More Practice with Gas Laws KEY Chemistry Directions: For each question, identify the applicable law and solve for the correct answer using dimensional analysis. Express your answer to the correct number of significant figures. Use scientific notation where appropriate. Record all work in your science notebooks. I. Gas Law Problems 1. A sample of hydrogen gas occupies a volume of 1.8 L at 0.80 atm. What would its volume be at 1.0 atm? Boyle s Law P 1 = 0.80 atm V 1 = 1.8 L P 2 = 1.0 atm V 2 =?? (.8 atm)(1.8 L) = (1.0 atm)(v 2 ) 1.44 atm x L = 1 atm V 2 V 2 = 1.4 L 2. A balloon full of helium has a volume of 1.75 L at a temperature of 28 o C. What would the balloon's volume be at 50 o C? Charles Law V 1 = V 2 V 1 = 1.75 L V 2 =?? T 1 = 301 K T 2 = 323K V 2 = 1.9 L 3. If you have 5.00 mol of fluorine gas at 273 K and 1.00 atm of pressure, what will be the volume of the gas? Ideal Gas Law PV = nrt (1.00 atm)(v) = 5.00 mol (.0821 L x atm/mol x K)(273 K) V = 112 L = 1.12 x 10 2 L
Chemistry 4. How many moles of nitrogen are present in a 2.0 liter container at 27 C and 1.0 atm? n =.081 moles Ideal Gas Law 5. A 375 ml sample of air at PV = nrt STP is heated at constant volume until its pressure increases to (1.0 atm)(2.0 L) = n (.0821 L x atm/mol x K)(300 K) 890 mm Hg. What would be the new temperature of the sample? Combined Gas Law P 1 = 760 mm Hg V 1 = 375 ml T 1 = 273 K P 2 = 890 mm Hg V 2 = 375 ml T 2 =?? = 320 K 6. A 1.5 L balloon is filled with helium at 1.1 atm. If the balloon is squeezed into a 0.500 L box and doesn t burst, what would be the pressure of the helium? Boyles Law P 1 = 1.1 atm P 2 =?? V 1 = 1.5 L V 2 = 0.500 L 3.3 atm = P 2
Chemistry 7. A balloon is filled with 4.0L of helium at 310 K and 1.0 atm. The balloon is placed in an oven where the temperature reaches 345 K and the pressure is maintained. What would be the new volume of the balloon? Charles Law V 1 = V 2 V 1 = 4.0 L V 2 =?? T 1 = 310 K T 2 = 345 K V 2 = 4.5 L 8. The volume of a scuba tank is 10.0 L. It contains a mixture of oxygen and nitrogen at 29.0 atm. What volume of this mixture could the tank supply to a diver at 2.6 atm? Boyles Law P 1 = 29.0 atm V 1 = 10.0 L P 2 = 2.6 atm V 2 =?? V 2 = 110 L = 1.1 x 10 2 L 9. A welding torch requires 4500 L of acetylene gas at 2 atm. If the acetylene is supplied by a 125 L tank, what is the pressure of the acetylene in the tank? Boyle s Law P 1 = 2 atm V 1 = 4,500 L P 2 =??? V 2 = 125 L P 2 = 72 atm
10. Convert 3.50 atm of pressure to the following units: Chemistry a. 3.50 atm x 760 mm Hg/1 atm = 2660 mm Hg b. 3.50 atm x 101.3 kpa/1 atm = 355 kpa c. 3.50 atm x 760 mm Hg/1 atm x 14.7 psi/760 mm Hg = 51.5 psi d. Bonus: 2660 mm Hg x 1 in/25.4 mm = 105 in Hg 11. The volume of a sample of nitrogen is 88 ml at 25 C and 1.0 atm. What is its volume in L at STP? Charles Law V 1 = V 2 V 1 = 88 ml V 2 =??? T 1 = 298 K T 2 = 273 K 81 ml = V 2 = 0.081 L 12. Suppose you have a 1 L sample of neon gas and a 1 L sample of nitrogen gas. Each sample is at STP. a. How do the number of gas particles in each sample compare? Avogadro s principle states that equal volumes of gases at the same temperature and pressure contain equal numbers of particles, so the 1 L samples contain equal numbers of gas particles. b. How do the masses of the samples compare? The mass of a nitrogen molecule is 28.0 atomic mass units and the mass of a neon atom is 20.2 atomic mass units, so the nitrogen sample has a greater mass than the helium sample.
Chemistry 13. On a cold winter day when the temperature is -2 C, you notice the tires on your bicycle appear to be low. You use the pressure gauge to measure the air pressure and the gauge reads 54 psi. The next afternoon, the temperature has warmed up to 13 C. If you measure the pressure in your tires again, what would you expect the reading on the pressure gauge to be? (Assume the volume of the air in the tires is constant and there are no holes in the tires.) Combined Law (with constant volume) P 1 = 54 psi P 2 =? T 1 = 271 K T 2 = 286 K P 1 = P 2 P 2 = 57 psi 14. Calculate the mass of 400 ml of CO 2 collected over water at 30 C and 749 mm Hg. The vapor pressure of water at 30 o C is 31.8 mm Hg. Dalton s Law of Partial Pressure and Ideal Gas Law P total = P CO2 + P water = 749 mm Hg P CO2 = 749 mm Hg 31.8 mm Hg = 717 mm Hg R = 62.4 L x mm Hg/mol x K V = 400 ml = 0.400 L T = 30 C = 303 K PV = nrt n = PV/RT n = 717 mm Hg x 0.400 L 62.4 L x mm Hg/mol x K x 303 K n = 0.0152 mol CO 2 g CO 2 = 0.0152 mol CO 2 x 44.01 g CO2 = 0.669 g CO 2 1 mol CO2 II. Applying Chemistry Answer with complete sentences using gas law concepts to describe. 1. Use the kinetic molecular theory to explain why pressurized cans include the message, Do Not Incinerate. Heating increases the temperature (average kinetic energy) of gas particles and therefore, the pressure. If the can is heated, the pressure of the gas may exceed the strength of the can and it could explode.
2. What are the three factors that affect gas pressure? Chemistry Three factors that affect gas pressure are temperature, volume, and number of particles (moles). 3. Why does an air mattress support the weight of a person sleeping on it? An air mattress supports the person sleeping on it because the volume is decreased when a person lies on it. As long as it doesn t leak, as the volume decreases, the pressure increases. This increased pressure supports the added weight of the individual. 4. How does an increase in atmospheric pressure affect the boiling point of water? Why? Water boils when its vapor pressure equals atmospheric pressure. Therefore, an increase in the atmospheric pressure increases the boiling point of water.