Chapter 10 Gases Characteristics of Gases Elements that exist as gases: Noble gases, O 2, N 2,H 2, F 2 and Cl 2. (For compounds see table 10.

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1 Chapter 10 Gases 10.1 Characteristics of Gases Elements that exist as gases: Noble gases, O 2, N 2,H 2, F 2 and Cl 2. (For compounds see table 10.1) Unlike liquids and solids, gases expand to fill their containers (highly compressible). have extremely low densities ( 1/1000 liquids). mixtures of gases are always homogeneous. particles are far apart Pressure What is it and how can we change it? What is Atmospheric Pressure and how does it change with altitude? Units of Pressure Pascals: 1 Pa = 1 N/m 2 ; 1 mm Hg = 1 torr = Pa Bar: 1 bar = 10 5 Pa = 100 kpa Standard value of P atm (sea level): 1 atm = 760 torr (or mm Hg) = 14.7 psi = 101,325 Pa What is a manometer and what does it measure? Changing the Liquid What happens if we use a different liquid (not Hg) to measure P? P = d h g ; d 1 h 1 = d 2 h 2 Example What would be the height of a column of water that measures the atmospheric pressure at sea level? (d Hg = 13.6 g/cm 3 ) h H2 O = d 1 h 1 = d 2 h 2 ; h H2 O = d Hg h Hg d H2 O 13.6 g cm 3 760mmHg 1.00 g = mmh 2 O (10.3 m or 34.2 ft) cm 3 1

2 Manometric and Absolute Pressure P gas = P atm ΔP = P man = h atm h gas ΔP = P man = h atm h gas P gas = P atm + ΔP P gas = P atm + ΔP 10.3 The Gas Laws The following gas laws summarize the observations made on lots of experiments in the 17 th and 18 th centuries. (No need to memorize them!) Boyle s law: The relation between the volume of a gas and its pressure (keeping the number of moles, n, and the temperature, T, constant). P = k 1 ; P 1 1 = P 2 2 How does it look graphically? Charles s law: The relation between the volume of a gas and its temperature (keeping the number of moles, n, and the pressure, P, constant). T = k 1 2 ; = 2 T 1 T 2 How does it look graphically? What is Absolute Zero Temperature? Where does the concept come from? Avogadro s law: The relation between the volume of a gas and its number of moles (keeping the temperature, T, and the pressure, P, constant). n = k 1 3 ; = 2 n 1 n 2 Restating Avogadro s Law Equal volumes of gases (at the same T and P) contain equal number of molecules. When gases react, the ratios are proportional to the mole ratios: N 2(g) + 3 H 2(g) 2NH 3(g) 1L N 2(g) : 3L H 2(g) : 2 L NH 3(g) 2

3 Problem 1 CH 4(g) + 2O 2(g) CO 2(g) + 2 H 2O (g) If 22.4 L CH 4(g) is burned, what volume of O 2(g) is required? (Consider T and P constant.) 6.4 The Ideal-Gas Equation Memorize it, please! What is the meaning of R and which are its units? Working with the Ideal-Gas Equation 1. One state problems (you ll know all, but one value): P = nrt 2. Two state problems: P 1 1 n 1 T 1 = P 2 2 n 2 T 2 What is the combined gas law? Problem 2 Obtain the equations for the three laws (Boyle s, Charles s and Avogadro s) starting with the ideal gas equation; the conditions are: a. and P change (T and n constant). b. and T change (P and n constant). c. and n change (T and P constant). Problem 3 If you have of CO 2(g) at 25 C and 1.00 atm, what is the volume of this sample at atm and 25 C? 3

4 Problem 4 A balloon filled with gas occupies at 23 C and 1.00 atm. What will its volume be at -5 C and 1.00 atm? Problem 5 If of CO 2 gas occupies a volume of 1.00L at 20. C, what is the pressure? Which are the values for Standard Temperature and Pressure (STP)? What is the molar volume at STP? 10.5 Further Applications of the Ideal-Gas Equation We can rearrange the equation to find more information: P = nrt ; n = m MM ; d = m Replacing the equation for n and rearranging: MM = drt P Problem 6 The density of an unknown gas is 2.08 g/l at 100 C and ; d = P(MM) RT torr. What is the molar mass of the gas? 4

