9.1 K-M Theory and Ideal Gases

Transcription

1 9.1 K-M Theory and Ideal Gases The Kinetic-Molecular (K-M) Theory is a series of ideas and simplifications which allow us to describe and predict the behavior of gases. #1) Gas particles travel randomly, but in straight lines between collisions. This explains diffusion, how gases spread through other gases. Think of farts... #2) Gas particles are infinitely small compared to the space they occupy (volume). V 0 By comparison, solids and liquids are very-tightly packed together with little space between particles. ~ 1 ~

2 #3) Gas particles have elastic (bouncing) collisions with each other and the walls of their containers. Gases striking the walls create pressue, high-speed gas particles ricochet when they hit other particles. #4) Gas particles neither attract nor repel. Meh... Real gases, such as oxygen and hydrogen, actually DO attract each other a bit. We normally ignore this as it greatly simplifies calculations involving gases These 4 concepts describe what is called an ideal gas. Real-world gases are more likely to have ideal behavior at high temps, and low pressures. ~ 2 ~ Meh...

3 Ex.1) Out of each of the following pairs of gas samples, which would you expect to display the most ideal behavior? H 2 (g) at 450 C OR H 2 (g) at 7600 C CO 2 (g) at 1.4 atm OR CO 2 (g) at 0.09 atm Ex.2) Unlike liquids and solids, gases are highly compressible. Among other things, this allows scuba divers to carry massive volumes of air in their tanks. Which part of K-M theory (1-4) best explains the compressibility of gases? Ex.3) Dry ice (solid CO 2 ), liquid oxygen (LOX) and liquid nitrogen can all be formed by exposing certain gases to conditions which do NOT favor ideal behavior. Under which two conditions will gases liquify or solidify? ~ 3 ~

4 Ex.4) Match each of the observations below with the aspect of K-M theory responsible: 1 - Gases travel randomly between collisions. 2 - Gases have large volumes, tiny particles. 3 - Collisions with container, each other. 4 - No attraction/repulsion between particles. // Gases have extremely low density. // Gases expand to fill their containers. // More gas particles = higher pressure. // All gases have nearly identical behaviors under ideal conditions (high temp/low pressure). // Your ears "pop" when you travel between high and low altitudes (planes, diving). // The smell of spilled gasoline is very noticeable, even from a significant distance. ~ 4 ~

5 Gases are described using the following terms: Pressure (P) Moles (n) Volume (V) Temperature (T) Pressure: a "push" outward created by the countless collisions between gas particles and the walls of their containers. At sea level, the air pressure is 1.0 atmospheres, (atm). Pressure can also be measured in torr (torr), kilopascals (kpa), and millimeters mercury (mmhg). The device shown above is used to measure atmospheric pressure and is called a barometer. ~ 5 ~

6 The relationships between pressures is shown below. Use DA to solve the following questions: 1.00 atm = 760 mmhg = 760 torr = kpa Ex.5) A barometer has a reading of mmhg. Using DA, what is this in atmospheres? Ex.6) Most car tires are inflated to approximately 238 kpa. What is this in torr? Ex.7) atm kpa? Ex.8) 270 torr atm? ~ 6 ~

7 Volume (V): the space occupied by a gas. Unlike liquids and solids, gases expand to completely fill their containers. Common conversions: 1.00 dm 3 = 1.00 L = 1000 ml = 1000 cm 3 (cc) Ex.9) In lab, you collect 48.2 ml of chlorine gas. What is this in liters? Ex.10) Get me 45 ccs of ketamine, STAT! Or dm 3? Ex.11) 58.0 ml N 2 (g) = cm 3 N 2 (g)? Ex.12) L of H 2 (g) is formed as a sample of zinc metal is consumed by an acid at STP. What is this in milliliters? ~ 7 ~

8 Moles (n): the amount of gas particles. 1 mol gas = 22.4 L STP = Molar Mass Ex.13) What is the volume of 5.4 mol O 2 (g) at STP, in ml? Ex.14) What is the mass of 280 ml CO 2 (g) at STP? Ex.15) How many moles of chlorine gas, Cl 2 (g), are contained at STP within a 15.0 L gas cylinder? Ex.16) What is the mass, in mg, of neon gas in a full 2.00 L soda bottle at STP? ~ 8 ~

