Boyle’s Law The First Gas Law

Objectives Upon completion of this presentation, you will be able to describe the relationship between the pressure and the volume of an ideal gas use Boyle’s law to calculate the final volume of a gas when given the initial pressure and volume and the final pressure use Boyle’s law to calculate the final pressure of a gas when given the initial pressure and volume and the final volume

Introduction In 1662, Robert Boyle was investigating the properties of gases. He found a relationship between pressure, P, and volume, V, when the temperature, T, is held constant. Pressure is inversely related to volume. As the pressure increases, the volume decreases. As the pressure decreases, the volume increases.

Introduction We can write Boyle's law two different ways: P ⋅ V = k where "k" is a constant. P 1 V 1 = P 2 V 2 where P 1 and V 1 are initial pressure and volume where P 2 and V 2 are final pressure and volume

Introduction Boyle stated his law in the first notation, P ⋅ V = k. The product of pressure and volume is a constant for a given mass of confined gas as long as the temperature is constant. We most often use the second notation, P 1 V 1 = P 2 V 2, to solve problems.

Application When we are trying to solve a Boyle's law problem, we will need to know three of the four variables. For P 1 V 1 = P 2 V 2 we can solve for: P 1 = P2V2P2V2 V1V1 V 1 = P2V2P2V2 P1P1 P 2 = P1V1P1V1 V2V2 V 2 = P1V1P1V1 P2P2

Example 1 – Finding P 2 What is the final pressure, P 2, of 3.00 L of helium gas at an initial pressure of 1.05 atm if the volume of the gas is reduced to 1.50 L? P 1 = 1.05 atm V 1 = 3.00 L P 2 = ? atm V 2 = 1.50 L P 2 = P1V1P1V1 V2V2 = (1.05 atm)(3.00 L) 1.50 L = 2.10 atm

Sample Problems – Finding P 2 1. What is the final pressure of hydrogen gas with an initial pressure of 3.00 atm, an initial volume of L, and a final volume of L? 2. What is the final pressure of oxygen gas with an initial pressure of 12.0 atm, an initial volume of 24.0 L, and a final volume of 96.0 L? 3. What is the final pressure of chlorine gas with an initial pressure of 2.10 atm, an initial volume of 3.50 L, and a final volume of 1.40 L? 4. What is the final pressure of carbon monoxide gas with an initial pressure of 4.27 atm, an initial volume of 1.22 L, and a final volume of 3.73 L? P 2 = 12.0 atm P 2 = 3.00 atm P 2 = 5.25 atm P 2 = 1.40 atm

Example 2 – Finding V 2 What is the final volume, V 2, of 5.00 L of argon gas at an initial pressure of 7.50 atm if the pressure of the gas is reduced to 2.50 atm? P 1 = 7.50 atm V 1 = 5.00 L P 2 = 2.50 atm V 2 = ? L V 2 = P1V1P1V1 P2P2 = (7.50 atm)(5.00 L) 2.50 atm = 15.0 L

Sample Problems – Finding V 2 1. What is the final volume of neon gas with an initial pressure of 4.00 atm, an initial volume of 1.20 L, and a final pressure of atm? 2. What is the final pressure of helium gas with an initial pressure of 2.50 atm, an initial volume of 5.00 L, and a final pressure of 10.0 atm? 3. What is the final pressure of argon gas with an initial pressure of atm, an initial volume of 4.20 L, and a final pressure of atm? 4. What is the final pressure of fluorine gas with an initial pressure of 5.72 atm, an initial volume of 3.88 L, and a final pressure of 2.43 atm? V 2 = 48.0 L V 2 = 1.25 L V 2 = 12.6 L V 2 = 9.12 L

Example 3 – Finding P 1 What was the initial pressure, P 1, of neon gas that had an initial volume of 2.00 L, a final volume of L, and a final pressure of 1.60 atm? P 1 = ? atm V 1 = 2.00 L P 2 = 1.60 atm V 2 = L P 1 = P2V2P2V2 V1V1 = (1.60 atm)(0.500 L) 2.00 L = L

Sample Problems – Finding P 1 1. What is the initial pressure of nitrogen gas with an initial volume of L, a final pressure of atm, and a final volume of L? 2. What is the initial pressure of oxygen gas with an initial volume of 12.0 L, a final pressure of 24.0 atm, and a final volume of 3.00 L? 3. What is the initial pressure of chlorine gas with an initial volume of 1.80 L, a final pressure of 8.00 atm, and a final volume of 1.44 L? 4. What is the initial pressure of hydrogen gas with an initial volume of 57.9 L, a final pressure of atm, and a final volume of 37.3 L? P 1 = atm P 1 = 6.00 atm P 1 = 6.40 atm P 1 = atm

Example 4 – Finding V 1 What was the initial volume, V 1, of argon gas at an initial pressure of 4.80 atm, a final pressure of 6.40 atm, and a final volume of 1.20 L? P 1 = 4.80 atm V 1 = ? L P 2 = 6.40 atm V 2 = 1.20 L V 1 = P2V2P2V2 P1P1 = (6.40 atm)(1.20 L) 4.80 atm = 1.60 L

Sample Problems – Finding V 1 1. What is the initial volume of radon gas with an initial pressure of 4.00 atm, a final pressure of atm, and a final volume of 10.0 L? 2. What is the initial volume of neon gas with an initial pressure of 12.0 atm, a final pressure of 24.0 atm, and a final volume of 3.00 L? 3. What is the initial volume of helium gas with an initial pressure of 7.20 atm, a final pressure of 8.00 atm, and a final volume of 12.0 L? 4. What is the initial volume of ammonia gas with an initial pressure of 15.2 atm, a final pressure of atm, and a final volume of 275 L? V 1 = L V 1 = 6.00 L V 1 = 13.3 L V 1 = 2.23 L

Summary Boyle’s Law: At a constant temperature, the pressure of a gas is inversely proportional to its volume. Equations: P ⋅ V = k, where k is a constant P 1 V 1 = P 2 V 2