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# Dalton’S Law Of Partial Pressure

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### Dalton’S Law Of Partial Pressure

1. 1. Dalton’s Law of Partial Pressure Dalton’s Law of partial pressure : The total pressure of a mixture of non-reacting gases in a system is the sum of their partial pressure. P Total = P 1 + P 2 + P 3 +P 4 + …….+P n Partial pressure of a component : The pressure that would be exert if it were present alone and occupied the same volume as in the mixture. If a container with a volume of V, having three type of gases X, Y, Z will exert partial pressure of P x , P y , P z on the wall.
2. 2. <ul><li>For gas X, P x = n X RT </li></ul><ul><li>V </li></ul><ul><li>For gas Y, P y = n y RT </li></ul><ul><ul><ul><ul><ul><li>V </li></ul></ul></ul></ul></ul><ul><li>For gas Z, P z = n z RT </li></ul><ul><li> V </li></ul><ul><li>The total pressure of the system: </li></ul><ul><li>P Total = P x + P y + P z </li></ul><ul><li>= (n X + n y + n z ) (RT) </li></ul><ul><li> V </li></ul><ul><li>Hence, P Total =n Total (RT) where n Total = n X + n y + n z </li></ul><ul><li> V </li></ul><ul><li>The mol fraction of gas x in the container : X x = n x / n Total </li></ul><ul><li>= P x / P Total. </li></ul>
3. 3. A mixture of gases at 800 torr contain 20% nitrogen, 10% hydrogen, 50% oxygen and 20% CO 2 by volume. What is partial pressure of each gas in torr ? (Assume that the total volume of the mixture is 100 dm 3 .) <ul><li>Answer: </li></ul>Ouestion 1
4. 4. The Molecular Behavior of Gases <ul><li>Kinetic Molecular Theory of Gases –the gaseous particles in an </li></ul><ul><li>ideal gas exhibit no interactive or repulsive forces, and the </li></ul><ul><li>volumes of the gases particles are assumed to be negligible. </li></ul><ul><li>This theory can be summarized as follows </li></ul><ul><li>Gases are composed of molecules that are </li></ul><ul><li>continuous, completely random motion in all </li></ul><ul><li>directions. </li></ul><ul><li>The molecules move in straight line and change direction only </li></ul><ul><li>when they collide with other molecules or with the walls of the </li></ul><ul><li>container. </li></ul><ul><li>The pressure of gas in a container results from the </li></ul><ul><li>collision with the walls of the container by the gaseous </li></ul><ul><li>molecules. </li></ul>
5. 5. <ul><li>At a given T, The P of the container does not change in time. Thus, the collisions among the molecules and between molecules and wall must be elastic.( No energy is lost during collision) </li></ul><ul><li>At Relatively low P, the average distance between gas molecules is large compared of the size molecules. The attractive forces between gaseous molecules when they are relatively widely separated, are of no significance and can be ignored. </li></ul><ul><li>Because the molecules are small compared to the distance between them ; the have mass but have negligible volume. </li></ul><ul><li>The average kinetic energy of the particles is α absolute temperature. </li></ul>
6. 6. Relationship of the Gas laws to the Kinetic Molecular Theory of Gases <ul><li>Gas laws derived from the assumption of the theory: </li></ul><ul><li>a) Boyle’s Law (P α 1/V) </li></ul><ul><ul><li>The pressure exerted by a gas in a container results from the impact of its molecules on the walls of the container. </li></ul></ul><ul><ul><li>The pressure varies directly with the number of molecules hitting the walls per unit time. </li></ul></ul><ul><ul><li>b) Charle’s Law (V α T ) </li></ul></ul><ul><ul><li>At constant volume, an increase in T will increase the P of a gas as the average speed and kinetic energy of the molecules increase. </li></ul></ul><ul><ul><li>In order to keep the pressure constant when T increases , the V must be increased and each molecule travels further. Hence, smaller number of molecules will strike the wall at a given time. </li></ul></ul>
