8.2 Pressure and Volume, (Boyle’s Law) The inverse relationship between the pressure and volume of a gas is known as Boyle’s law. Changes occur in opposite directions. When volume increases, the pressure decreases, provided the temperature and moles of the gas remains constant. The anesthetic N2O gas, is used for pain relief. Learning Goal Use the pressure–volume relationship (Boyle’s law) to determine the final pressure or volume when the temperature and amount of gas are constant.

Boyle’s Law Boyle’s law states that the pressure of a gas is inversely related to its volume when T is constant. the product P  V is constant when temperature and amount of a gas is held constant if volume decreases, the pressure increases. P1V1 = P2V2

Boyle’s Law: PV = Constant Pressure × volume is a constant, provided the temperature and amount of the gas remains the same. P1V1 = 8.0 atm × 2.0 L = 16 atm L P2V2 = 4.0 atm × 4.0 L = 16 atm L P3V3 = 2.0 atm × 8.0 L = 16 atm L Boyle’s law can be stated as P1V1 = P2V2 (T is constant.)

Chemistry Link to Health: Boyle’s Law and Breathing During an inhalation, the lungs expand. the pressure in the lungs decreases. air flows toward the lower pressure in the lungs.

Chemistry Link to Health: Boyle’s Law and Breathing During an exhalation, lung volume decreases. pressure within the lungs increases. air flows from the higher pressure in the lungs to the outside.

Guide to Using Gas Laws

Calculations Using Boyle’s Law Freon-12, CCl2F2, was used in refrigeration systems. What is the new volume of an 8.0 L sample of Freon gas initially at 550 mmHg after its pressure is changed to 2200 mmHg at constant temperature and moles? STEP 1 Organize the data in a table of initial and final conditions. Temperature and moles remain constant. ANALYZE Conditions 1 Conditions 2 Know Predict THE P1 = 550 mmHg P2 = 2200 mmHg P increases PROBLEM V1 = 8.0 L V2 = ? V decreases

Calculations Using Boyle’s Law STEP 2 Rearrange the gas law equation to solve for the unknown quantity. P1V1 = P2V2 Boyle’s law To solve for V2 , divide both sides by P2. STEP 3 Substitute values into the gas law equation and calculate. × ×

Study Check A sample of oxygen gas has a volume of 12.0 L at 600. mmHg. What is the new pressure when the volume changes to 36.0 L at a constant T and n? A. 200. mmHg B. 400. mmHg C. 1200 mmHg

Solution A sample of oxygen gas has a volume of 12.0 L at 600. mmHg. What is the new pressure when the volume changes to 36.0 L at a constant T and n? STEP 1 Organize the data in a table of initial and final conditions. Temperature and moles remain constant.

Solution A sample of oxygen gas has a volume of 12.0 L at 600. mmHg. What is the new pressure when the volume changes to 36.0 L at a constant T and n? STEP 2 Rearrange the gas law equation to solve for the unknown quantity. ×

Solution A sample of oxygen gas has a volume of 12.0 L at 600. mmHg. What is the new pressure when the volume changes to 36.0 L at a constant T and n? STEP 3 Substitute values into the gas law equation and calculate. The answer is A, 200. mmHg. ×

Study Check For a cylinder containing helium gas, indicate if cylinder A or cylinder B represents the new volume for the following changes (n and T are constant). 1. pressure decreases 2. pressure increases

Solution For a cylinder containing helium gas, indicate if cylinder A or cylinder B represents the new volume for the following changes (n and T are constant). 1. pressure decreases cylinder B 2. pressure increases cylinder A

Study Check If a sample of helium gas has a volume of 120 mL and a pressure of 850 mmHg, what is the new volume if the pressure is changed to 425 mmHg at a constant T and n? 60 mL 120 mL 240 mL

Solution If a sample of helium gas has a volume of 120 mL and a pressure of 850 mmHg, what is the new volume if the pressure is changed to 425 mmHg at a constant T and n? STEP 1 Organize the data in a table of initial and final conditions. Temperature and moles remain constant.

Solution If a sample of helium gas has a volume of 120 mL and a pressure of 850 mmHg, what is the new volume if the pressure is changed to 425 mmHg at a constant T and n? STEP 2 Rearrange the gas law equation to solve for the unknown quantity. STEP 3 Substitute values into the gas law equation and calculate. × ×

Study Check A sample of helium gas in a balloon has a volume of 6.4 L at a pressure of 0.70 atm. At 1.40 atm (T and n are constant), is the new volume represented by A, B, or C?

Solution A sample of helium gas in a balloon has a volume of 6.4 L at a pressure of 0.70 atm. At 1.40 atm (T and n are constant), is the new volume represented by A, B, or C? At a higher pressure (T and n constant), the new volume is represented by the smaller balloon A.