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Gas Mixtures Daltons Law

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Gas Mixtures--Partial Pressure So far: pure gases Many gases are actually mixtures of two or more gases: – air: O 2, N 2, H 2 O, etc How do mixtures of gases behave?

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Gas Mixtures--Partial Pressure P= 8 psi N 2 (g) P= 6 psi O 2 (g) P= 9 psi CO 2 (g)

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Gas Mixtures--Partial Pressure What happens when you put all three samples of gas together into one container (the same size container as each was in alone)? The gases form a homogeneous mixture. The pressure in the container increases, V and T stay the same – How do you know what the new pressure will be? P

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Gas Mixtures--Partial Pressure Each gas in a mixture behaves independently of the other gases present. – Each gas exerts its own pressure on the container. P O = pressure exerted by O 2 P N = pressure exerted by N 2 P CO = pressure exerted by CO 2 2 2 2

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Gas Mixtures--Partial Pressure Partial pressure: the pressure exerted by a particular gas present in a mixture Dalton's Law of Partial Pressure: The total pressure of a mixture of gases equals the sum of the pressures that each would exert if it were present alone. P total = P 1 + P 2 + P 3 + ………

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Gas Mixtures--Partial Pressure P total = P O + P N + P CO So for this example: P total = 6 psi + 8 psi + 9 psi = 23 psi 2 2 2

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Partial Pressure In other words, at constant T and V, – P total depends only on the total number of moles of gas present – P total is independent of the type (or types) of gases present.

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Partial Pressure-Mole Fraction When describing a mixture of gases, it is useful to know the relative amount of each type of gas. Mole fraction (X): a dimensionless number that expresses the ratio of the number of moles of one component compared to the total number of moles in a mixture.

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Mole Fraction If a gas mixture contains 5.0 mol O 2 (g), 3.0 mol H 2 O (g), and 12.0 mol N 2 (g), XO=XO= On the exam, you must be able to calculate the mole fraction of each component of a gas mixture. nO2nO2 ntnt = 5.0 mol 20.0 mol = 0.25

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Partial Pressure The partial pressure of a gas in a mixture can be found: P A = X A P total whereP A = partial pressure of gas A X A = mole fraction of gas A P total = total pressure of mixture

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Partial Pressure Calculation A mixture of gases contains 0.51 mol N 2, 0.28 mol H 2, and 0.52 mol NH 3. If the total pressure of the mixture is 2.35 atm, what is the partial pressure of H 2 ? P H 2 = X H 2 P total XH2=XH2= 0.28 mol 0.28 mol + 0.51 mol + 0.52 mol = 0.21 P H 2 = 0.21 x 2.35 = 0.50 atm

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Daltons law of Partial Pressure The simple gas laws and idea gas law apply to individual gases as well as to a mixture of nonreactive gases. What is responsible for the pressure in a gas mixture? Since the pressure of pure gas at constant V and T is proportional to its amount (P=nRT/V), the pressure contribute from each individual gas in a mixture is also its amount in the mixture. In other words, the total pressure exerted by a mixture of gases in a container at constant V and T is equal to the sum of the partial pressure of each individual gas in the container, a statement known as Daltons law of partial pressure P tot = P A + P B + P C ….at constant V and T Where P A, P B, P C …. refer to the pressure each individual gas would have if it were alone.

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Daltons law of partial pressures The pressure exerted by a particular gas in a mixture, P A, P B, P C is called partial pressure and refer to the pressure each individual gas would exert if it were alone in the container. That is, Here V = V A =V B = V tot The Concentration of any individual component in a gas mixture is usually expressed as mole fraction (X). The mole fraction of a component in a mixture is the fraction of moles of that component in the total moles of gas mixture.

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Which can be rearrange to solve P A, the partial pressure of component A: P A = X A ·P tot

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At constant P and T, where P = P A =P B = P C = P tot, the volume of each gas would individually occupy at a pressure equal to P tot is V A = n A RT/P tot ; V B =n B RT/P tot … and so on.

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Ideal Gas Law The equality for the four variables involved in Boyle’s Law, Charles’ Law, Gay-Lussac’s Law and Avogadro’s law can be written PV = nRT R.

Ideal Gas Law The equality for the four variables involved in Boyle’s Law, Charles’ Law, Gay-Lussac’s Law and Avogadro’s law can be written PV = nRT R.

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