7. 7. <ul><li>C) Dalton’s Law </li></ul><ul><ul><li>Because of the relatively large distance between the molecules of a gas, the molecules of one component in a mixture of gases collide with walls of the container with the same frequency in the presence of other kinds of molecules as in their absence. </li></ul></ul><ul><ul><li>The total pressure of a mixture of gases equals the sum of the partial pressures of the individual gases. </li></ul></ul>
8. 8. Maxwell-Boltzmann Distribution <ul><li>In the context of the Kinetic Molecular Theory of Gases, a gas contains a large number of particles in rapid motions. Each particle has a different speed, and each collision between particles changes the speeds of the particles. </li></ul><ul><li>An understanding of the properties of the gas and the distribution of this particle speeds. </li></ul>
9. 9. <ul><li>this graph shows the speed-density relationship of a few noble gases at a temperature of 298.15 K (25 °C). The y-axis is in s/m so that the area under any section of the curve (which represents the probability of the speed being in that range) will be unitless . </li></ul><ul><li>Graph: Relationship of Kinetic Energy - Density </li></ul>Important features of Maxwell-Boltzmann distribution :
10. 10. Real Gases – Deviation from Ideality <ul><li>Real gas – do not obey Boyle’s Law and Charles’ Law </li></ul><ul><li>Behave almost ideal at low pressure & high temperature </li></ul><ul><li>Behave non-ideal at high pressure and low temperature. </li></ul><ul><li>The molecules in real gas has practically no attraction between each other because they are very far apart. </li></ul><ul><li>But at high pressure the molecules are close together and the force attraction between the molecules increases.(non-ideal) </li></ul><ul><li>At low temperature molecules are close together and exist the force of attraction between the particles due to its slow motion, and smaller kinetic energy .(non-ideal) </li></ul>
11. 11. Deviation from ideal Behavior <ul><li>Deviation of real gas from ideal gas behavior can be shown by plotting PV against P for 1 mol of real gases at 273K </li></ul><ul><li>RT </li></ul>PV/RT 1.0 P N 2 O 2 H 2 Ideal gas NH 3 For ideal gas = PV/RT = n = 1 (dotted line).
12. 12. <ul><li>Above dotted line : PV/RT > 1.0  positive deviation </li></ul><ul><li>Below dotted line : PV/RT < 1.0  negative deviation </li></ul><ul><li>At very low pressure (P< 5 atm) all real gases behave almost ideally . </li></ul>
13. 13. Van der Waals equation <ul><li>An equation which takes into account the corrections for pressure and volume ( intermolecular forces of attraction and volume associated with the molecules). </li></ul><ul><li>(P + n 2 a ) (V-nb) = nRT </li></ul><ul><li>V 2 </li></ul>
14. 14. <ul><li>a = corrections due to intermolecular attraction , </li></ul><ul><li>unit : L 2 atm mol -2 </li></ul><ul><li>b = total volumes of the molecules themselves and is subtracted from V , the total volume of gas. </li></ul><ul><li>unit : Lmol -1 . </li></ul><ul><li>V large  nb and n 2 a are negligible, </li></ul><ul><li> V 2 </li></ul><ul><li>van der Waals equation =>PV = nRT. </li></ul><ul><li>Low pressure  correction for the intermolecular attraction a , is more important than the molecular volume, b. </li></ul><ul><li>High pressure and low volumes, the correction for the volumes of the molecules b, becomes important . </li></ul>
15. 15. Ouestion 2 <ul><li>A quantity of 3.50 moles of NH 3 occupies 5.20 L at 47 o C. Calculate the pressure of the gas (in atm) using </li></ul><ul><li>(R=0.0821 L atm/mol ; a for NH 3 4.17atm L 2 mol 2 ; b=0.0371L/mol) </li></ul><ul><ul><li>a) ideal gas equation </li></ul></ul><ul><ul><li>b) van der Waals equation. </li></ul></ul>