9 Temperature, (T): a measurement of the average kinetic energy (KE) of gas particles. 500 K 200 K High KE Low KE Measured by degrees Celsius ( C ), and Kelvin, K. We ONLY use Kelvin for " T " in gas laws. There are no negatives in this temperature scale (hence, no "degrees"). Zero Kelvin is called "absolute zero" and occurs when there is no molecular motion. Abs. Zero = F -273 C 0.00 K H 2 O Freezes = 32 F 0 C 273 K Body Temp. = 98.6 F 32 C 330 K H 2 O Boils = 212 F 100 C 373 K Calculating Kelvin and Celsius Temperatures: K = C F = 1.8 x ( C) + 32 "To get K from C, just add 273" ~ 9 ~

10 Use temp. conversions to solve the problems below. K = C F = 1.8 x ( C) + 32 Ex.17) Room temperature is 25 C. What is this in Kelvin? Ex.18) Liquid nitrogen has a temperature of 78 K. What is this in degrees Fahrenheit? Ex.19) The core of a nuclear reactor can reach 950 C. What is this temperature in Kelvin? Ex.20) Complete the following relationships: 18 C = K C = 210 K -30 C = K F = 670 K ~ 10 ~

11 Common Lab Conditions: Gases are greatly influenced by both the temperature and pressure of your lab environment. To control these factors, chemists often make measurements under the following standardized conditions:. STP = Standard Temp and Pressure: 0.0 C and 1.0 atm SATP = Standard Ambient Temp and Pressure: 25.0 C and 1.0 atm Self Check: answer the following questions on your own. Show work and check your answers online at chemhelp.us. Good luck! SC.1) A cylinder contains 5.4e27 molecules CO 2 at standard temperature and pressure. What is its volume, in liters? ~ 11 ~

12 SC.2) Match each of the observations below with the aspect of K-M theory responsible: #1 - Gases travel randomly between collisions. #2 - Gases have large volumes, tiny particles. #3 - Collisions with container, each other. #4 - No attraction/repulsion between particles. // 22.4 L of H 2 (g) has a mass of g. An equal volume of Fe(s) has a mass of ~176,000 g. // When pressurized, large volumes of gas can be stored in very small containers. // Tires rupture when over-filled with air. // Air is a homogeneous mixture of gases. SC.3) Helium liquifies at -269 C. What is this in Kelvin? ~ 12 ~

13 SC.4) What pair of conditions would cause a gas to solidify or liquify? Why? SC.5) Why do gases behave ideally (more like gases) under low pressures and high temperatures? SC.6) The temperature outside while I write this question (2/4/17, 10:47 pm) is exactly 48 F. What is this temperature in Kelvin? SC.7) What is the mass, in mg, of ml chlorine gas if it is collected at STP? ~ 13 ~

14 SC.8) What is the volume, in cm 3, of 1.8 kg argon gas? SC.9) A 20.0 lb block of dry ice, CO 2 (s), is allowed to sublime (solid g) at STP. What is the new volume of this substance, in liters? (2.2 lbs = 1 kg) SC.10) How many atoms of hydrogen would be found in 18.0 L of hydrogen gas? (Let me know if you get this one on the first try!) ~ 14 ~

15 9.2 The Laws and Behavior of Gases Gas laws are mathematical functions which describe the relationships between P, V, n, and T. Almost all of them are expressed in the combined gas law shown below: P 1 V 1 = P 2 V 2 T 1 n 1 T 2 n 2 When reading a problem, identify the variables (changing) and constants (not changing). Cross out constants from the combined gas law and you'll have the equation you need. Ex.1) A sample of methane, CH 4, occupies 30.0 L at a pressure of 2.0 atm. What volume will this gas occupy at 1.0 atm? P 1 V 1 = P 2 V 2 T 1 n 1 T 2 n 2 ~ 15 ~

16 Variables which are "side by side" in the equation have an inverse relationship. When one goes up, the other goes down. Variables which are above or below one another have a direct relationship- they go up or down together. P 1 V 1 = P 2 V 2 T 1 n 1 T 2 n 2 Ex.2) Determine the relationship for each pair of variables described below: Variables: Known as: Relationship: P and V V and T P and T V and n Boyle's Law Charles' Law Gay-Lussac's Law Avogadro's ~ 16 ~

