Ideal Gas Law March 13, 2015

Do Now 5L of oxygen undergoes a change of temperature from 15ºC to 30ºC. What is the new volume of the oxygen? Remember to convert from Celsius to Kelvin!

Do Now 5L of oxygen undergoes a change of temperature from 15ºC to 30ºC. What is the new volume of the oxygen? Remember to convert from Celsius to Kelvin!  15ºC = 288 K  30ºC = 303 K V 1 /T 1 = V 2 /T 2 5/288 = x/ = x/303 (303)(0.017) = x 5.26 L = x Charles’ Law Problem: Volume and Temperature

Objective I can use the Ideal Gas Law to solve for the pressure, volume, number of moles, or temperature of a gas in independent practice problems.

Agenda 1. Do Now, objective (10 min) 2. Vocabulary (5 min) 3. Ideal Gas Law Guided Reading (15 min) 4. Class Discussion (5 min) 5. Ideal Gas Law Notes (15 min) 6. Ideal Gas Law Practice Problems (15 min) 7. Quiz: Boyle’s, Charles’ and Ideal Gas Laws (15 min)

Homework HW11: Ideal Gas Law Practice Problems

Vocabulary Ideal Gas: a gas in which all collisions between atoms or molecules are perfectly elastic and in which there are no intermolecular attractive forces.

Vocabulary Standard Temperature and Pressure (STP): standard sets of conditions for experimental measurements used in chemistry.

Ideal Gas Law Guided Reading Read the Ideal Gas Law ChemTalk and answer the questions on a separate sheet of paper as you go. By the end of the reading you should know ◦ The equation for the ideal gas law ◦ How to use the ideal gas law to answer practice problems ◦ The value of the universal gas constant ‘R’ ◦ How ideal gases and common gases differ

Ideal Gas Law Reading Questions 1. What is the formula for the Ideal Gas Law? 2. What is ‘R’? 3. What is the volume of 1 mole of any gas at standard conditions (STP)? 4. What is the volume of 6.5 moles of oxygen gas if the temperature is 40.0ºC and the pressure is 6.2 atm?

Class Discussion 1. What is the volume of 1 mole of any gas at standard conditions (STP)? 2. What is the formula of the Ideal Gas Law? 3. What does the Ideal Gas Law let you solve for?

Ideal Gas Law Notes PV = nRT P = pressure in atm V = volume in L n = the number of moles of gas R = the universal gas constant ( L  atm/mol  K or 62.4 L  mm Hg/mol  K) T = temperature in kelvins

Example Problem What is the volume of 3 moles of oxygen gas if the temperature is 32ºC and the pressure is 3.1 atm? PV = nRT P = 3.1 atm V = ? n = 3 R = T = 32ºC  = 305 K

Example Problem What is the volume of 3 moles of oxygen gas if the temperature is 32ºC and the pressure is 3.1 atm? PV = nRT (3.1)(V) = (3)(0.0821)(305) 3.1V = V = /3.1 V = 24.2 L

Example Problem A sample of dry gas weighing 1.05 g is found to occupy 1.43L at 23.5ºC and atm. How many moles of the gas are present? PV = nRT P = atm V = 1.43 L n = ? R = T = 23.5ºC  = K

Example Problem A sample of dry gas weighing 1.05 g is found to occupy 1.43L at 23.5ºC and atm. How many moles of the gas are present? PV = nRT (0.951)(1.43) = (n)(0.0821)(296.5) 1.36 = (n)(24.34) 1.36/24.34 = n = n There are moles of dry gas

Practice Question A sample of dry gas weighing 1.05 g is found to occupy 1.43L at 23.5ºC and atm. There are moles of the dry gas. What is the mass of one mole of this gas? a)18.8 g/mol b)0.05 g/mol c)0.059 g/mol d)1.5 g/mol

Practice Question A sample of dry gas weighing 1.05 g is found to occupy 1.43L at 23.5ºC and atm. There are moles of the dry gas. What is the mass of one mole of this gas? a)18.8 g/mol b)0.05 g/mol c)0.059 g/mol d)1.5 g/mol 1.05 g moles

Guided Practice Let’s say that you are designing a toy that requires the generation of 1.0 L of oxygen gas to operate it. How many moles of oxygen will be generated at 1.0 atm and 20ºC? PV = nRT P = 1.0 atm V = 1.0 L n = ? R = T = 20ºC  = 293 K

Guided Practice Let’s say that you are designing a toy that requires the generation of 1.0 L of oxygen gas to operate it. How many moles of oxygen will be generated at 1.0 atm and 20ºC? PV = nRT (1.0)(1.0) = (n)(0.0821)(293) 1 = (n)(24.05) 1/24.05 = n moles = n

