Ch. 14 Gas Laws Mrs. Fox

Ideal Gas Law PV=nRT P= pressure (atm) V= volume (L) n= number of moles (moles) R= 0.0821 (mol*atm/L*K) T= temperature (kelvin)

Also note: Temperature must be in Kelvin To convert from Celsius to Kelvin “convert from C add 273” 23 degrees Celsius = ___________ Kelvin 23 + 273 = 296K

Try some: Calculate the number of moles of gas contained in a 3.0 L vessel at 300K with a pressure of 1.50 atm 0.2 mole If the pressure exerted by a gas at 25°C in a volume of 0.044L is 3.81 atm, how many moles of gas are present? 6.9x10-3 mol Determine the Celsius temperature of 2.49 moles of gas contained in a 1.00L vessel at a pressure of 143 kPa. -266°C

Boyle’s Law Boyle Potatoes Violently Look at the Ideal Gas Law: PV=nRT only use the symbols P & V Make sure both are on the left of the equal sign Set it equal to itself P1V1=P2V2

Charles’s Law Charles The Velociraptor Look at the Ideal Gas Law: PV= nRT only use the symbols T & V Make sure both are on the left of the equal sign Set it equal to itself V1 = V2 T1 T2

Gay-Lussac’s Law Gay-Lussac’s Potty Training Look at the Ideal Gas Law: PV=nRT only use the symbols P & T Make sure both are on the left of the equal sign Set it equal to itself P1 = P2 T1 T2

Steps to figure out which gas law to use for each question: Underline each variable in the question There will be 2 circumstances of each (before and after) Ignore all constant variables Write the initial circumstances under “before” Write final circumstances under “after” You are solving for the unknown variable Move your variables BEFORE you insert numbers

A sample of helium gas in a balloon is compressed from 4. 0L to 2 A sample of helium gas in a balloon is compressed from 4.0L to 2.5 L at a constant temperature. If the pressure of the gas in the 4.0L volume is 210 kPa, what will the pressure be at 2.5 L? BEFORE AFTER V1= 4.0 L P1= 210 kPa V2= 2.5 L P2 = ?? Which gas law uses V & P? Boyle’s Law!! P1V1=P2V2 Solve for P2 first: P2= P1V1/V2 Now plug in the numbers: P2 = (210 x 4.0) / (2.5) Solve: 340 kPa

A gas sample at 40. 0°C occupies a volume of 2. 32 L A gas sample at 40.0°C occupies a volume of 2.32 L. If the temperature is raised to 75°C , what will the volume be, assuming the pressure remains constant? BEFORE AFTER T1= 40.0°C + 273= 313K V1= 2.32 L T2= 75°C + 273 = 348K V2= ?? Which gas law uses T & V? Charles’s Law!! V1/T1= V2/T2 Solve for V2 first: V2= (V1/T1)*T2 Now plug in the numbers: V2 = (2.32/313) * (348) Solve: 2.58L  2.6L

Gay-Lussac’s Law!! P1/T1= P2/T2 The pressure of a gas in a tank is 3.20 atm at 22.0°C. If the temperature rises to 60.0°C what will the pressure in the tank be? BEFORE AFTER P1= 3.20 atm T1= 22.0 + 273= 295K P2=? T2= 60.0 + 273= 333K Which gas law uses T & P? Gay-Lussac’s Law!! P1/T1= P2/T2 Solve for P2 first: P2= ( P1/T1)/T2 Now plug in the numbers: P2 = (3.2/295) / (333) Solve: 3.61 atm

Combined Gas Law P1V1 = P2V2 T1 T2 Combines/uses all of the variables with the exception of n & R in the Ideal Gas Law PV=nRT

BEFORE AFTER Solve for V2: A gas at 110 kPa and 30.0°C fills a flexible container with an initial volume of 2.00L. If the temperature is raised to 80.0°C and the pressure increased to 440kPa, what is the new volume? BEFORE P1=110 kPa T1= 30.0°C V1= 2.00 L AFTER P2=440 kPa T2= 80.0°C V2= ?? Which Gas Law should we use? Combined Gas Law!! P1V1/T1= P2V2/T2 Solve for V2: V2= V1(P1/T1)(T2/P2) V2= 0.58 L

Avogadro’s Principle Equal volumes of gasses at the same temperature and pressure contains equal number of moles STP(standard temperature & pressure) When volume is 22.4L When pressure is 1 atm When temperature is 0 degrees Celsius If at STP, the number of moles is always 1 mole Remember that 1 mole = 6.02x1023 particles Therefore, at STP: 1 mole=22.4L 1 mole= 1 atm 1 mole = 0.0°C

Calculate the volume that 0.881 mole of gas at STP will occupy Since at STP: T=0.0°C V= 22.4L P= 1 atm n= 0.881 moles 0.881 mole x 22.4L = 19.7L 1 mole

Challenge question! If you are given grams instead of moles, can you solve a volume at STP?? Calculate the volume that a 2.0kg of CH4 will occupy at STP: Convert kg into grams Convert grams into moles Convert moles into L (1 mole= 22.4L) 2.0kg= 2000g 2000g CH4 x 1 mole = 125 mole 16.05g 125 mole x 22.4L = 2800L 1 mole