17 Most problems will only use 2 or 3 of the variables in the combined gas law- not all 4. You can write all of these smaller laws by removing variables which are NOT changing from the combined gas law: Ex.3) Derive all 5 of the basic gas laws below: Combined: P 1 V 1 = P 2 V 2 T 1 n 1 T 2 n 2 a.) Boyle's: b.) Charles': c.) Gay-Lussac's: d.) Avogadro's: ~ 17 ~

18 Using the correct gas law is just as important. Identify the variables, how they are changing, and which of the gas laws would apply in each of the real-world scenarios described below: Ex.4) Pumping air into a tire causes it to expand: V n Gas Law = Ex.5) Metal cans of spray paint and soda explode when heated beyond a certain temperature: Ex.6) Balloons shrink in cold weather and no longer float: Ex.7) As the Titanic sank, closed compartments in the ship were crushed as the depth increased: Ex.8) Weather balloons expand as they rise towards the edge of Earth's atmosphere: ~ 18 ~

19 Next, you will want to rearrange gas laws in order to solve for specific variables. You'll find this to be an easy process, especially if you do well in algebra: Ex.9) Solve Boyle's Law for P 2 : P 1 V 1 = P 2 V 2 Ex.10) Solve Avogadro's law for n 1 : V 1 = V 2 n 1 n 2 Ex.11) Solve Charles' Law for V 2 : V 1 = V 2 T 1 T 2 Ex.12) Solve the PVT form of the combined gas law for T 1 : P 1 V 1 = P 2 V 2 T 1 T 2 ~ 19 ~

20 For each of the problems below: Identify the variables which are changing and how. What are we trying to find? Name, write, and rearrange the gas law. Make a prediction for your answer. Ex. 13) Hydrogen gas at a pressure of kpa occupies a volume of 1400 ml. What is the new pressure if the volume increases to 2.00e3 ml? Variables Changing: Name/Rel: Finding? Prediction: Equation: Rearrange: ~ 20 ~

21 Ex.14) A 40.0 L sample of gas at 1.0 atm and K is heated to 720 K and a pressure of 2.5 atm. What is its new volume, in liters? Variables Changing: Name/Rel: Finding? Prediction: Equation: Rearrange: Ex.15) A balloon at room temperature, 25 C, has a volume of 10.2 L. What is the volume of the same balloon if it is immersed in steaming water at 98 C? Variables Changing: Name/Rel: Finding? Prediction: Equation: Rearrange: ~ 21 ~

22 Ex.16) A tire has a volume of 12.1 L and contains 2.4 mol of gas. If the volume increases to 14.0 L, how many moles of gas were added? Variables Changing: Name/Rel: Finding? Prediction: Equation: Rearrange: Ex.17) A rigid bottle of nitrogen gas has a pressure of 45 atm at room temperature. If the bottle can survive up to a pressure of 180 atm, what is the highest temperature it can reach, in C? Variables Changing: Name/Rel: Finding? Prediction: Equation: Rearrange: ~ 22 ~

23 Ex. 18) A gas at 80.0 C has a volume of 450 L. If the gas contracts to 24.0 L, what is its temperature, in C? Variables Changing: Name/Rel: Finding? Prediction: Equation: Rearrange: Ex.19) A hot air balloon has a volume of 2.5 x 10 5 L at 34.0 C. If the balloon climbs into cooler air at a higher altitude and a temperature of 12.0 C, what is the new volume, in liters? Variables Changing: Name/Rel: Finding? Prediction: Equation: Rearrange: ~ 23 ~

24 Ex.20) An 85,000 L steel cargo container falls off the deck of a ship during a storm. While on the ship, the pressure was 1.01 atm. What is the new external pressure on the container if it is crushed to a volume of 470 L as it sinks to the ocean floor? Variables Changing: Name/Rel: Finding? Prediction: Equation: Rearrange: Self Check: answer the following questions on your own. Show work and check your answers online at chemhelp.us. Good luck! SC.1) Deep sea fish (angler fish, etc) swell up and die if they swim to the surface too quickly. Which variables are involved? What is their relationship and which gas law describes it? ~ 24 ~

