CHEM 105 Problem Set 21 PDF

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Problem Set 21 – Gas Laws Chem 105 1. Which of the following are not characteristics of an ideal gas? a) The molecules of gas have little volume compared with the volume that they occupy. b) Its volume is independent of temperature. c) The density of all ideal gases is the same. d) Gas atoms or molecules do not interact with one another. 2. What would happen to the pressure of an ideal gas under each of the following conditions? a) Doubling the volume while keeping the temperature and moles constant. Pressure will decrease by ½ ; inverse relationship between volume and pressure b) Reducing the temperature (in Kelvin) to 1/3 the original value while keeping the volume and moles constant. Pressure will decrease by 1/3 ; p and t are directly proportional c) Quadrupling the number of moles while keeping the volume and temperature constant. Pressure will quadruple. Pressure and number of mole directly proportional d) Doubling the volume and doubling the number of moles while keeping the temperature constant Wont change the pressure e) Reducing the temperature (in Kelvin) by 1/3 while doubling the volume and keeping the number of moles constant. Pressure drops by 1/6 f) Quadrupling the number of moles while decreasing the volume by ½ and reducing the temperature (in Kelvin) to ¾ the original value. Pressure increases by a factor of 6 3. One cold winter night, you discover that your thermometer is broken and you decide to use your knowledge of the gas laws to determine the outside temperature. In your warm 75.0 F house, you fill a balloon with an ideal gas to a diameter of 1.560 feet. You place the balloon outside until it equilibrates with the cold. You measure the new diameter to be 1.510 feet. What is the temperature outside? (Note: treat the balloon as a sphere, with volume � = # ��$) T2 =297.0 K (1.510/1.560) ^2 = 269.3 K = -3.85 degrees C = 25.1 degrees F 4. A spherical weather balloon has a diameter of 3.50 feet at a temperature of 78 F inside an arctic weather station at sea level (P = 1.0 atm). a) If the temperature is –35 F outside, what will be the diameter of the weather balloon (in feet) outside the weather station? Assume a constant pressure. T1 = 5/9 (78 f – 32) = 26 c + 273.15 K = 299K T2 = 5/9 (-35 -32) = -37 c + 273.15 K = 236 K D2/d1 ^2 = d2 = d1 (t2/t1) = 3.50 ft (236 k/ 299 k) ½ = 3.23 ft b) If the balloon is released and rises to an altitude where the pressure is 100 torr (and the T is still 35 F), what will be the diameter? 3.50 ft (760 torr/ 100 torr) ½ = 6.88 ft 5. The world record for diving without supplemental air tanks (“breath-hold diving”) is about 125 m, a depth at which water pressure is about 12.5 atm. If a diver’s lungs have a volume of 6 L at the surface of the water, what is their volume at a depth of 125 m? (1 atm) (6 L) = (12.5 atm) V2 = 0.5 L

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A bicycle racer inflates his tires to 7.1 atm on a warm autumn afternoon when temperatures reached 27°C. By morning the temperature has dropped to 5.0°C. What is the pressure in the tires if we assume that the volume of the tire does not change significantly? 7.1 atm / 300 k = p2 / 278.2 K p2 = 6.6 atm

7. Suppose atmospheric temperature and pressure at the top of a ski run are –5°C and 713 mmHg. At the bottom of the run, the temperature and pressure are 0°C and 734 mmHg. How many more moles of oxygen does a skier take in with a lungful of air at the bottom of the run than at the top? Express your answer as a percentage. 734 mmHg x 268 K/ 713 mmHg x 273 = 1.01 or 101% The skier breathes in 1% more air at the bottom of the ski run than he breathes in at the top of the run...