Teori Kinetik Gas

Zainal AbidinSMAN 3 Bandar Lampung, 8 Maret 2014

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Persamaan Keadaan Gas Ideal

Pengertian Mol dan Massa Molekul

Massa molekul (M) suatu zat adalah massa dalam kilogram dari satu kilomol zat.

Massa sebuah atom atau molekul

Hubungan massa dan mol

Count of Quaregna and Cerreto (9 August 1776, Turin, Piedmont – 9 July 1856) was an Italian scientist. He is most noted for his contributions to molecular theory, including what is known as Avogadro's law. In tribute to him, the number of elementary entities (atoms, molecules, ions or other particles) in 1 mole of a substance, 6.02214179(30)×1023, is known as theAvogadro constant.

Lorenzo Romano Amedeo Carlo Avogadro di Quaregna e di Cerreto

http://en.wikipedia.org/wiki/Amedeo_Avogadro

Penurunan Persamaan Keadaan Gas Ideal

Jika suhu yang berada dalam bejana tertutup (tidak bocor) dijaga tetap, tekanan gas berbanding terbalik dengan volumnya.

Hukum Boyle:

Jika tekanan gas yang berada dalam bejana tertutup (tidak bocor) diajaga tetap, volum gas sebanding dengan suhu mutlaknya.

Hukum Charles-Gay Lussac:

Persamaan Boyle-Gay Lussac:

http://id.wikipedia.org/wiki/Joseph_Louis_Gay-Lussac

http://en.wikipedia.org/wiki/Robert_Boyle

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Molecular Mass, the Mole, and Avogadro's Number

To set up atomic mass scale, a reference value (along with a unit) is chosen for one of the elements. The unit is called the atomic mass unit (symbol: u). By international agreement, the reference element is chosen to be the most abundant type or isotope* of carbon, which is called carbon-12. Its atomic mass * is defined to be exactly twelve atomic mass units, or 12 u. The relationship between the atomic mass unit and the kilogram is

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A portion of the periodic table showing the atomic number and atomic mass of each element. In the periodic table it is customary to omit the symbol “u” denoting the atomic mass unit.

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The molecular mass of a molecule is the sum of the atomic masses of its atoms.

Macroscopic amounts of materials contain large numbers of atoms or molecules. Even in a small volume of gas, 1 cm3, for example, the number is enormous. It is convenient to express such large numbers in terms of a single unit, the gram-mole, or simply the mole (symbol: mol). One gram-mole of a substance contains as many particles (atoms or molecules) as there are atoms in 12 grams of the isotope carbon-12.

12 grams of carbon-12 contain 6.022 × 1023 atoms. The number of atoms per mole is known as Avogadro’s number NA, after the Italian scientist Amedeo Avogadro (1776–1856):

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The mass per mole (in g/mol) of a substance has the same numerical value as the atomic or molecular mass of the substance (in atomic mass units).

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Example 1.  The Hope Diamond and the Rosser Reeves Ruby

The Hope diamond (44.5 carats), which is almost pure carbon. The Rosser Reeves ruby (138 carats), which is primarily aluminum oxide (Al2O3). One carat is equivalent to a mass of 0.200 g.

Determine (a) the number of carbon atoms in the diamond and (b) the number of Al2O3 molecules in the ruby.

http://www.harrywinston.com/our-story/hope-diamond

The 45.52 carat, deep-blue Hope Diamond is shown here inside its surrounding pendant of 16 pear- and cushion-cut white diamonds. (Photo by Chip Clark)

http://smithsonianscience.org/2009/08/blue-hope-diamond-glows-an-erie-red-after-exposure-to-ultraviolet-light/

Rosser Reeves Star Ruby [G4257]

http://geogallery.si.edu/index.php/en/1001784/rosser-reeves-star-ruby

The Rosser Reeves Ruby

This 138.7 carat ruby is from Sri Lanka and was owned by Rosser Reeves. The description: "This is one of the world's largest and finest star rubies, with superb color and a well-defined star. Rosser Reeves, an American advertising executive, carried it as a lucky stone and called it his 'baby'."

http://hyperphysics.phy-astr.gsu.edu/hbase/minerals/ruby.html

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(a) m = (44.5 carats)[(0.200 g)/(1 carat)] = 8.90 g

(b) m = (138 carats)[(0.200 g)/(1 carat)] = 27.6 g.