25 SC.2) Identify the gas law involved and complete the statements below. Assuming all other variables are constant, if... - Pressure increases, volume will... - Temperature decreases, pressure will... - Volume increases, temperature will... - Pressure decreases, temperature will... - Volume increases, pressure will... - Moles increase, volume will... SC.3) An equal mass of helium gas is placed into a variety of cylinders at different temperatures and volumes. Which cylinders would have the lowest pressure. The cylinder with the greatest or the lowest would have the lowest pressure. ~ 25 ~

26 SC.4) A L balloon expands to 4.30 L when heated to 450 K. What was the balloon's initial temp, in C? Variables Changing: Name/Rel: Finding? Prediction: Equation: Rearrange: SC.5) A tire has a volume of 16.0 L when it contains mol of air. If 5.5 L of air leaks through a puncture in the tire, how many moles of air still remain? Variables Changing: Name/Rel: Finding? Prediction: Equation: Rearrange: ~ 26 ~

27 SC.6) When used rapidly, propane cylinders become exceedingly cold. Which gas law explains this? SC.7) Which of the following statements are true? - Double the pressure, double the volume. - Half the temperature, half the pressure. - Triple the temperature, one third the volume. - Four times the volume, one fourth the pressure. SC.8) A fish's swim bladder has a volume of 40.0 ml at 30.0 C. At what temperature, in C, will the bladder contract to a volume of 10.0 ml? Variables Changing: Name/Rel: Finding? Prediction: Equation: Rearrange: ~ 27 ~

28 SC.9) A 10.0 L propane cylinder at a pressure of 140 atm is struck by an armor-piercing bullet. What volume, in liters, will the propane occupy when it is released into standard pressure? Variables Changing: Name/Rel: Finding? Prediction: Equation: Rearrange: SC.10) A gas sample at standard pressure is compressed to 470 kpa at a temperature of 680 K. Determine the original temperature, in C. Variables Changing: Name/Rel: Finding? Prediction: Equation: Rearrange: ~ 28 ~

29 9.3 Solving Gas Laws To solve gas laws, put all of your skills together: Identify changing variables, write a gas equation. Rearrange the equation for the correct variable. Verify that you have the correct units (T= Kelvin!) and re-write the equation with all known variables. Solve, label your answer, and move on! Ex. 1) Hydrogen gas at a pressure of kpa occupies a volume of 1400 ml. What is the new pressure if the volume increases to 2.00e3 ml? ~ 29 ~

30 Ex.2) A 40.0 L sample of gas at 1.0 atm and K is heated to 720 K and a pressure of 2.5 atm. What is its new volume, in liters? Ex.3) A balloon at room temperature, 25 C, has a volume of 10.2 L. What is the volume of the same balloon if it is immersed in steaming water at 98 C? ~ 30 ~

31 Ex.4) An 85,000 L steel cargo container falls off the deck of a ship during a storm. While on the ship, the pressure was 1.01 atm. What is the new external pressure on the container if it is crushed to a volume of 470 L as it sinks to the ocean floor? Ex. 5) A hot air balloon has a volume of 2.5 x 10 5 L at 34.0 C. If the balloon climbs into cooler air at a higher altitude and a temperature of 12.0 C, what is the new volume, in liters? ~ 31 ~

32 Ex.6) A rigid bottle of nitrogen gas has a pressure of 45 atm at room temperature. If the bottle can survive up to a pressure of 180 atm, what is the highest temperature it can reach, in C? Ex.7) A tire has a volume of 12.1 L and contains 2.4 mol of gas. If the volume increases to 14.0 L, how many moles of gas were added? Ex.8) A gas at 80.0 C has a volume of 450 L. If the gas contracts to 24.0 L, what is its temperature, in C? ~ 32 ~

33 Self Check: answer the following questions on your own. Show work and check your answers online at chemhelp.us. Good luck! SC.1) A L balloon expands to 4.30 L when heated to 450 K. What was the balloon's initial temp, in C? SC.2) A tire has a volume of 16.0 L when it contains mol of air. If 5.5 L of air leaks through a puncture in the tire, how many moles of air still remain? ~ 33 ~

