when and how a system changes from one phase to another. Chapter Goal: To learn the properties of macroscopic systems called bulk properties (mass, volume, temperature, pressure).
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FLOATING ICEBERG
Chapter 16. A Macroscopic Description of Matter Topics: Solids, Liquids, and Gases Atoms and Moles Temperature Phase Changes Ideal Gases Ideal-Gas Processes
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The Atomic Model of Matter
We will use atomic model to represent matter as being made of particle-like atoms and to understand the thermal properties of matter. Three phases of matter: Gas
Liquid
Solid
Crystal: Periodic arrangement of atoms Amorphous: Random arrangement
A macroscopic system is best described by state variables (mass, volume, temperature, pressure, .......).
Density (...a new state variable)
The ratio of a system's mass to its volume is called the mass density, or sometimes simply "the density."
The SI units* of mass density are kg/m3. In this chapter we'll use an uppercase M for the system mass and lowercase m for the mass of an atom.
* The International System of Units (abbreviated SI from French: Systme international d'units)
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1 metric ton!!!
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Atoms and Moles
(moles ...another new state variable)
Let's begin with atoms...
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Atoms and Moles
What is the mass of an oxygen molecule?
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Atoms and Moles
(moles ...another new state variable)
The mass of an atom is determined primarily by its most
massive constituents, the protons and neutrons in its nucleus. The sum of the number of protons and neutrons is called the atomic mass number A. Note: this is not the same as the atomic number (which is the number of protons in the nucleus) The atomic mass scale is established by defining the mass of 12C to be exactly 12 u, where u is the symbol for the atomic mass unit. The conversion factor between atomic mass units and kilograms is
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The Definition of the Mole
By definition, one mole of matter (gas, liquid or solid) is the amount of substance containing as many basic particles as there are atoms in 12 g of 12C. Experiments have determined that there are 6.02x1023 atoms in 12 g of 12C. Avogadro's number, NA 1 mole of matter contains 6.02x1023 basic particles. For a monatomic gas such as helium atom, 1 mol of helium contains 6.02x1023 helium atoms For a diatomic gas such as oxygen gas, 1 mol of oxygen gas contains 6.02x1023 molecules of O2 which means 2x6.02x1023 oxygen atoms.
The number of moles n of a substance containing N basic particles is
The molar mass of a substance Mmol is the mass (in grams) of 1 mol of substance. By definition, the molar mass of 12C is Mmol (12C) = 12 g/mol. For other substance, the numerical value of the molar mass = the numerical value of the atomic mass or molecular mass. The molar mass of 4He is Mmol(He) = 4 g/mol. The molar mass of O2 is Mmol(O2) = 32 g/mol. The number of moles contained in a system of mass M (in grams) consisting of atoms or molecules with molar mass Mmol is
number of moles n
M (in grams) M mol
Moles of Oxygen
100 g of oxygen gas is how many moles of oxygen?
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EXAMPLE 16.2 Moles of oxygen
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One mole of helium (in the balloon), sulfur, copper, and mercury
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Temperature (related to system's thermal energy)
Other thermometers:
bimetallic strips thermocouples
Thermal expansion of the liquid in the thermometer tube pushes it higher in the hot water than in ice water
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Temperature (related to system's thermal energy)
The Celsius temperature scale is defined by setting TC=0 for the freezing point of pure water, and TC=100 for the boiling point. (also called the centigrade scale) The Kelvin temperature scale has the same unit size as Celsius, with the zero point at absolute zero. The conversion between the Celsius scale and the Kelvin scale is
The Fahrenheit scale, still widely used in the United States, is defined by its relation to the Celsius scale, as follows:
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CONSTANT VOLUME GAS THERMOMETER
There is a linear relationship between pressure and temperature All gases extrapolate to zero pressure at the same temperature To = - 273 oC
...all motion cease, and Eth = 0
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Temperature
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Phase Changes
The temperature at which a solid becomes a liquid or, if the thermal energy is reduced, a liquid becomes a solid is called the melting point or the freezing point. Melting and freezing are phase changes. The temperature at which a gas becomes a liquid or, if the thermal energy is increased, a liquid becomes a gas is called the condensation point or the boiling point. Condensing and boiling are phase changes. The phase change in which a solid becomes a gas is called sublimation.
