Unit IX: Gases

Behavior of Gasses The push or pull particles exert over a particular area is called pressure Pressure plays a role in our everyday lives Examples: The pascal (Pa) is the SI unit of pressure

A device that measures atmospheric pressure is called the barometer Invented in 1643 by Evangelista Torricelli (Italian; ) Student of Galileo’s

Units of Pressure The SI unit for pressure is the Pascal (Pa) Sample Equations Note: Solve by dimensional analysis, with the correct number of significant figures! Not necessarily in standard scientific notation mm Hg→ Pa psi→atm bars →torr atm →kPa atm →mm Hg

Boyle’s Law The first careful experiments on gases was conduced by Robert Boyle Irish (1627 – 1691) Performed J – Tube experiments

Formula: P 1 V 1 = P 2 V 2 Pressure (before) (Can be in any units) Volume (before) (Can be in any units) Pressure (before) (units consistent with P 1 ) Volume (after) (units consistent with V 1 )

Gas Law Problem Solving Set-up an Information Matrix The abbreviations STP or ST or SP are often used in place of numbers 1 st set of conditions (Before Change) 2 nd set of conditions (After Change) Pressure Volume Temperature

Sample Problem 1: A sample of helium gas has a pressure of 3.54 atm in a container with a volume of 23.1 L. What is the new volume of the container if the pressure decreases to 1.87 atm? P V T Condition 1 Condition atm 1.87 atm 23.1 L? V 2 = P1V1P1V1 P2P2 (3.54 atm ● 23.1 L) (1.87 atm) = 43.7 L

Charles’ Law Jacques Charles was the 1 st to fill a balloon with H 2 gas French Physicist (1746 – 1823) Showed the volume of a given gas (at constant pressure) increases with temperature

Formula: V 1 T 2 = V 2 T 1 Volume (before) (Can be in any units) Temperature (after) (Kelvin – K) Volume (after) (units consistent with V 1 ) Temperature (before) (Kelvin - K)

Sample Problem 2: Your are given 1.2 L of oxygen gas measured at 380 torr and 18 °C. What will be the volume when the temperature goes up to 307°C? P V T Condition 1 Condition torr 1.2 L? V2 =V2 = V1T2V1T2 T1T1 V 2 = (1.2 L ● 580 K) (291 K) = 2.4 L 18°C 291 K 307°C 580 K

Combined Gas Law Boyle’s and Charles’ Law can be combined Pressure, Volume, and Temperature are inter-related Formula: P 1 V 1 P 2 V 2 T 1 T 2 = OR P 1 V 1 T 2 = P 2 V 2 T 1

Sample Problem 3A: A helium balloon with a volume of 410. mL is cooled from 27 °C to -27°C. The pressure on the gas is reduced from 110. kPa to 25 kPa. What is the new volume of the gas? P V T Condition 1 Condition kPa 25 kPa 410. mL ? V 2 = P1V1T2P1V1T2 P2T1P2T1 V2 =V2 = (110 kPa 410. mL 246 K) (25 kPa 300 K) = 1.5 x 10 3 mL 27°C 300 K -27°C 246 K

Sample Problem 3B: A gas sample is originally at STP. If the volume was originally 10.5 L, then what will happen to the pressure when the temperature rises to 109 °F? P V T Condition 1 Condition atm ? 10.5 L P 2 = P1V1T2P1V1T2 V2T1V2T1 P2 =P2 = (1.00 atm 316 K) (273 K) = 1.16 atm 273 K 109°F 316 K

The Ideal Gas Law The Ideal Gas Law relates the number of particles to pressure, volume, and temperature Based on Avogadro’s Principle Equal volumes of gases at the same temperature and pressure contain equal numbers of particles

Formula : P V = n R T Pressure (atm) Volume (L) Moles (mol) Temperature (K) Universal Gas Constant ( L atm / K mol)

There are some limitations to the Ideal Gas Law 1. Works well at low pressures & high temperatures 2. Most gases do not behave ideally at 1 atm 3. Does not work well near the condensation conditions of a gas

Remember the Gas Law Problem Solving Matrix Condition 1 Condition 2 P V n T All Gas Law matrices should include mol ( n ) from this point! You won’t necessarily know what Gas Law you will be solving! The Ideal Gas Law will not use Condition 2!

Sample Problem 4A: A 333 g sample of Radon gas has a volume of 2.1 x 10 4 mL at 33°C. What is the pressure of the gas? P = n R T V P = (1.5 mol.08206… 306 K) 21 L 1.8 atm = Condition 1 Condition 2 P V n T ? 2.1 x 10 4 mL 333 g Rn gas 33°C 21 L 1.5 mol 306 K

Sample Problem 4B: Calculate the volume of hydrogen produced at 1.50 atm and 19°C by the reaction of 26.5 g of Zn with excess hydrochloric acid? 1 Zn (s) + 2 HCl (aq) → 1 ZnCl 2 (aq) + 1 H 2 (g) 12 P V n T 1.50 atm ? 2.65 g Zn 19°C ?.405 mol 292 K 1.50 atm V = n R T P V = (.405 mol.08206… 292 K) 1.50 atm 6.5 L H 2 =

The density of a gas can be determined by using the Ideal Gas Law Formula: D = M P R T Density (g/L) Universal Gas Constant ( L atm / K mol) Temperature (K) Pressure (atm) Molar Mass (g)