Add to table of Contents Gas Law Calculations Pg. 58 Properties of Gases Pg. 59 Boyle’s Law Calculations Pg. 60 Boyle’s & Charles’ Laws Pg. 61

Boyle’s Law

Boyle’s Law Pressure of a gas is inversely proportional to its volume. Constant T and amount of gas. As P increases, V decreases by the same factor. P x V = constant. Boyle’s Law: P1 x V1 = P2 x V2 .

Boyle’s Experiment Added Hg to a J-tube with air trapped inside. Used length of air column as a measure of volume.

Boyle’s Experiment, P x V

When you double the pressure on a gas, the volume is cut in half (as long as the temperature and amount of gas do not change).

Gas Laws Explained— Boyle’s Law Boyle’s law says that the volume of a gas is inversely proportional to the pressure. Decreasing the volume forces the molecules into a smaller space. More molecules will collide with the container at any one instant, increasing the pressure.

Boyle’s Law and Diving Since water is more dense than air, for each 10 m you dive below the surface, the pressure on your lungs increases 1 atm. At 20 m the total pressure is 3 atm. If your tank contained air at 1 atm of pressure, you would not be able to inhale it into your lungs. You can only generate enough force to overcome about 1.06 atm. Scuba tanks have a regulator so that the air from the tank is delivered at the same pressure as the water surrounding you. This allows you to take in air even when the outside pressure is large.

Boyle’s Law and Diving, Continued If a diver holds her breath and rises to the surface quickly, the outside pressure drops to 1 atm. According to Boyle’s law, what should happen to the volume of air in the lungs? Since the pressure is decreasing by a factor of 3, the volume will expand by a factor of 3, causing damage to internal organs. Always Exhale When Rising!!

Example—A Cylinder with a Movable Piston Has a Volume of 6. 0 L at 4 Example—A Cylinder with a Movable Piston Has a Volume of 6.0 L at 4.0 atm. What Is the Volume at 1.0 atm?

Example—A Cylinder with a Movable Piston Has a Volume of 6. 0 L at 4 Example—A Cylinder with a Movable Piston Has a Volume of 6.0 L at 4.0 atm. What Is the Volume at 1.0 atm? Given: Find: V1 =6.0 L, P1 = 4.0 atm, P2 = 1.0 atm V2, L Solution Map: Relationships: P1 ∙ V1 = P2 ∙ V2 V1, P1, P2 V2 Solution: Check: Since P and V are inversely proportional, when the pressure decreases ~4x, the volume should increase ~4x, and it does.

Temperature Scales Celsius Kelvin Fahrenheit Rankine 100°C 373 K 212°F BP Water 0°C 273 K 32°F 459 R MP Ice -38.9°C 234.1 K -38°F 421 R BP Mercury -183°C 90 K -297°F 162 R BP Oxygen BP Helium -269°C 4 K -452°F 7 R -273°C 0 K -459 °F 0 R Absolute Zero Celsius Kelvin Fahrenheit Rankine

Gas Laws and Temperature Gases expand when heated and contract when cooled, so there is a relationship between volume and temperature. Gas molecules move faster when heated, causing them to strike surfaces with more force, so there is a relationship between pressure and temperature. In order for the relationships to be proportional, the temperature must be measured on an absolute scale. When doing gas problems, always convert your temperatures to Kelvin!! K = °C + 273 & °C = K - 273 °F = 1.8 °C + 32 & °C = 0.556(°F-32)

Standard Conditions (Means common reference points for comparing): Standard pressure = 1.00 atm. Standard temperature = 0 °C = 273 K STP

Volume and Temperature In a rigid container, raising the temperature increases the pressure. For a cylinder with a piston, the pressure outside and inside stay the same. To keep the pressure from rising, the piston moves out increasing the volume of the cylinder. As volume increases, pressure decreases.

Volume and Temperature, Continued As a gas is heated, it expands. This causes the density of the gas to decrease. Because the hot air in the balloon is less dense than the surrounding air, it rises.

Charles’s Law Volume is directly proportional to temperature. Constant P (pressure) and amount of gas. (Graph of V vs. T is a straight line.) As T increases, V also increases. Kelvin T (Celsius T + 273) V = constant x T. If T is measured in kelvin.

We’re losing altitude. Quick, Professor, give your lecture on Charles’s law!

Practice—The Temperature Inside a Balloon Is Raised from 25 Practice—The Temperature Inside a Balloon Is Raised from 25.0 °C to 250.0 °C. If the Volume of Cold Air Was 10.0 L, What Is the Volume of Hot Air?

Practice—The Temperature Inside a Balloon Is Raised from 25 Practice—The Temperature Inside a Balloon Is Raised from 25.0 °C to 250.0 °C. If the Volume of Cold Air Was 10.0 L, What Is the Volume of Hot Air?, Continued Given: Find: V1 =10.0 L, t1 = 25.0 °C L, t2 = 250.0 °C V2, L Solution Map: Relationships: T(K) = t(°C) + 273.15, V1, T1, T2 V2 Solution: Check: Since T and V are directly proportional, when the temperature increases, the volume should increase, and it does.

Absolute Zero Theoretical temperature at which a gas would have zero volume and no pressure. Kelvin calculated by extrapolation. 0 K = -273.15 °C = -459 °F Never attainable. Though we’ve gotten real close! All gas law problems use the Kelvin temperature scale.

Determining Absolute Zero William Thomson, the Lord of Kelvin, extrapolated the line graphs of volume vs. temp- erature to determine the theoretical temperature that a gas would have given a volume of 0.