5 Problem 7 If you heat 2KClO 3 (s) 2KCl (s) + 3O 2 (g) of KClO 3, what volume of O 2 will be produced at 1.00 atm, 70 C? Problem g of Al is placed in of 1.00M HCl. What volume of hydrogen can be collected at 25 C and 1.00atm? 2 Al (s) + 6 HCl (aq) 2 AlCl 3(s) + 3 H 2(g) 10.6 Gas Mixtures and Partial Pressures Dalton s Law: The total pressure of a mixture of gases equals the sum of the pressures that each would exert if it were present alone (partial pressure). P Total = P 1 + P 2 + P 3 + P Total = P 1 + P 2 + P 3 + = n 1RT An interesting outcome of the above is the following: + n 2RT + n 3RT + P Total = (n 1 + n 2 + n 3 + ) ( RT ) = n Total ( RT ) P i P T = n i RT n T RT = n i n T = χ i Where χ i is the mole fraction. Therefore, the partial pressure of a gas in a mixture is the total pressure of the mixture multiplied by the mol fraction of the particular gas. P i = P T χ i ; χ i = n i n T Problem 9 A mixture of gases contains mol of N 2 and mol of O 2. The total pressure is pressure of each gas in the mixture. torr. Find the partial 5

6 Collecting Gases over Water Usually done by water displacement, so there is water vapor mixed in with the gas. The vapor pressure of H 2O is the partial pressure of H 2O (g) over H 2O (l) there are tables to find it out. Problem 10 Zn (s) + 2HCl (aq) ZnCl 2(aq) + H 2(g) If 75.8mL of H 2 is collected over water at 24 C when P atm= (vp H 2O at 24 C = 22.4 torr) torr, what mass of Zn was used? 10.7 The Kinetic-Molecular Theory of Gases This is a model that helps us understand why gases behave the way they do. 1. A gas consists of many particles moving about at random (no interactions among them). 2. of the gas particles is negligible. 3. Collisions of gas particles are elastic (i.e. total KE of the particles is constant). 4. The average KE of gas particles is proportional to T (in Kelvin). kg m3 E = ( sec 2 ) = J(Joule) m = mass(kg) ; v = velocity ( m sec ) ; KE = 1 2 mv2 KM Theory and Gas Laws Use ideas of from the KM Theory to explain the observed behavior of gases (i.e. the gas laws). Why does the pressure increase when we decrease the volume (constant T and n)? Why does the pressure increase when we increase the temperature ( and n constant)? Why does the volume increase when we increase the temperature (P and n constant)? What when we increase the number of moles in a rigid container and in a flexible container? 6

7 Distribution of Molecular Speed What is the difference among the most probable speed, the average speed and the root-mean-square (rms) speed? Root-Mean-Square (rms) Speed For one mol of ideal gas, the average kinetic energy is calculated as: KE = 1 J 2 mv2 ; R = mol K ; (1 L atm = J) For one molecule: Combining and rearranging the terms: KE = 3 2 RT v rms = 3RT MM ; MM = Molar Mass ( kg mol ) v rms = root mean square velocity ( m sec ) Problem 11 Calculate the rms speed for CO 2(g) at 25 C Molecular Effusion and Diffusion What is Effusion? Graham's Law Two gases: same T, P and identical containers. The rates of effusion would be: r 1 = v 3RT rms1 MM 1 = r 2 v rms2 3RT = MM 2 ; MM 1 MM 2 r 1 r 2 = MM 2 MM 1 The lighter gas has the higher effusion rate. 7

8 Diffusion What is it? What is the means free path and how does it depend on pressure? We can compare: For all these: ratio = MM 2 MM 1 -rates of effusion or diffusion -distance traveled -time needed -number of moles effused *Arrange the MM ratio as needed, because is not always the inverse, so that the answer makes sense (lighter faster)*. Problem x10-4 mol N 2 effuses in 105 sec. How long would it take for 2.2x10-4 mol H 2 to effuse through the same hole under the same conditions? 10.9 Real Gases: Deviations from Ideal Behavior What is the compressibility factor (Z) and why does its curve with respect to pressure look like this? How does the Z curve change if we increase the temperature and why? Under which conditions does the ideal gas model break down and why? 8

9 Real Gas Models (AKA State Equations) Which are the two requirements for a real gas model equation to be valid? The first real equation was proposed by an der Waals and it looks like this: RT = (P + a m 2 ) ( m b) What corrections did dw make to the ideal gas equation? What is the problem with the dw equation? Ideal Model dw Model 9

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