34 SC.3) A 10.0 L propane cylinder at a pressure of 140 atm is struck by an armor-piercing bullet. What volume, in liters, will the propane occupy when it is released into standard pressure? SC.4) A fish's swim bladder has a volume of 40.0 ml at 30.0 C. At what temperature, in C, will the bladder contract to a volume of 10.0 ml? ~ 34 ~

35 9.4 Advanced Gas Laws This chapter discusses the same laws and properties practiced in 9.2 with several additional concepts: Examples 1 and 2: STP and SATP are commonlyused references. Refer back to 9.1 if necessary. Ex.1) A balloon at STP has a volume of 4.03 L. What is the new volume at a temperature of 350 K and a pressure of 2.00 atm? Ex.2) A test tube is sealed at STP. What is the new pressure (atm) if the test tube is heated to 240 C? ~ 35 ~

36 Examples 3 and 4: You will often have to convert units so they are the same on both sides and/or solve for the correct unit. Ex.3) In order to fend off a ravening zombie horde, you throw a 15.5 L propane tank at 90.0 atm and 18.1 C into them. Assuming the outside conditions match SATP, what volume will the propane occupy outside the tank when it ruptures, in ml? Ex.4) A balloon on Earth at a pressure of 1.02 atm has a volume of 450 ml. What volume would this balloon have on Mars, in L, where the pressure is 0.60 kpa? ~ 36 ~

37 Example 5: you may have to convert g mol. Ex. 5) A large balloon has a volume of 7.4 L when it contains 0.58 g of hydrogen. Assuming temperature and pressure are held constant, to what volume (in L) will the balloon expand when an additional 2.36 g of hydrogen gas is added? Example 6: Other times, you will have to use Kelvin in your calculations and return to Celsius at the end: Ex.6) A 360 ml gas sample at STP expands to a volume of L at a pressure of 120 kpa. What is the new temperature of the sample, in C? ~ 37 ~

38 Mixed practice - use your knowledge of gas laws and DA to solve the following problems. Ex.7) A 90.0 L balloon contains 50.0 g of oxygen gas. How many grams of oxygen gas must be added in order to expand the balloon to L? Ex.8) L of nitrogen gas at room temperature is heated to 480 K. What is its new volume, in ml? ~ 38 ~

39 Ex.9) L of uranium hexafluoride gas, UF 6 (g), at STP is heated to 230 C at a new pressure of 550 mmhg. What is the new volume of this gas sample, in ml? Ex.10) A L cylinder of gas contains nitrous oxide, N 2 O(g), at SATP. If the cylinder is cooled to 5.00 K, what is the new pressure, in kpa? ~ 39 ~

40 Self Check: answer the following questions on your own. Show work and check your answers online at chemhelp.us. Good luck! SC.1) A balloon has a volume of 32.0 L when it contains 20.0 g of chlorine gas. What mass of chlorine gas must be removed from the balloon in order to decrease its volume by 10.0 L under the same conditions? SC.2) 3.05e6 L of helium gas at SATP are used to provide lift in a blimp during the Super Bowl. At what Kelvin temperature would the blimp theoretically have a volume of exactly 1.00 ml? ~ 40 ~

41 SC.3) Scuba tanks typically have a volume of 1.22e4 ml and store an air mixture at approximately 2.33e4 kpa. If released at standard pressure, what volume will the air mixture occupy, in L? SC.4) A 40.0 ml gas sample at standard temperature is heated to the surface temperature of the sun, 5505 C. What is its new volume, in L? SC.5) 1.00 L of chlorine gas at STP is compressed to 2.00 ml. Assuming constant temperature, what pressure, in atm, would be required? ~ 41 ~

42 9.5 The Ideal Gas Law / Partial Pressures The ideal gas law allows us to calculate the moles of a gas from the current conditions of that gas - P, V, and T. This equation is useful for determining the mass of a gas (from the moles) as it is very difficult to measure otherwise. P V = n R T P = pressure in atm, mmhg/torr, or kpa V = volume, in L. n = moles (can be calculated from mass) R = ideal gas contant (see below ) T = temperature, in K. "R" changes depending on the units of pressure: For atm: R = (L atm) / (mol K) For kpa: R = 8.31 (L kpa) / (mol K) For mmhg/torr: R = 62.4 (L mmhg) / (mol K) ~ 42 ~