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Temperature as a function of time as ice undergoes phase changes
A system at the melting temperature is said to be in phase equilibrium for example, ice and water co-exist at 0 oC.
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Ideal Gases
The ideal-gas model is one in which we model atoms in a gas as being hard spheres. Such hard spheres fly through space and occasionally interact by bouncing off each other in perfectly elastic collisions. Experiments show that the ideal-gas model is quite good for gases if two conditions are met:
1. The density is low (i.e., the atoms occupy a volume much smaller than that of the container), and 2. The temperature is well above the condensation point.
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The Ideal-Gas Law
The pressure p, the volume V, the number of moles n and the temperature T of an ideal gas are related by the ideal-gas law as follows:
where R is the universal gas constant, R = 8.31 J/mol K. The ideal gas law may also be written as
where N is the number of molecules in the gas rather than the number of moles n. The Boltzmann's constant is kB = 1.38 10-23 J/K.
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The Boltzmann's constant is kB = 1.38 10-23 J/K.
N is the number of molecules in the gas.
The Ideal-Gas Law
Find the Volume of a Mole What volume is occupied by one mole of an ideal gas at a pressure of 1.00 atm and a temperature of 0o C?
p 1.00 atm 1.013 105 Pa T 0 273 273 K
pV nRT nRT (1.00 mol)(8.31 J/mol K)(273 K) V p 1.013 105 Pa 0.0224 m3 22.4 L
Calculating a Gas Pressure 100 g of oxygen gas is distilled into an evacuated 600 cm3 container. What is the gas pressure at a temperature of 150o C? MODEL: The gas can be treated as an ideal gas: pV = nRT. Oxygen is a diatomic gas of O2 molecules.
number of moles of 100 g O2 is n M (in grams) 100 g 3.13 mol M mol 32 g/mol
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Ideal-Gas Processes process by which the gas changes from one state to another
If the initial and final states for an ideal gas has a constant amount of molecules (in a sealed container) : pfVf piVi nR constant Tf Ti
It's useful to represent ideal-gas processes on a graph called a pV diagram.
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Isochoric Processes
Many important gas processes take place in a container of constant, unchanging volume. A constant-volume process is called an isochoric process. Consider the gas in a closed, rigid container. Warming the gas with a flame will raise its pressure without changing its volume.
V1 V2
pfVf piVi Tf Ti
pf pi Tf Ti
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Isobaric Process
A constant-pressure process is called an isobaric process.
Consider a cylinder of gas with a tightfitting piston of mass M that can slide up and down but seals the container so that no atoms enter or escape. In equilibrium, the gas pressure inside the cylinder is
Mg p patmos A
p1 p2
pfVf piVi Tf Ti
Vf Vi Tf Ti
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MODEL: Treat the gases as ideal gases.
A. Equilibri um Pressures are the same : p patmos Mg A
B. Pressures are still the same, however V2 because T2 increases.
nRT2 increases P2
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Isothermal (Constant-Temperature) Process A constant-temperature process is called an isothermal process.
pfVf piVi Tf Ti
nRT constant p V V
pfVf piVi
isothermal compression if Vf < Vi.
isothermal expansion if Vf > Vi.
Compressing Air in the Lungs
A snorkeler takes a deep breath at the surface, filling his lungs with 4.0 L of air. He then descends to a depth of 5.0 m, where the pressure is 1.5 atm. At this depth, what is the volume of air in the snorkeler's lungs?
Ti = Tf
The initial and final states of the ideal gas have a constant amount of molecules (in a sealed container) : pfVf piVi nR constant Tf Ti
pi Tf 1.0 atm Vf Vi (4.0 L) 2.7 L pf Ti 1.5 atm
A MultiStep Process
A gas at 2.0 atm pressure and a temperature of 200o C is first expanded isothermally until its volume has doubled. It then undergoes an isobaric compression until it returns to its original volume. First show this process on a pV diagram. Then find the final temperature and pressure.
1 2: p2 p1 T2 V1 T1 V2
V1 1 p1 p1 1.0 atm 2V1 2
2 3: T3 T2 p3 V3 p2 V2
1 2
V2 1 T2 T2 236.5 K -36.5o C V2 2