# Temperature. Number of moles. Constant Terms. Pressure. Answers Additional Questions 12.1

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1 Answers Additional Questions A gas collected over water has a total pressure equal to the pressure of the dry gas plus the pressure of the water vapor. If the partial pressure of water at 25.0 degrees Celsius is 3.2 KPa and the total pressure is KPa, what fraction of the total pressure is the water vapor? Pressure H 2 O = Molecules H 2 O = Volume H 2 O Total Pressure Total Molecules Total Volume 3.2 KPa = 3.2% water vapor KPA 2. Divers under great pressure breath a mixture of 79% helium and 21% oxygen by volume to prevent nitrogen from being forced into the bloodstream. If the tank's total pressure is 9120 mm Hg what is the partial pressure of oxygen? Pressure O 2 = 21% 0.21 * 9120 mmhg = 1900 mmhg O 2 Total Pressure 3. What conditions are held constant in Charles' Law? # moles and pressure are constant Volume P V = N R T Constant Temperature Pressure Number of moles Volume = Number Moles * Constant Temperature Pressure Constant Terms Volume 1 = Volume 2 Temperature must be in Kelvin Temperature 1 Temperature 2 Volume is directly proportional to Temperature Why does a gas expand when heated? Think of a balloon as having constant pressure due to the flexibility of the covering. As the temperature increases the kinetic energy of the gas increases, causing the molecules to move faster, striking the covering more often and with greater force. The covering expands under the increased force making the volume larger.

2 4. A balloon with a volume of 1.35 liters at 27.0 degrees Celsius is brought outside to a temperature of 12.0 degrees Celsius. What will the new volume of the balloon be? V1 = 1.35 liters V2 =? T1 = 27 Celsius T2 = 12 Celsius Kelvin = Celsius Kelvin 285 Kelvin P1 = P2 Volume 1 = Volume L = V2 V2 = 1.28 L Temperature 1 Temperature K 285 K 5. What conditions are held constant in Gay-Lussac's Law? # moles, volume constant Constant terms P = N * R P1 = P2 T V T1 T2 Pressure is directly proportional to temperature (Kelvin) Why does the pressure of a gas decrease when it's cooled? As temperature decreases the kinetic energy drops, decreasing the number of collisions and the force of collisions with the container walls. 6. A car tire with a constant volume is filled with 202 KPa pressure at 25.0 Degrees Celsius when a trip begins. What will the new tire pressure be if the temperature rises to 30.0 Degrees Celsius during the trip? P1 = 202 KPa P2 =? T1 = 25 Celsius T2= 30 Celsius 298 Kelvin 303 Kelvin V1 = V2 P1 = P2 202 KPa = P2 P2 = 205 KPa T1 T2 298 K 303 K 7. A diver needs to compress liters of air at 760 mm Hg pressure into a tank with a volume of 30.0 liters. If the temperature stays the same, what will the air pressure in the tank be? V1 = 400 L V2 = 30 L P1 = 760 mm Hg P2 =? T1 = T2 P * V = N * R * T Constant terms Pressure is inversely proportional to volume (Boyles Law) 400 L * 760 mmhg = P2 * 30 L P2 = mmhg P1 * V1 = P2 * V2

