How many moles are in a breath of air whose volume is 2.32L at body temperature (37 C) and a pressure of 745 torr?

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1 Lecture 9 State of gas described by (n,p,v,t) n # moles P pressure V volume T (absolute) temperature (K) Sample Problem A balloon filled with helium has a volume of 1.60 L at 1.00 atm and 25oC. What will the volume of the balloon be after it is cooled in liquid N2 to 196oC while remaining at a pressure of 1.00 atm? Ideal Gas Law PV = nrt T in absolute T (K) R gas constant Units of R are important Latm R = mol K J R = mol K Sample Problem: How many moles are in a breath of air whose volume is 2.32L at body temperature (37 C) and a pressure of 745 torr? Summer Chem 6 Study Guide

2 Lecture 9 STP Standard Temperature and Pressure 0 C and 1 atm V STP = 22.4L/mol Note STP for gases is not the same as standard state conditions used for H density = d = P M RT Molecular weight = M = drt P Sample problem What is the molecular weight of a gas that has a density of 2.05g/L at STP? Summer Chem 6 Study Guide

3 Ideal Gas Laws 1. Assume that one of the cylinders of an automobile engine has a volume of 400 cm 3. The engine takes in air at a pressure of 1.00 atm and a temperature of 27 C and compresses it to a volume of 50.0 cm 3 at 77 C. What is the final pressure of the gas in the cylinder? (The ratio of before and after volumes, in this case 400:50 or 8:1, is called the compression ratio.) a) 8.00 atm b) 9.33 atm b) 11.4 atm c) 22.8 atm 2. At 46 C and atm pressure, a gas occupies a volume of L. How many liters will it occupy at STP? a) L b) L c) 0.452L d) 22.4 L 3. A) A large 250 L tank is evacuated and then connected to a 50.0 L bulb filled with compressed argon. After they are joined, the pressure in the bulb falls to 2.2 atm. If the temperature remains at 25 o C throughout this process, what was the initial pressure in the 50 L bulb? HINT Draw a picture of the tank and bulb connected to one another. (a) 2.6 atm (b) 4.4 atm (c) 11.0 atm (d) 13.2 atm (e) 17.6 atm B) How many moles of argon are in the tank and the bulb at the end of the experiment? (a) (b) (c) (d) (e) 22.5 moles 4.50 moles 53.6 moles 27.0 moles 322 moles Summer Chem 6 Study Guide

4 Gas Density 1. A) Calculate the density of SO 3 gas at 0.96 atm and 35 C. a) g/l b) 2.43 g/l c) 3.04 g/l d) 21.4g/L e) 26.7 g/l B) Calculate the molar mass of a gas if 4.40 g occupies 3.50 L at 560 torr and 41 C. a) 5.74g/mole b) g/mole c) 44.0g/mole d) 75.gg/mole e) 35.9g/mole 2. A hydrocarbon used with oxygen as a general anesthetic is 85.7% C and 14.3% H by mass. If 1.56 g of this hydrocarbon occupies a volume of 1.00 L at atm and 50.0 o C, what is the molecular formula of the gas? (a) CH 4 (b) CH 2 (c) C 3 H 6 (d) C 6 H 12 (e) C 4 H Forty miles above the earth s surface the temperature is 250 K and the pressure is only 0.20 mmhg. What is the density of air at this altitude. (For this calculation assume that air is an ideal gas with an average molecular mass of 29.0 g/mol) a) 0.283g/L b) g/l c) g/l d) g/l e) g/l Summer Chem 6 Study Guide

5 Lecture 10 Partial pressure: the pressure a gas would have if it was the only gas in the container. Dalton s Law of Partial Pressures Total pressure is equal to the sum of partial pressures. The fraction of the total pressure contributed by each gas is equal to its mole fraction: Χ i Χ i = P P i = TOT n n Sample Problem TOT Use the table of data to answer the questions about the following mixture of gases. P TOT = 824 torr Gas Mole fraction T = C Ar V TOT =5.00 L N CO Ne O 2? a. What is the partial pressure of O 2 in the vessel? i b. How many moles of gas are in the container? c. How many moles of Ar are in the mixture? d. What is the volume occupied by the CO 2? Summer Chem 6 Study Guide

6 Lecture 10 KINETIC MOLECULAR THEORY gives a view of gases on a molecular level 5 key postulates 1. Molecules move in straight lines; their direction is random. 2. Molecules are small. (The volume they occupy is small compared to the total V.) 3. Molecules do not attract or repel each other (no intermolecular forces). 4. Elastic collisions 5. Mean kinetic energy ε T(K) There are three flasks of gas, all at room temperature (25 C); one has Ne at 1 atm, the second has N 2 at 2 atm, and the third has CO 2 at 1 atm. a) Which gas has the greatest average molecular speed? b) Which gas has the greatest average kinetic energy? c) Which gas has the greatest number of collisions with the walls? Summer Chem 6 Study Guide

