Ideal Gas LawMarch 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 Now5L 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 + 273 = 288 K 30ºC + 273 = 303 K

V1/T1 = V2/T2

5/288 = x/3030.017 = x/303(303)(0.017) = x5.26 L = x

Charles’ Law Problem: Volume and Temperature

ObjectiveI 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)

HomeworkHW11: Ideal Gas Law Practice

Problems

VocabularyIdeal Gas: a gas in which all

collisions between atoms or molecules are perfectly elastic and in which there are no intermolecular attractive forces.

VocabularyStandard Temperature and

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

Ideal Gas Law Guided ReadingRead 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 Questions1. 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 atmV = volume in Ln = the number of moles of gasR = the universal gas constant (0.0821

Latm/molK or 62.4 Lmm Hg/molK)

T = temperature in kelvins

Example ProblemWhat is the volume of 3 moles of

oxygen gas if the temperature is 32ºC and the pressure is 3.1 atm?

PV = nRTP = 3.1 atmV = ?n = 3R = 0.0821T = 32ºC 32 + 273 = 305 K

Example ProblemWhat 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 = 75.1215V = 75.1215/3.1

V = 24.2 L

Example ProblemA sample of dry gas weighing 1.05 g

is found to occupy 1.43L at 23.5ºC and 0.951 atm. How many moles of the gas are present?

PV = nRTP = 0.951 atmV = 1.43 Ln = ?R = 0.0821T = 23.5ºC 23.5 + 273 = 296.5 K

Example ProblemA sample of dry gas weighing 1.05

g is found to occupy 1.43L at 23.5ºC and 0.951 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

0.056 = nThere are 0.056 moles of dry gas

Practice QuestionA sample of dry gas weighing 1.05

g is found to occupy 1.43L at 23.5ºC and 0.951 atm. There are 0.056 moles of the dry gas. What is the mass of one mole of this gas?

a) 18.8 g/molb) 0.05 g/molc) 0.059 g/mold) 1.5 g/mol

Practice QuestionA sample of dry gas weighing 1.05

g is found to occupy 1.43L at 23.5ºC and 0.951 atm. There are 0.056 moles of the dry gas. What is the mass of one mole of this gas?

a) 18.8 g/molb) 0.05 g/molc) 0.059 g/mold) 1.5 g/mol

1.05 g0.056 moles

Guided PracticeLet’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 = nRTP = 1.0 atmV = 1.0 Ln = ?R = 0.0821 T = 20ºC 20 + 273 = 293 K

Guided PracticeLet’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

0.042 moles = n

Guided PracticeMany gases are stored in their compressed form (under pressure). Calculate the mass of N2 that could be stored at 22ºC and 125 atm in a cylinder with a volume of 45.0 L. The molecular mass of N2 is 28.0 g/mole

PV = nRTP = 125 atmV = 45.0 Ln = ?R = 0.0821T = 22ºC 22 + 273 = 295 K

Guided PracticeMany gases are stored in their compressed form (under pressure). Calculate the mass of N2 that could be stored at 22ºC and 125 atm in a cylinder with a volume of 45.0 L. The molecular mass of N2 is 28.0 g/mole

PV = nRT(125)(45) = (n)(0.0821)(295)

5625 = (n)(24.2195)5625/24.2195 = n

232.25 = n232.25 moles of N2

Guided Practice

Many gases are stored in their compressed form (under pressure). Calculate the mass of N2 that could be stored at 22ºC and 125 atm in a cylinder with a volume of 45.0 L. The molecular mass of N2 is 28.0 g/mole

232.25 moles of N2

232.25 moles of N2

28 g

1 mole of N2232.25 * 28 = 6503 g of N2

Independent Practice Problem 1Calculate 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 1Calculate 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 90 + 273 = 363 K

(750)(400,000) = (n)(62.4)(363)13244 moles of air = n

13244 moles of air 30 g

1 mole of air= (13244*30)= 397,320 g of air

Independent Practice Problem 2A 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 2A 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 = nRTP = 3.8 atm V = 2.0 L – 0.30 L 1.7 Ln = ?R = 0.0821T = 25ºC 273 + 25 = 298 K

(3.8)(1.7) = (n)(0.821)(298)6.46 = (n)(24.47)6.46/24.47 = n

0.266 moles of air = n

Independent Practice Problem 3A 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 3A 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 He

1000 g He

1 mole He

1 kg He 4 g He= (30*1000)/4= 7500 moles of He

Independent Practice Problem 3A 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 = nRTP = 1.15 atmV = ?n = 7500 moles HeR = 0.0821T = 20ºC 20 + 273 = 293 K

Independent Practice Problem 4You want to send chlorine gas, Cl2, 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 = nRTP = 100 atmV = 5000 Ln = ?R = 0.0821T = 2ºC 2+ 273 = 275 K

Independent Practice Problem 4You want to send chlorine gas, Cl2, 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 = 22.5775n500,000/22.5775 = n

22,145.9 moles of Cl2 = n

Weekly QuizSilently work on your quiz. When you

are finished turn it into Ms. Bergman

Gas Laws EquationsP1V1 = P2V2

V1/T1 = V2/T2

PV = nRTUniversal Gas Constant = 0.0821

L*atm/mol*K