# Chapter 10 Gases. Characteristics of Gases. Pressure. The Gas Laws. The Ideal-Gas Equation. Applications of the Ideal-Gas Equation

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1 Characteristics of Gases Chapter 10 Gases Pressure The Gas Laws The Ideal-Gas Equation Applications of the Ideal-Gas Equation Gas mixtures and partial pressures Kinetic-Molecular Theory Real Gases: Deviations from Ideal Behavior

2 10.1 Characteristics of Gases Gases differ from Solids and Liquids These molecular properties define the physical properties of gases

3 Physical properties common to all gases

4 10.2 Pressure Pressure, P, is the force, F that acts on a given area, A.

5 Atmospheric Pressure Gravity causes the atmosphere as a whole to press down on the Earth s surface Force, F, exerted by a column of air 1m 2 in cross section extending through the entire atmosphere is given by: F = ma Considering that the mass of air in that column is 10,000 Kg, we can calculate the force from this column in a 1 m 2 surface.

6 Pressure exerted by our 1m 2 column of air can be calculated using P = F/A Standard Atmospheric Pressure (typical pressure at sea level) First demonstrated using a mercury barometer Be able to convert gas pressures from one set of units to another Sample exercise 10.1 Remember: 1 atm = 760 mmhg = kpa

7 A manometer is used to measure the pressure of enclosed gases Sample exercise The Ideal Gas Laws Physical State of a gas is defined by four variables The gas Laws express the relationship between these variables.

8 Boyle s Law : The relationship between pressure and volume If we have a certain amount of gas at a state 1 with pressure P 1 and volume V 1 and then we move it to a state 2 with pressure P 2 and volume V 2 at constant temperature, we get:

9 Charles s Law : The relationship between temperature and Volume A balloon will shrink when the gas in it is cooled A plot of Volume vs. Temperature in Kelvin (K) will be linear (ideal gas) If we have a certain amount of gas at a state 1 with temperature T 1 and volume V 1 and then we move it to a state 2 with temperature T 2 and volume V 2 at constant pressure, we get: Always use Absolute Temperature (in Kelvin) for gas problems

10 Avogadro s Hypothesis : The relationship between Quantity and Volume Double the number of moles of an ideal gas will cause the volume to double if T and P remain constant.

11 10.4 The Ideal-Gas equation Boyle s Law V α 1/P (constant n,t) Charles s Law V α T (constant n,p) Avogadro s Law V α n (constant P,T) Combine these to give: This constant is called the gas constant R Ideal gas no interaction between molecules (only during collisions) the volume of each molecule is negligible obey the idea-gas equation

12 Combined Ideal-Gas Law When P, V and T all change for a fixed number of moles of gas Sample exercise 10.6 Remember always check your answer does it seem reasonable? 10.5 Further applications of the Ideal-Gas equation Gas Densities and Molar Mass Knowing the Molar Mass, M, the Pressure and the Temperature of an ideal gas allows us to calculate its density, d

13 The density of a gas INCREASES with increasing pressure The density of a gas DECREASES with increasing temperature The Molar Mass of a gas can therefore be calculated if the density is known Sample exercise 10.7 and 10.8 Volumes of gases in chemical reactions Useful to be able to calculate the volumes of gases consumed or produced in chemical reactions Sample exercise 10.9

14 10.6 Gas Mixtures and Partial Pressures Imagine different amounts of 3 ideal gases in 3 distinct containers with same volume (V) and same temperature (T) What would be the total pressure (P T ) if I mix all these ideal gases in the same container with volume V and temperature T?

15 10.6 Gas Mixtures and Partial Pressures The total pressure of a mixture of gases equals the sum of the pressures that each would exert if it were present on its own. If P t is the total pressure exerted by a mixture of gases, and the partial pressure of each individual gas is P 1, P 2, P 3 etc. then Dalton s Law of partial pressures states: At constant temperature and volume, and assuming each gas in the mixture obeys the ideal-gas equation then: The total pressure is determined by the total number of moles of gas present, whether this is one gas or a mixture of gases. Sample exercise 10.10

16 Partial Pressures and Mole fractions Each gas in a mixture behaves independently. We can relate the mole fraction of a gas in a mixture to its partial pressure. The sum of the mole fractions of a mixture MUST = 1, i.e. Σ X i = 1 The partial pressure of a particular gas in a mixture can be calculated from its mole fraction and the Total Pressure:

17 Collecting Gases over water Often the gas produced in a chemical reaction is collected over water When the gas has been collected, the bottle is raised or lowered until the water levels inside and out are equal. The total pressure P total, is the sum of the pressure of gas(es) collected and the pressure exerted by the water vapor. The pressure exerted by water vapor P H2O at various temperatures is given in a table (data sheet) Sample exercise 10.12

18 10.7 Kinetic Molecular Theory The ideal-gas equation describes how gases behave, but does not explain why they behave as they do. Kinetic Molecular Theory developed to help understand the physical properties of gases.

19 Distribution of Molecular Speed Gas molecules have an average speed. However at any instant the molecules have a wide range of speeds. Boltzmann Curves plot the molecular speed vs. the number of molecules. Root mean square (rms) speed, μ μ = 3RT M

20 10.9 Real Gases All real gases fail to obey the ideal-gas equation to some degree Real gases deviate from ideal behavior because:

21 Pressure deviation from ideal gas behaviour For one mole (n =1) of ideal gas PV/RT = 1 (at all pressures)

22 Temperature deviation Deviation from ideal behavior also depends on temperature

23 The Van der Waals equation Introduces two constants ( a and b) into the Ideal-Gas equation to account for real gas behavior ( P + n 2 a/v 2 ) ( V - nb ) = nrt

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