Gas Laws Friday, April 7th, 2017

Opening thoughts… Have you ever: Seen a hot air balloon? Had a soda bottle spray all over you? Baked (or eaten) a nice, fluffy cake? These are all examples of gases at work!

Gases Variable volume and shape Expand to occupy volume available Volume, Pressure, Temperature, and the number of moles present are interrelated Can be easily compressed Exert pressure on whatever surrounds them Easily diffuse into one another 3

Properties of Gases You can predict the behavior of gases based on the following properties: Pressure Volume Amount (moles) Temperature Lets review each of these briefly…

Pressure Pressure is defined as the force the gas exerts on a given area of the container in which it is contained. The SI unit for pressure is the Pascal, Pa. If you’ve ever inflated a tire, you’ve probably made a pressure measurement in pounds (force) per square inch (area).

Volume Volume is the three-dimensional space inside the container holding the gas. The SI unit for volume is the cubic meter, m3. A more common and convenient unit is the liter, L. Think of a 2-liter bottle of soda to get an idea of how big a liter is. (OK, how big two of them are…)

Amount (moles) Amount of substance is tricky. As we’ve already learned, the SI unit for amount of substance is the mole, mol. Since we can’t count molecules, we can convert measured mass (in kg) to the number of moles, n, using the molecular or formula weight of the gas. By definition, one mole of a substance contains approximately 6.022 x 1023 particles of the substance. You can understand why we use mass and moles!

Temperature Temperature is the measurement of heat…or how fast the particles are moving. Gases, at room temperature, have a lower boiling point than things that are liquid or solid at the same temperature. Remember: Not all substance freeze, melt or evaporate at the same temperature. Water will freeze at zero degrees Celsius. However Alcohol will not freeze at this temperature.

How do they all relate? Some relationships of gases may be easy to predict. Some are more subtle. Now that we understand the factors that affect the behavior of gases, we will study how those factors interact.

Boyle’s Law This law is named for Charles Boyle, who studied the relationship between pressure, p, and volume, V, in the mid-1600s. Boyle determined that for the same amount of a gas at constant temperature, results in an inverse relationship: when one goes up, the other comes down. pressure volume

Boyle’s Law P1V1 = P2V2 A graph of pressure and volume gives an inverse function A graph of pressure and the reciprocal of volume gives a straight line

Sample Problem 1: If the pressure of helium gas in a balloon has a volume of 4.00 mL at 210 kPa, what will the pressure be at 25.0 cL? P1 V1 = P2 V2

Sample Problem 1: If the pressure of helium gas in a balloon has a volume of 4.00 mL at 210 kPa, what will the pressure be at 25.0 cL? P1 V1 = P2 V2 (210 kPa) (4.00 mL) = P2(250mL) P2 = (210 kPa) (4.00 mL) (250 mL) = 3.4 kPa

Charles’ Law This law is named for Jacques Charles, who studied the relationship volume, V, and temperature, T, around the turn of the 19th century. This defines a direct relationship: With the same amount of gas he found that as the volume increases the temperature also increases. If the temperature decreases than the volume also decreases. volume temperature

Charles’ Law According to Charles’ Law the volume of a gas is proportional to the Kelvin temperature as long as the pressure is constant Note: The temperature for gas laws must always be expressed in Kelvin! where Kelvin = oC +273 V1 = T1 V2 T2

Charles’ Law A graph of temperature and volume yields a straight line. Where this line crosses the x axis (x intercept) is defined as absolute zero

Sample Problem 2 A gas sample at 40 oC occupies a volume of 2.32 L. If the temperature is increased to 75 oC, what will be the final volume? V1 = V2 T1 T2

Sample Problem 2 A gas sample at 40 oC occupies a volume of 2.32 dm3. If the temperature is increased to 75 oC, what will be the final volume? V1 = V2 T1 T2 Convert temperatures to Kelvin. 40oC = 313K 75oC = 348K 2.32 L = V2 313 K 349K (313K)( V2) = (2.32 L)(348K) V2 = 2.58 L

Gay-Lussac’s Law P1 = P2 T2 T1 Gay-Lussac’s Law defines the relationship between pressure and temperature of a gas. The pressure and temperature of a gas are directly proportional P1 = P2 T2 T1

Sample Problem 3: The pressure of a gas in a tank is 3.20 atm at 22 oC. If the temperature rises to 60oC, what will be the pressure in the tank? P1 = P2 T1 T2

Sample Problem 3: The pressure of a gas in a tank is 3.20 atm at 22 oC. If the temperature rises to 60oC, what will be the pressure in the tank? P1 = P2 T1 T2 Convert temperatures to Kelvin. 22oC = 295K 60oC = 333K 3.20 atm = P2 295 K 333K (295K)( P2) = (3.20 atm)(333K) P2 = 3.6 atm

Scheffler The Combined Gas Law If the amount of the gas is constant, then Boyle’s Charles’ and Gay-Lussac’s Laws can be combined into one relationship P1 V1 = P2 V2 T1 T2

Sample Problem 4: A gas at 110 kPa and 30 oC fills a container of 2.0 L. If the temperature rises to 80oC and the pressure increases to 440 kPa, what is the new volume? P1V1 = P2V2 T1 T2 23

Sample Problem 4: A gas at 110 kPa and 30 oC fills a container of 2.0 L. If the temperature rises to 80oC and the pressure increases to 440 kPa, what is the new volume? P1V1 = P2V2 T1 T2 Convert temperatures to Kelvin. 30oC = 303K 80oC = 353K V2 = V1 P1 T2 P2 T1 = (2.0 L) (110 kPa ) (353K) (440 kPa ) (303 K) V2 = 0.58 L 24