Gas Laws

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SAMPLE PROBLEM 2 A container of oxygen has a volume of 349 mL at a temperature of 22°C. What volume will the gas occupy at 50.°C? SOLUTION 1. ANALYZE • What is given in the the original volume and temperaproblem? ture of the oxygen sample, and the new temperature of the sample • What are you asked to find? the volume at the new temperature Items Data Original volume, V 1 Original temperature, t 1 Original Kelvin temperature, T 1 New volume, V 2 New temperature, t 2 New Kelvin temperature, T 2 2. PLAN • What steps are needed to Rearrange the Charles’s law equacalculate the new volume tion to solve for V 2, substitute of the gas? known quantities, and calculate. V 1 T 1 122 Chapter 11 1 V2 T2 349 mL O 2 22°C (22 273) K 295 K ? mL O 2 50.°C to solve for V2 , multiply both sides of the equation by T2 to isolate V2 insert data and solve for V2 (50. 273) K 323 K V 1 T 2 T 1 2 V 2 3. COMPUTE Substitute data for the terms of the equation, and compute the result. V 2 V 1T 2 T 1 349 mL O 2 323 K 295 K 382 mL O 2 4. EVALUATE • Are the units correct? Yes; units canceled to give mL O2. • Is the number of significant Yes; the number of significant figfigures correct? ures is correct because data were given to three significant figures. • Is the answer reasonable? Yes; the temperature increased, so the volume must also increase.
PRACTICE In each of the following problems, assume that the pressure and molar quantity of gas do not change. 1. Calculate the unknown quantity in each of the following measurements of gases. V 1 T 1 V 2 T 2 a. 40.0 mL 280. K ? mL 350. K b. 0.606 L 300. K 0.404 L ? K c. ? mL 292 K 250. mL 365 K d. 100. mL ? K 125 mL 305 K e. 0.0024 L 22°C ? L 14°C ans: 50.0 mL ans: 200. K ans: 200. mL ans: 244 K ans: 0.0021 L 2. A balloon full of air has a volume of 2.75 L at a temperature of 18°C. What is the balloon’s volume at 45°C? ans: 3.01 L 3. A sample of argon has a volume of 0.43 mL at 24°C. At what temperature in degrees Celsius will it have a volume of 0.57 mL? ans: 121°C GAY-LUSSAC’S LAW You may have noticed a warning on an aerosol spray can that says something similar to Do not incinerate! Do not expose to temperatures greater than 140°F! Warnings such as this appear because the pressure of a confined gas increases with increasing temperature. If the temperature of the can increases enough, the can will explode because of the pressure that builds up inside of it. The relationship between the pressure and temperature of a gas is described by Gay-Lussac’s law. Gay-Lussac’s law states that the pressure of a sample of gas is directly proportional to the absolute temperature when volume remains constant. Gay-Lussac’s law can be expressed as follows. P T and P T k, or P kT According to Gay-Lussac’s law, when the temperature of a sample of gas increases, the pressure of the gas increases by the same factor. Therefore, doubling the temperature of a gas will double its pressure. Reducing the temperature of a gas to 75% of its original value will also reduce the pressure to 75% of its original value. <strong>Gas</strong> <strong>Laws</strong> 123
Page 1 and 2: CHAPTER 11 Gas Laws Chemists found
Page 3 and 4: SAMPLE PROBLEM 1 A sample of nitrog
Page 5: According to Charles’s law, when
Page 9 and 10: SAMPLE PROBLEM 3 A cylinder of gas
Page 11 and 12: These three gas laws can be combine
Page 13 and 14: 4. EVALUATE • Are the units corre
Page 15 and 16: • What are you asked to find? the
Page 17 and 18: Solve for V 2 as in Sample Problem
Page 19 and 20: 8. Calculate the unknown quantity i
Page 21 and 22: 23. A chemistry student collects a
Page 23: space; add the partial pressures of

Gas Laws

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