3 8. A weather balloon with 775 liters of gas is released at 102 KPa pressure and 25.0 Degrees Celsius. What will its volume be when it reaches maximum height with a pressure of 45 KPa and a temperature of 5.7 Degrees Celsius? V1 = 775 L V2 =? P1 = 102 KPa P2 = 45 KPa T1 = 25 Celsius T2 = 5.7 Celsius 298 Kelvin 279 Kelvin Constant Terms P * V = N * R P1 V1 = P2 V2 (Combined Gas law) T T1 T2 102 KPa 775 L = 45 KPa V2 V2 = 1640 L 298 Kelvin 279 Kelvin 9. Standard temperature is 0 degrees Celsius (273 Kelvin), standard pressure is 760 mm Hg (101.3 KPa). If 1.0 mole of a gas occupies 22.4 liters at standard temperature and pressure, calculate the ideal gas law constant R for volume in liters and pressure in mmhg. R = P * V = 760 mmhg 22.4 L = 62.4 mmhg L N * T 1.0 mole 273 Kelvin or KPa 22.4 L = 8.31 KPa L 1.0 mole 273 Kelvin 10. Use the ideal gas law to find the volume of 13.5 grams of nitrogen gas at 105 KPa and 29.0 degrees Celsius. Hint: Convert grams to moles g N 2 * 1 mole N 2 =.482 moles N g N 2 V = N * R * T = moles * 8.31 KPa L * 302 Kelvin = 11.5 L P mole Kevin 105 KPa 11. What mass will 5.75 liters of carbon dioxide gas have at 97.5 KPa and 17.0 degrees Celsius? Hint: Find moles and convert to grams. N = P * V = 97.5 KPa 5.75 L = moles R * T 8.31 KPa L 280 Kelvin moles CO 2 * 44.0 grams CO 2 = 10.3 g CO 2 1 mole CO 2

4 12. What is the density of water vapor at 25.0 Degrees Celsius and 755 mm Hg pressure? Hint: Find the mass and volume of 1.0 mole of water vapor. N = P = 755 mmhg = mole V R * T 62.4 mmhg L 298 Kelvin L mole H 2 O * 18.0 g H 2 O = g 1 mole H 2 O L 13. What volume of oxygen gas is produced when 37.5 grams of potassium chlorate decomposes at 45.0 degrees Celsius and 115 KPa pressure? Hint: Find the moles of oxygen gas produced and then calculate the volume. 2 KClO 3 -> 2 KCl + 3 O g KClO 3 * 1 mole KClO 3 * 3 moles O 2 = mole O grams KClO 3 2 moles KClO 3 V= N * R * T = moles * 8.31 KPa L 318 Kelvin = 10.5 L O KPa 14. Show that the volume of a gas is directly proportional to the number of moles of the gas if the pressure and temperature are held constant. (Think of blowing up a balloon) P * V = N * R * T P, V constant V = R * T V1 = V2 Volume is directly proportional N P N1 N2 to number of moles liters of nitrogen gas and 3.5 liters of hydrogen gas react at constant temperature and pressure to produce ammonia (NH 3 ). What volume of ammonia is produced? Hint: Use the proportion in question 17. N H 2 -> 2 NH 3 Since the temperature and pressure are constant the ratio of moles is also the ratio of gas volumes 1.5 L N 2 * 2 moles NH 3 = 3.0 L NH 3 1 mole N L H 2 * 2 moles NH 3 =2.3 L NH 3 3 moles H 2 Hydrogen gas limits the reaction because it produces a smaller amount of ammonia gas.

5 16. Air has an average mass of 29 amu. What is the ratio of velocities between air and gasoline vapor (C 8 H 18 ) if the temperature is the same? Graham's Law Velocity of gas 1 = Mass of gas 2 Velocity of gas 2 Mass of gas 1 At equal temperatures the heavier gases travel more slowly Velocity Air = Mass of Gasoline = 114 amu = 2.0 Velocity Gasoline Mass Air 29 amu The air travels at twice the speed of gasoline vapor 17. A chemist collects 1040 ml of gas over water at 25 Degrees Celsius and 122 KPa total pressure. The partial pressure of water at 25 degrees Celsius is 3.2 KPa. What is the volume of the dry gas at standard temperature and pressure? Percentage = Pressure = Total - Water vapor = 122 KPa KPa = 97% dry gas dry gas pressure pressure 122 KPa Total pressure Total pressure Percentage of = Percentage of = Percentage of Dry gas pressure Dry gas volume moles of Dry gas 0.97 % * 1040 ml = 1009 ml of Dry Gas

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