7 Gas Law Problems 1. What volume (in ml) of ammonia gas will be produced if 50ml of N 2 gas reacts with 150 ml of H 2 gas via the equation below? The pressure and temperature are held constant. N 2 (g) + 3H 2 (g) 2 NH 3 (g) a) 50 ml b) 100 ml c) 150 ml d) 200 ml e) There is insufficient information to answer this question. 2. If 34g of NH 3 gas and 36.5g of HCl gas are combined in a 2 L flask at STP, the following reaction will occur. What will the final pressure in the flask be if the volume and temperature are held constant during the reaction? a) 1.00 atm b) 5.65 atm c) 11.2 atm d) 22.4 atm e) 24.5 atm Partial Pressures NH 3 (g) + HCl(g) NH 4 Cl(s) 3. A) 2.5 L of He(g) at 4.2 atm pressure and 25 C and 3.1 L of O 2 (g) at 7.4 atm pressure and 25 C are combined at constant temperature into a 7.5 L flask. What is the mole fraction of He(g) in the 7.5 L flask? (a) 0.31 (b) 0.69 (c) 0.45 (d) 0.55 (e) 0.33 (f) 0.66 B. What are the partial pressures of O 2 and He in the 7.5 L flask? C. What is the total pressure in the 7.5 L flask? Summer Chem 6 Study Guide

8 4. If a sample of air at 750 torr and 25 C contains 6.0 ppm CO, how many moles of CO are in a 1-L sample? a) moles b) moles c) moles d) moles Kinetic Molecular Theory 5. There are three flasks of gas, all at room temperature (25 C); one has Ne at 1 atm, the second has N 2 at 2 atm, and the third has CO 2 at 1 atm. HINT: You should be able to answer this without doing any calculation. a) Which gas has the greatest average molecular speed? b) Which gas has the greatest average kinetic energy? c) Which gas has the greatest number of collisions with the walls? 3. A) At 25 C, which of the following molecules has the greatest average kinetic energy? A. CH 4 B. CO 2 C. Ar D. The molecules will have the same average kinetic energy. B) Which one of the following molecules has the greatest average molecular speed? A. CH 4 B. CO 2 C. Ar D. The molecules will have the same average molecular speed. 6. N 2 gas effuses through a pinhole in 5.5 seconds. An equivalent amount of an unknown gas effuses through the same pinhole in 4.2 seconds. What is the molecular weight of the unknown? (a) 48 g/mole (b) 37 g/mole (c) 21 g/mole (d) 16 g/mole HINT: Before you try to figure out the answer, decide if the unknown gas is heavier or lighter than N 2? Eliminate any choices that are not consistent with your response. Summer Chem 6 Study Guide

9 Additional Questions 1. Under what conditions is a gas most likely to behave as an ideal gas? (a) T = 300K (b) T = 300 C (c) T = 30K (d) T = 30K (e) STP P = 25 atm P = 25 torr P = 25 torr P = 25 atm 2. Under which conditions would the gas be least likely to have ideal behavior? (a) T = 300K (b) T = 300 C (c) T = 30K (d) T = 30K (e) STP P = 25 atm P = 25 torr P = 25 torr P = 25 atm 3. Which of the following plots correspond to ideal gas behavior? V V PV nrt P n P I II III a) I only b) II only c) III only d) II and III only e) All of them Summer Chem 6 Study Guide

10 Atmospheric 1. Use the reactions below to answer the following questions. (a) N 2 (g) + hν 2N(g) (b) Cl(g) + O 3 (g) O 2 (g) + ClO(g) (c) O(g) + O 2 (g) O 3 (g) (d) O 3 (g) + hν O(g) + O 2 (g) (e) N 2 (g) + hν N + 2 (g) (f) CF 2 Cl 2 (g) + hν CF 2 Cl(g) + Cl(g) a) Which one of the reactions is an example of photoionization? b) Which of the reactions are examples of photodecomposition? c) Which of the reactions are partially responsible for filtering out high energy solar radiation in the thermosphere? (Which regions of the electromagnetic spectrum correspond to these wavelengths?) 2. The photoionization of N 2 in the thermosphere requires 80.1 nm light. From this information, determine how much energy is needed to ionize a mole of N 2 molecules. (a) 2.48 x J (b) 2.48 x J (c) 1.49 x 10 6 J (d) 1.49 x 10 3 J (e) 8.01 x 10 8 J (f) 8.01 x 10 6 J HINTS: How much energy is needed to ionize one N 2 molecule? (Remember: in the equation, E = hν, E is the energy of one photon, not a mole of photons.) How much energy is needed to ionize one mole of N 2? 3. When the photodecomposition of nitrogen occurs in the upper atmosphere: hν + N 2 (g) 2N(g) H = 941 kj/mol What wavelength of light is absorbed? In which region of the electromagnetic spectrum is the light found? (a) 941 nm (b) 533 nm (c) 412 nm (d) 300 nm (e) 127 nm Summer Chem 6 Study Guide

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