Gas Law Practice

Gas Law Practice Gas behavior can be explained qualitatively by using the kinetic molecular theory. Gas molecules are moving constantly, filling the volume of the container in which they are confined. Collisions between gas molecules and the walls of their container cause gas pressure. The average kinetic energy of the gas molecules in the container is directly proportional to the Kelvin temperature. Use these concepts to solve the following problems. • At a birthday party a child sits on a partially filled balloon, decreasing its volume by 1/2. What happens to the pressure inside the balloon? V decreases, P increases. If V decreases by ½, the P increases by 2 • In a cryogenics (extreme cold) demonstration, a scientist takes a small, partially inflated balloon out of liquid nitrogen (at a very low temperature). As the balloon rests on the table, it begins to grow in size. Explain this phenomenon. Low KE means lower P; increase KE and increase P Low Temp goes with low V. Raise the T and raise the V. • Huge weather balloons partially filled with helium are sent high into the earth’s atmosphere to examine the air. As a balloon rises into the air, the air pressure outside the balloon decreases rapidly. If the atmospheric pressure becomes one-third of its original pressure, what will happen to the balloon volume? Explain. (assume constant T) P increases as V decreases. If you decrease P by 1/3, V is increased by 3. The rest of this worksheet will give you practice in solving quantitative problems involving gas laws. The variables associated with gases are: pressure, volume, number of moles and temperature. You will begin by solving simple problems involving only two variables, gradually developing the skills necessary to solve more difficult problems involving three, and four, variables. • Calculate the final pressure in the cylinder of a car engine if the original volume was 450 mL at a pressure of 0.80 atm and the final volume is 120 mL. Assume no change in the number of molecules or temperature. P1V1 = P2V2 , 0.8atm x 450mL = P2 x 120 mL; P2 = 3 atm • The gas inside a piston was heated until the volume of gas had increased from 125 mL to 250 mL. If the temperature inside the piston was originally 15°C, calculate the new temperature in °C. Assuming that amount of the gas and the pressure do not change. V1/T1 = V2/T2; 0.125L/288K = 0.25L/T2; Therefore T2 = 576K or 303 C • One of the cylinders in an automobile engine is heated and the piston moves. allowing the gas inside to expand, The original pressure was 1,85 atm, while its original volume was 175 mL, measured at 18°C. The final measured pressure was 0.86 atm and the temperature was measured at 382°C. Calculate the final volume of the cylinder P1V1 /T1 = P2V2/T2; 1.85 atm x 175 mL/291 K = 0.86 x V2/655K; V2 = 847 mL Graphing Gas-Law Relationships The various gas laws express the relationships between quantities such as pressure, volume, and temperature representing the variations between pressure, volume, and temperature data helps to reveal the mathematical nature of the relationships. Consider the two examples that follow: • An expandable container is filled with a given volume of gas. While the pressure of the gas is kept constant, the container is heated. The temperature is recorded in degrees Celsius, and the volume of the contained gas is recorded as well. The data are shown in the following table. Temperature (°C) 0°C 50°C 100°C 150°C Temperature (K) ______273______ ______323______ ______373______ ______423______ Volume 293 mL 347 mL 401 mL 455 mL Convert °C into Kelvins and write these values into the table. Then plot the data on Graphical Analysis. Should be a straight line a. What type of proportion does this graph illustrate? Explain. Directly proportional. As T or V increases, the other increases. b. What is the value of V/T for this experiment? 54/50 = 1.08 mL/K c. To what graphical quantity does V/T correspond? The slope or m in y = mx +b for the line created. d. Is V/T constant or does it vary? It is constant e. Extrapolate values for the volume occupied by the gas at 150 K 160.16 mL_ 75 K_79.16 mL_ 0 K_-1.84 mL_ f. What gas law does the graph illustrate? Charles’ law at constant pressure. V1/T1 = V2/T2 g. Express this relationship in the form of a mathematical equation. At constant P, V1/T1 = V2/T2 for the graph V = 1.08 T -1.84