PART V: REVIEWING PCAT CHEMISTRY in Visual Studio .NET

Draw DataMatrix in Visual Studio .NET PART V: REVIEWING PCAT CHEMISTRY

PART V: REVIEWING PCAT CHEMISTRY
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Ptotal = P1 + P2 + P3 + nRT , and recognizing that all of the gases in V the container are at the same temperature and volume, Dalton s law becomes: Using the ideal gas law in the form P = Ptotal = P1 + P2 + P3 + K = RT n1RT n2 RT n3RT + + + K = (n1 + n2 + n3 + K) V V V V
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The sum of the moles of gases in the mixture, n1 + n2 + n3 + is the total number RT Dalton s law is especially of moles of gases present, ntotal, so that Ptotal = ntotal V useful when a gas is collected over water The collected gas will actually be a mixture of the gas and water from evaporation Pgas = Ptotal Pwater, where Pgas is the pressure of the dry gas The mole fraction, , is de ned as the moles of a substance divided by the total moles present in the system The range of a mole fraction is 00 10 and the total of all the mole fractions is 10 1 = n1 n total
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Dividing the equation for the partial pressure of a gas by the equation for the total pressure generates another expression for the mole fraction RT n1 V
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P1 = Ptotal
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RT n1 + n2 + n3 + V
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P1 n1 = = 1 P1 = 1Ptotal Ptotal n1 + n2 + n3 +
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EXAMPLE: A mixture is prepared from 1200 g of O2 and 3600 g of Ne The total pressure of the mixture is 840 torr What is the partial pressure of each gas 1200 g O2 1 mole O2 1 mole Ne = 03750 mol O2 and 3600 g Ne = 1784 mol Ne 3200 g O2 2018 g Ne
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The total mol of the two gases is 03750 + 1784 = 2159 mol O2 = 0375 mol 1784 = 0174 and Ne = = 08263 2159 mol 2159
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PO 2 = O 2 P total = 0174(840 torr) = 146 torr and PHe = Ne P total = 08263(840 torr) = 694 torr
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Kinetic Molecular Theory
In the discussion of gases above, the macroscopic properties of gases such as pressure, temperature, and volume were described The behavior of gases is explained on the molecular level by the kinetic molecular theory, which has the following postulates: Particles of gases are separated from one another by large distances when compared to the size of the particles Particles of a gas are in constant and random motion When the particles of a gas collide with other particles or the sides of the container, no energy is lost, that is, the collisions are elastic The particles exert neither repulsive nor attractive forces on one another The average kinetic energy of gas particles is directly proportional to the absolute temperature in Kelvin The rst four points are relatively clear and explain many of the properties of gases such as compressibility, pressure, and the similar behavior of different gases The last point is important because it means that regardless of the gases involved, at the same temperature all gases have the same average kinetic energy The last point can also be taken as a de nition of temperature In a large sample of a gas such as oxygen there is a distribution of velocities As the temperature increases, the speeds of the oxygen molecules shift to greater velocities and the distribution curve skews to higher velocities A sample distribution of oxygen molecules at two temperatures is shown below At the higher temperature the distribution broadens and attens
CHAP 10: GENERAL CHEMISTRY
at lower temperature the distribution is narrow at higher temperature the distribution is wider and flatter
relative number of gas particles
velocity
PART V: REVIEWING PCAT CHEMISTRY
The average kinetic energy of an individual molecule of a gas is given by KE = 1 2 mu2 where u2 is the average of the squares of the velocities of the molecules The bar over a quantity indicates the average The average kinetic energy of a mole of molecules is obtained by multiplying by Avogadro s number, NA The middle equation below simpli es to the rightmost equation because the mass of NA molecules is the molar mass KE molecule = 1 1 1 mu2 KE mole = (N A m)u2 KE mole = ( 2 2 2 )u2
The kinetic molecular theory states that the average kinetic energy is proportional to the temperature in Kelvin The constant of proportionality for one mole of gas is 3 2 RT KE mole = 3 RT 2
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