Calculations like those in part (a) reveal that the Rosser Reeves ruby contains 0.271 mol or

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The Ideal Gas Law An ideal gas is an idealized model for real gases that have sufficiently low densities.

Persamaan keadaan gas ideal:

Massa jenis gas (ρ):

Persamaan keadaan gas ideal:

Tetapan Boltzmann

Ludwig Eduard Boltzmann (February 20, 1844 – September 5, 1906) was an Austrian physicist and philosopher whose greatest achievement was in the development of statistical mechanics, which explains and predicts how the properties of atoms (such as mass, charge, and structure) determine the physical properties of matter (such as viscosity, thermal conductivity, and diffusion).

http://en.wikipedia.org/wiki/Ludwig_Boltzmann

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The absolute pressure of an ideal gas is proportional to the number of molecules or, equivalently, to the number of moles n of the gas (P n).

P    nT/V.

IDEAL GAS LAW

The absolute pressure P of an ideal gas is directly proportional to the Kelvin temperature T and the number of moles n of the gas and is inversely proportional to the volume V of the gas: P = R(nT/V). In other words,

where R is the universal gas constant and has the value of 8.31 J/(mol·K).

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The constant term R/NA is referred to as Boltzmann’s constant, in honor of the Austrian physicist Ludwig Boltzmann (1844–1906), and is represented by the symbol k:

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Example 2.  Oxygen in the Lungs In the lungs, the respiratory membrane separates tiny sacs of air (absolute pressure = 1.00 × 105 Pa) from the blood in the capillaries. These sacs are called alveoli, and it is from them that oxygen enters the blood. The average radius of the alveoli is 0.125 mm, and the air inside contains 14% oxygen. Assuming that the air behaves as an ideal gas at body temperature (310 K), find the number of oxygen molecules in one of the sacs.

                    .

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One mole of an ideal gas occupies a volume of 22.4 liters at a temperature of 273 K (00C) and a pressure of one atmosphere (1.013 × 105 Pa). These conditions of temperature and pressure are known as standard temperature and pressure (STP).

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Kinetic Theory of Gases

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THE DISTRIBUTION OF MOLECULAR SPEEDS

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KINETIC THEORY

The pressure that a gas exerts is caused by the collisions of its molecules with the walls of the container.

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A gas particle is shown colliding elastically with the right wall of the container and rebounding from it.

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Tekanan dan Energi Kinetik menurut Teori Kinetik Gas

(1)Gas terdiri dari molekul-molekul yang sangat banyak dan jarak misah antar molekul jauh lebih besar dari pada ukurannya.

(2)Molekul-molekul memenuhi hukum gerak Newton, tetapi secara keseluruhan mereka bergerak lurus secara acak dengan kecepatan tetap.

Beberapa asumsi tentang gas ideal:

(3)Molekul-molekul mengalami tumbukan lenting sempurna satu sama lain dan dengan dinding wadahnya.

(4) Gaya-gaya antar molekul dapat diabaikan, kecuali selama satu tumbukan yang berlangsung sangat singkat.

(5) Gas yang dipertimbangkan adalah suatu zat tunggal, sehingga semua molekul adalah identik.

Formulasi Tekanan Gas dalam Wadah Tertutup

L³ adalah volum gas V.

Tekanan gas:

Energi Kinetik Rata-rata Molekul Gas

Energi kinetik rata-rata

(1)Suhu gas tidak mengandung besaran N/V

(2)Suhu gas hanya berhubungan dengan gerak molekul

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Conceptual Example 3  Does a Single Particle Have a

Temperature? Each particle in a gas has kinetic energy. Furthermore, the equation establishes the relationship between the average kinetic energy per particle and the temperature of an ideal gas. Is it valid, then, to conclude that a single particle has a temperature?

A single gas particle does not have a temperature.

Kelajuan Efektif Gas

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Example 4.  The Speed of Molecules in Air

Air is primarily a mixture of nitrogen N2 (molecular mass = 28.0 u) and oxygen O2 (molecular mass = 32.0 u). Assume that each behaves as an ideal gas and determine the rms speeds of the nitrogen and oxygen molecules when the temperature of the air is 293 K.