43 When to use it: the ideal gas law is a state equation, meaning that it describes a substance as it is right now. Look for several variables (usually P, V, and T) with NONE of them changing (no Var). Ex.1) Last chapter, I taught you that a mole of an ideal gas would occupy 22.4 L at STP. Prove this by solving the ideal gas law for the volume of 1.00 mol of a gas at STP. Ex.2) A sample of fluorine gas at SATP has a volume of 80.0 L. How many moles of fluorine are in the sample? ~ 43 ~

44 Ex.3) A 10.0 L diver's tank contains 14.5 mol of O 2 at C. What is the pressure, in atm, inside the tank? Ex.4) 2.4 mol Cl 2 (g) is stored in a 3.00 L container at 25 C. What is the pressure inside the container, in kpa? Ex.5) In lab, you collect 22.1 ml of butane gas from a lighter. Assuming SATP, what mass of butane, C 4 H 10 (M r = ), have you collected? ~ 44 ~

45 Ex.6) A student captures 55.6 ml of O 2 from a reaction in a small flask. If the barometer reads 737 mmhg and the temperature is 23 C, how many grams of O 2 have you collected? Ex.7) Prior to lab, you determine that a decomposition reaction will produce 46 g of carbon dioxide. If you plan to capture this gas at SATP, what volume of container (in liters) will be necessary? ~ 45 ~

46 The final gas law, Dalton's Law of Partial Pressures, states that the total pressure of a mixture of gases is equal to the sum of all individual (partial) gas pressures: P t = P 1 + P 2 + P 3... Like most gas laws, the unit of pressure does not matter as long as you are consistent. Use this equation when you are given multiple pressures and no other useful information. Ex.8) The air around you has a total pressure of about 1.00 atm. If nitrogen gas, N 2, has a pressure of 0.77 atm in air, and other gases add up to about 0.01 atm, what is the pressure due to O 2, oxygen gas? ~ 46 ~

47 Ex.9) A diver's tank contains 33.4 atm of oxygen gas and 12,000. torr of nitrogen gas. What is the total pressure in the tank, in atm? Ex.10) A sample of chlorine gas is generated over water at an atmospheric pressure of mmhg, creating a mixture of both water vapor and chlorine gas. If the water vapor has a pressure of 23.5 mmhg under these conditions, what is the pressure of the chlorine gas, in atm? ~ 47 ~

48 Self Check: answer the following questions on your own. Show work and check your answers online at chemhelp.us. Good luck! SC.1) Determine the mass, in g, of an oxygen gas sample with a volume of L at SATP. SC.2) How many moles of argon are found in a L sample at STP? SC.3) A mixture of water and carbon dioxide gases is collected at a pressure of 740 mmhg. If the partial pressure of the water is 26 torr, what is the partial pressure of the carbon dioxide gas, in mmhg? ~ 48 ~

49 SC.3) Calculate the mass, in mg, of a 430 ml sample of hydrogen gas at 230 C and 140 kpa: SC.4) A dive tank contains a mixture of helium and oxygen gases at pressures of 34,000 mmhg and 160 atm, respectively. What is the total pressure of the dive tank, in kpa? SC.5) Determine the volume, in L, of 84 g oxygen gas stored at SATP: ~ 49 ~

50 SC.6) Calculate the volume of 450 g argon gas at STP, in L: SC.7) What is the partial pressure of hydrogen gas, in torr, if a container has a total pressure of 1.80 atm and also holds 920 mmhg of xenon gas? SC.8) What is the temperature, in C, of a 12.0 g sample of nitrogen gas if it is stored in a 2.50 L bottle at 95.0 atm? ~ 50 ~

51 SC.9) A reaction produces 350 ml of hydrogen gas at SATP. What mass of hydrogen gas, in mg, has been produced? SC.10) A mixture of water vapor and carbon dioxide gas is produced by a combustion reaction at standard pressure. If the water vapor has a partial pressure of 68 kpa, what is the pressure of the carbon dioxide, in atm? ~ 51 ~

