Gases 1

 Describe a gas sample. Describe the position and motion of atoms/molecules in a sample. Gases assume the volume and shape of their containers. Gases are the most compressible state of matter. Gases will mix evenly and completely when confined to the same container. Gases have much lower densities than liquids and solids. 2

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4 Pressure = force/area Pa = N/m 2 1 atm = 760 torr = 760 mm Hg = kPa Sea level1 atm 4 miles0.5 atm 10 miles0.2 atm

 Atmospheric Pressure: pressure exerted by Earth’s atmosphere; measured by a barometer  Standard atmospheric pressure: column of mercury is 760 mm high at 0 o C at sea level.  What is 475 mmHg in atm? 5

 Which image shows P atm > P gas ?

 What causes the observed ideal gas behavior?  Model of gases is Kinetic Molecular Theory ◦ 1. A gas consists of tiny particles, either atoms or molecules, moving about at random.  low density and compressible ◦ 2. Volume of particles is negligible compared to the total volume of the gas; most of the volume is empty space  Xe at STP, only 0.025% of the volume is occupied by the atoms 7

◦ 3. Gas molecules move independently of one another  no intermolecular forces to attract atoms/molecules ◦ 4. Pressure arises from collisions of atoms/ molecules with walls of containers  no net energy loss from collisions  pressure is proportional to number of moles ◦ 5. Average kinetic energy (KE) is proportional to the Kelvin temperature (T) 8 Gas Simulation

 Ideal gas: pressure-volume-temperature behavior can be accounted for by the ideal gas equation ◦ Many gases behave ideally at 0 o C and 1 atm  STP = Standard temperature (0 o C = K) and pressure (1 atm) ◦ Convert variables to Kelvin and atm to correctly solve problems  K = o C ; 1 atm = 760 torr  Ideal gases behave according to the Ideal Gas Law: PV = nRT

 We can calculate volume of 1 mole of gas at 0 o C and 1 atm. How many molecules (or atoms) will be in this sample?  1 mol = L

 What is the volume of g of nitrogen gas at STP?  How many grams of neon gas will occupy a volume of 1.0 L at STP?

 What happens if the pressure on the outside of a balloon is increased? What happens to the atoms inside the balloon?  What causes the can to be crushed? Crushing can be scaled up a little! Can crush

14 Bicycle Pump Boyle’s Law

 Why does a bag of potato chips expand as you drive from Phoenix to Flagstaff?  If a closed bag holds L of gas at atm, what is the volume of the bag if the pressure is decreased to atm?  P 1 V 1 = P 2 V 2  V 2 = L

 What happens if the balloon is slowly heated? What will happen to the atoms inside?

 Charles and Gay-Lussac 17 Balloons in LN 2

 If a balloon holds 3.97 L of gas at 2.0 o C, what will the volume be if the temperature of the gas increases to 90.0 o C?  V 1 /T 1 = V 2 /T 2  V 2 = 5.24 L

 What happens as more atoms are added to the balloon? Where have you experienced this before?

 Avogadro’s Law 20 Figure 9.9

 If we have a closed container that holds 1.08 moles of gas with a volume of 16.7 L. What will be the new volume of the container if 0.65 more moles of gas are injected?  V 1 /n 1 = V 2 /n 2  V 2 = 26.8 L

 Boyle’s Law (T, n constant) ◦ PV = constantP 1 V 1 = P 2 V 2  Charles’ Law (P, n constant) ◦ V / T = constantV 1 /T 1 = V 2 /T 2  Avogadro’s Law (P, T constant) ◦ V / n = constantV 1 /n 1 = V 2 /n 2  Combined Gas Law (n constant) ◦ P 1 V 1 / T 1 = P 2 V 2 / T 2 22 Pressure in basketball Gas Simulation

 Draw the level of the piston in (a) and (b) under the specified conditions.

 increase the pressure of a container at constant temperature?  increase temperature at constant pressure?  increase the temperature at a constant volume?  Increase number of gas particles? Cons Vol Double Atoms Dec Vol Cons Atoms Inc Temp Cons Vol

 A small bubble rises from the bottom of a lake, (T = 8.0 o C, P = 6.41 atm, V = 2.1 mL) to the water’s surface (T = 25.0 o C, P = 1.02 atm). What is the final volume of the bubble?  If a closed cylinder holds 50.0 L of O 2 gas at 18.5 atm and 21.0 o C, what volume will the gas occupy if the temperature is maintained while the pressure is reduced to 1.00 atm?  The volume of a nitrogen cylinder is L. What mass of nitrogen gas is in the cylinder if the pressure is 775 torr and the temperature is 5.3 o C? 14 mL; 925 L; 14 g N 2

 There are 2 methods for solving these problems. ◦ If 2 variables in Ideal Gas Law are unknown, use stoichiometry first to find moles of gas (n) to plug into equation. ◦ If only 1 variable in Ideal Gas Law is unknown, solve it first, then use moles of gas (n) in stoichiometry.  What is the volume of CO 2 produced at 37 0 C and 1.00 atm when 5.60 g of glucose are used up in the reaction: C 6 H 12 O 6 (s) + O 2 (g) --> CO 2 (g) + H 2 O (l) 26

 N 2 (g) + H 2 (g)  NH 3 (g)  How many grams of ammonia can be made with 689 L of hydrogen and excess nitrogen at 350 o C and 7.80 atm?  Answer:  How many L of O 2 are needed to react 28.0 g NH 3 at 24°C and atm? NH 3 (g) + O 2 (g)  NO(g) + H 2 O(g) Answer: 27 airbags

 What mass of solid sodium azide (NaN 3 ) is needed to generate 75.2 L of nitrogen gas (and solid sodium) at o C and 1.00 atm?  (Hint: Start with a balanced chemical equation!)

 Gas densities (d), units of g/L ◦ Use MM, P, R, and T to solve  Molar mass (MM), units of g/mol ◦ Use d, P, R, and T to solve  Use units to arrange variables to solve for density and molar mass 29

 Calculate the density of bromine gas at 50.0 o C and torr. 30 Pouring Br 2

 An unknown diatomic gas has a density of g/L at STP. What is the identity of the gas?  Answer: Cl 2 31

 Dalton’s Law of Partial Pressures: In a mixture of gases, each exerts a partial pressure the same as it would exert alone. 32

 We can only measure the total pressure of a system  Knowing what fraction of moles belong to each gas, we can calculate their partial pressures.  Mole fraction: ◦ X A = n A / (n A + n B ) (moles of A ÷ total moles)  Calculating partial pressure: ◦ P A = X A * P T (mole fraction * total pressure)

 A mixture of gases contains mol of CO, mol of CO 2, and mol of O 2. Calculate the mol fraction and partial pressures of the gases if the total pressure is 1.50 atm at room temperature.  Answers: ◦ X CO = ; P CO = atm ◦ X CO2 = 0.434; P CO2 = atm ◦ X O2 = 0.492; P O2 = atm

 Diffusion: gradual mixing of one gas with another (applet link)applet link ◦ Lighter gas diffuses more quickly than heavier gas  Effusion: escape of a gas through a pinhole (used to separate different mass species) 37 effusion

 Molecular Speeds depend on Temperature: 38 Avg KE of gas

 Which molecule will escape from a leaky balloon fastest? 39

 Which gas in each pair below will effuse faster?  CH 4 and N 2  O 2 and CO 2  CO and NH 3  Cl 2 andH 2  KrandSO 2