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Kelajuan efektif:

Hubungan Kelajuan Efektif Gasdengan Suhu Mutlaknya

Perbandingan Kelajuan Efektif Berbagai Gas

Kelajuan efektif:

Menghitung Kelajuan Efektif dari Data Tekanan

Teorema Ekipartisi Energi

Energi kinetik monoatomik:

Untuk suatu sistem molekul-molekul gas pada suhu mutlak T dengan tiap molekul memiliki f derajat kebebasan, rata-rata energi kinetik per molekul Ek adalah

Derajat Kebebasan Molekul Gas Diatomik

Energi kinetik gas diatomik:

Gas diatomik dapat memiliki sampai tujuh derajat kebebasan. Gas yang memiliki lebih dari dua atom (poliatomik) memiliki derajat kebebasan yang lebih banyak dan getarannya juga lebih kompleks.

Energi Dalam Gas

Energi dalam suatu gas ideal didefinisikan sebagai jumlah energi kinetik seluruh molekul gas yang terdapat di dalam wadah tertutup.

Untuk gas monoatomik

Untuk gas diatomik

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Diffusion The process in which molecules move from a region of higher concentration to one of lower concentration is called diffusion. The host medium, such as the air or water, is referred to as the solvent, while the diffusing substance, like the perfume molecules, is known as the solute. Relatively speaking, diffusion is a slow process, even in a gas.

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Conceptual Example 5.  Why Diffusion Is Relatively Slow

In Example 4 we have seen that a gas molecule has a translational rms speed of hundreds of meters per second at room temperature. At such a speed, a molecule could travel across an ordinary room in just a fraction of a second. Yet, it often takes several seconds, and sometimes minutes, for the fragrance of a perfume to reach the other side of a room. Why does it take so long?

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When a perfume molecule diffuses through air, it makes millions of collisions each second with air molecules. The speed and direction of motion change abruptly as a result of each collision. Between collisions, the perfume molecule moves in a straight line at a constant speed. Although a perfume molecule does move very fast between collisions, it wanders only slowly away from the bottle because of the zigzag path resulting from the collisions. It would take a long time for a molecule to diffuse in this manner across a room. Usually, however, convection currents are present and carry the fragrance across the room in a matter of seconds or minutes.

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(a) Solute diffuses through the channel from the region of higher concentration to the region of lower concentration. (b) Heat is conducted along a bar whose ends are maintained at different temperatures.

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FICK’S LAW OF DIFFUSION

The mass m of solute that diffuses in a time t through a solvent contained in a channel of length L and cross-sectional area A is

where C is the concentration difference between the ends of the channel and D is the diffusion constant.

SI Unit for the Diffusion Constant: m2/s

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Example 6. 

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Large amounts of water can be given off by plants. It has been estimated, for instance, that a single sunflower plant can lose up to a pint of water a day during the growing season. At figure shows a cross-sectional view of a leaf. Inside the leaf, water passes from the liquid phase to the vapor phase at the walls of the mesophyll cells. The water vapor then diffuses through the intercellular air spaces and eventually exits the leaf through small openings, called stomatal pores. The diffusion constant for water vapor in air is D = 2.4 × 10–5 m2/s. A stomatal pore has a cross-sectional area of about A = 8.0 × 10–11 m2 and a length of about L = 2.5 × 10–5 m. The concentration of water vapor on the interior side of a pore is roughly C2 = 0.022 kg/m3, while that on the outside is approximately C1 = 0.011 kg/m3. Determine the mass of water vapor that passes through a stomatal pore in one hour.

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Concepts & Calculations Example 7.  Hydrogen Atoms in Outer Space

In outer space the density of matter is extremely low, about one atom per cm3. The matter is mainly hydrogen atoms (m = 1.67 × 10–27 kg) whose rms speed is 260 m/s. A cubical box, 2.0 m on a side, is placed in outer space, and the hydrogen atoms are allowed to enter. (a) What is the magnitude of the force that the atoms exert on one wall of the box? (b) Determine the pressure that the atoms exert. (c) Does outer space have a temperature, and, if so, what is it?

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(a)

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(b)

(c)

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