52 9.6 Stoichiometry and Gas Laws When to use it: the problem has given you one substance, is asking you for another substance, and one or both are measured in terms of volume. These problems are identical to normal stoichiometry problems in all ways except when converting between moles and liters (or vice versa). At STP, this can be done using "22.4 L = 1 mol" as part of a DA. Under any other conditions, you must use PV = nrt to bridge moles and STP? Use DA (1 mol gas = 22.4 L) Not STP? Use PV = nrt (Ideal gas law) This is best visualized by comparing the "old" with the "new". Let's say I asked you to convert 25 g of substance "A" into milliliters of substance 25 g A mol A mol B 22.4 L B 1000 ml B g A mol A 1 mol B 1 L B ~ 52 ~

53 ...and under ANY other conditions, including SATP: 25 g A mol A mol B g A mol A P V = n R T answer, in liters B 1000 ml B = final answer 1 L B in ml B (Examples 1 and 2) These examples compare when to use the 22.4 L "shortcut" and when not to do so: Na 2 CO 3 (s) Na 2 O(s) + CO 2 (g) Ex.1) If the reaction above is carried out at STP, calculate the volume of carbon dioxide gas (in liters) formed by the decomposition of 48 g Na 2 CO 3 : ~ 53 ~

54 Ex.2) STP is not realistic in most labs. Recalculate the volume of CO 2 produced in Ex.1 if the reaction were carried out at 724 mmhg and 22.0 C: Only assume STP if it is stated in the problem! (Examples 3-5) Nitrogen dioxide is a gas produced by combustion engines most commonly known as "smog". This gas appears as a reddish haze over crowded cities and reacts with water in the air to form nitric acid, one of the components of acid rain, according to the equation below: 3 NO 2 (g) + H 2 O(l) 2 HNO 3 (aq) + NO(g) This acid can concentrate in lakes and ponds over time, leading to massive environmental damage. ~ 54 ~

55 Ex.3) If 3.5 L of nitrogen dioxide gas at STP is released into the atmosphere, what mass of nitric acid could potentially be produced? Ex.4) If those same 3.5 L of nitrogen dioxide gas are released by a jet engine at 1500 C and 1.6 atm, what mass of nitric acid could be produced? Ex.5) What is the predicted volume (in ml) of nitrogen monoxide gas produced by the reaction of 260 g of nitrogen dioxide gas at 36 C and 99.8 kpa? ~ 55 ~

56 (Ex.6 - Ex.10) 159 million tons of ammonia, NH 3 (g), is produced via the synthesis reaction shown below each year. This process fertilizes the crops which have allowed our population to expand beyond 7 billion. Balance the equation below and use it to answer the questions which follow: N 2 (g) + H 2 (g) NH 3 (g) Ex.6) If the reaction consumes L of nitrogen gas at STP, what volume of hydrogen gas will also be consumed, in liters? Ex.7) How many liters of nitrogen gas, at SATP, would be required to produce 1.00 kg of ammonia? ~ 56 ~

57 Ex.8) What volume of ammonia, in L, could be produced at 120 C and 170 atm from 150 g of hydrogen gas? Ex.9) What mass of nitrogen gas, in g, would be required to react with 45 L of hydrogen gas at STP? Ex.10) How many liters of ammonia could be produced from g of hydrogen gas at 35 C and 850 torr? ~ 57 ~

58 Self Check: answer the following questions on your own. Show work and check your answers online at chemhelp.us. Good luck! (SC.1 - SC.5) Balance the equation below and calculate the molar masses. Use this equation to answer the self-check questions which follow: O 3 (g) + H 2 O(l) H 2 (g) + O 2 (g) SC.1) If the reaction consumes L of ozone, O 3 (g), at STP, how many liters of hydrogen gas are produced? SC.2) How many moles of ozone and water are necessary to produce 10.0 L of hydrogen gas at STP? ~ 58 ~

59 SC.3) What volume of ozone gas at 150 K and 2.4 atm will be required to produce g of oxygen gas? SC.4) Assuming excess water, how many liters of oxygen gas at 250 C and 0.90 atm can be produced from 480 mg of ozone gas? SC.5) If the reaction consumes 0.25 mol of water, what volume of oxygen gas, in milliliters will be produced at 40.0 C and kpa? ~ 59 ~