Guided Practice Many gases are stored in their compressed form (under pressure). Calculate the mass of N 2 that could be stored at 22ºC and 125 atm in a cylinder with a volume of 45.0 L. The molecular mass of N 2 is 28.0 g/mole PV = nRT P = 125 atm V = 45.0 L n = ? R = T = 22ºC  = 295 K

Guided Practice Many gases are stored in their compressed form (under pressure). Calculate the mass of N 2 that could be stored at 22ºC and 125 atm in a cylinder with a volume of 45.0 L. The molecular mass of N 2 is 28.0 g/mole PV = nRT (125)(45) = (n)(0.0821)(295) 5625 = (n)( ) 5625/ = n = n moles of N 2

Guided Practice Many gases are stored in their compressed form (under pressure). Calculate the mass of N 2 that could be stored at 22ºC and 125 atm in a cylinder with a volume of 45.0 L. The molecular mass of N 2 is 28.0 g/mole moles of N 2 28 g 1 mole of N * 28 = 6503 g of N 2

Independent Practice Problem 1 Calculate the mass in grams of the air in a hot-air balloon that has a volume of 40,000 L when the temperature of the gas is 90.0ºC and the pressure is 750 mm Hg. Assume that the average molecular mass of air is 30.0 g/mole

Independent Practice Problem 1 Calculate the mass in grams of the air in a hot-air balloon that has a volume of 400,000 L when the temperature of the gas is 90.0ºC and the pressure is 750 mm Hg. Assume that the average molecular mass of air is 30.0 g/mole PV = nRT P = 750 mm Hg V = 400,000 L n =? R = 62.4 T = 90ºC  = 363 K (750)(400,000) = (n)(62.4)(363) moles of air = n moles of air30 g 1 mole of air = (13244*30) = 397,320 g of air

Independent Practice Problem 2 A 2.0 L soda bottle is used as a water rocket. If 0.30 L of water is in the bottle and it is pumped with air to a pressure of 3.8 atm at a temperature of 25ºC, how many moles of air are in the rocket?

Independent Practice Problem 2 A 2.0 L soda bottle is used as a water rocket. If 0.30 L of water is in the bottle and it is pumped with air to a pressure of 3.8 atm at a temperature of 25ºC, how many moles of air are in the rocket? PV = nRT P = 3.8 atm V = 2.0 L – 0.30 L  1.7 L n = ? R = T = 25ºC  = 298 K (3.8)(1.7) = (n)(0.821)(298) 6.46 = (n)(24.47) 6.46/24.47 = n moles of air = n

Independent Practice Problem 3 A balloon is to be filled with 30.0 kg of helium gas. What volume can be filled to a pressure of 1.15 atm if the temperature is 20.0ºC?

Independent Practice Problem 3 A balloon is to be filled with 30.0 kg of helium gas. What volume can be filled to a pressure of 1.15 atm if the temperature is 20.0ºC? 30.0 kg He1000 g He1 mole He 1 kg He4 g He = (30*1000)/4 = 7500 moles of He

Independent Practice Problem 3 A balloon is to be filled with 30.0 kg of helium gas. What volume can be filled to a pressure of 1.15 atm if the temperature is 20.0ºC? PV = nRT P = 1.15 atm V = ? n = 7500 moles He R = T = 20ºC  = 293 K

Independent Practice Problem 4 You want to send chlorine gas, Cl 2, safely across your state. Chlorine gas is very poisonous and corrosive. You have a 5000 L truck cylinder that will withstand a pressure of 100 atm. The cylinder will be kept at 2ºC throughout the trip. How many moles of chlorine gas can you safely ship? PV = nRT P = 100 atm V = 5000 L n = ? R = T = 2ºC  = 275 K

Independent Practice Problem 4 You want to send chlorine gas, Cl 2, safely across your state. Chlorine gas is very poisonous and corrosive. You have a 5000 L truck cylinder that will withstand a pressure of 100 atm. The cylinder will be kept at 2ºC throughout the trip. How many moles of chlorine gas can you safely ship? PV = nRT (100)(5000) = (n)(0.0821)(275) 500,000 = n 500,000/ = n 22,145.9 moles of Cl 2 = n

Weekly Quiz Silently work on your quiz. When you are finished turn it into Ms. Bergman Gas Laws Equations P 1 V 1 = P 2 V 2 V 1 /T 1 = V 2 /T 2 PV = nRT Universal Gas Constant = L*atm/mol*K