GAS LAW PROBLEM SETDirections: Read the information given in each gas law and answer the following problems with complete solution inGRESA format.A. BOYLE'S LAWIn 1662, Robert Boyle reported that the volume of gas decreased with increasingpressure. Within the limits of his experimental accuracy, he postulated the relationship existingbetween pressure and the volume was an inverse proportionality at constant temperature.Boyle's Law Equation: P1V1 = P2V2Sample Problem:Calculate the final volume of a gas if the pressure of a 4.0 L sample is changed from 2.5 atm to 5.0 atm.Given: V= 4.0L; P 2.5 atm; P, = 5.0 atmRequired: V,Equation: V2 =P2Solution:(25 alm)(4.OL)V2 == 2L5.0almAnswer:V2=2L1. A gas sample occupies a volume of 2.5 L at a pressure of 1.5 atm. What would be the volume of the gas if itspressure is reduced to 1 atm at the same temperature?2. The gas inside a balloon has a volume of 15.0L at a pressure of 2.0 atm. Calculate the pressure of the gas if itsvolume is compressed to 10.0L at the same temperature.B. CHARLES' LAWGas when heated at constant pressure will expand, and contract when cooled. Thisrelationship was studied by Jacques Charles. He stated that at constant pressure, thevolume of a given quantity of gas varies directly with the absolute temperature (K).V1Charles' Law Equation:T1V2=Note: The temperature must be expressed in Kelvin (K).-T2Sample Problem:At 30°C, the volume of a sample of air was 5.8 L. What would be the volume of the air sample if it is heated to60°C at the same pressure?Given: T, = 30°C + 273 = 303 K; V, = 5.8L; T, = 60°C + 273 = 333 KRequired: V,Equation: V1T2 = V2T1 ; V2 =Solution:(58L(333303X= 6.37 LVz =Answer:Va- 6.37 L3. A given amount of oxygen gas has a volume of 25.0 L at a temperature of 370C and a pressure of 1.0 atm. Atwhat temperature would this gas occupy a volume of 22.0 L at a pressure of 1.0 atm?4. A gas syringe contains 56.05 milliliters of a gas at 315.1 K. Determine the volume in L that the gas will occupy ifthe temperature is increased to 380.5 K.c. GAY-LUSSAC'S LAWGay Lussac's law defines the relationship between the pressure and temperatureof a gas. According to the law, when volume is held constant, the pressure of an ideal gasis directly proportional to its temperature.P2;Note: The temperature must be expressed in Kelvin (K).T2Gay-Lussac's Equation:Sample Problem:A 30.0 L sample of nitrogen inside a rigid, metal container at 20.0 *C is placed inside an oven whose temperatureis 50.0 "C. The pressure inside the container at 20.0 °C was at 3.00 atm. What is the pressure of the nitrogen after itstemperature is increased to 50.0 "C?Given: T, = 20.0'C + 273 = 293 K; P, = 3.00 atm; T= 50.0°C + 273 = 323 KRequired: P2Equation: PT2 = PT : Pz=Solution:P2 =(3.00 atm)(323)293= 3.31 atmAnswer:Pa= 3.31 atm5. Calculate the final pressure inside a scuba tank after it cools from 1.00x10 "C to 25.0 "C. The initial pressure in thetank is 130.0 atm.6. If a gas in a closed container is pressurized from 15.0 atm to 16.0 atm and its original temperature was 298 K,what would the final temperature of the gas be in degrees Celsius? Note: convert from K to "C and then round off. D. COMBINED GAS LAWThe combined gas law combines the first three gas law: Boyle's Law, Charles'Law, and Gay-Lussac's Law. It states that the ratio of the product of pressure andvolume and the absolute temperature of a gas is equal to a constant.Combined Gas Law Equation: 11 = 22; Note: The temperature must be expressed in Kelvin (K).Sample Problem:Find the volume of a gas at STP when 2.00 L is collected at 745.0 mmHg and 25.0 °C.Given: P, = 745.0 mmHg = 745.0 torr = 0.98 atm; V, = 2.00 L; T, = 25 + 273 = 298 K; STP (P2 = 760.0 mmHg = 760.0torr = 1 atm; T2 = 273 K)Required: V2P,V,T2Equation: PV,T2 = P2V2T1 ; V2 =Solution:(0.98 atm)(2.00L)(273 K)V2 == 1.80 L(1 atm)(298 K)Answer:V2 =1.80 L7. A gas takes up a volume of 17 L, has a pressure of 2.3 atm, and a temperature of 299 K. If the temperatureraised to 350 K and pressure is lowered at 1.5 atm, what is the new volume of gas?8.If you have 2.9 L of gas at a pressure of 5 atm and a temperature of 50°C, what will be the temperature in Kelvinof the gas if you decrease the volume to 2.4 L and pressure to 3 atm?E. IDEAL GAS LAWThe Ideal Gas Law was created to show the relationship betweenpressure, volume, number of moles of gas and temperature. It shows theequation of a hypothetical ideal gas.Ideal Gas Law Equation: PV = nRT; Note: The temperature must be expressed in Kelvin (K).Sample Problem:How many moles of gas are contained in 890.0 ml at 21°C and 750 mmHg?atm •Lmol •KGiven: P = 750 mmHg = 750 torr = 0.99 atm; V = 890 ml = 0.89 L; R = 0.0821 T = 21°C + 273 = 294 KRequired: nPVEquation: n =RTSolution:(0.99 atm) (0.89 L)n == 0.037 mol(0.0821 (294 K)mol-KAnswer:n=0.037 mol9. Calculate the volume if 3.00 moles of a gas will occupy at 24°C and 762.4 mmHg.10. What is gas' temperature in Kelvin when it has a volume of 25 L, 203 mol, and a pressure of 143.5 atm?

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10th Edition

ISBN:9781305957404

Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Chapter1: Chemical Foundations

Section: Chapter Questions

Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...