Ideal Gas LawP= pressure (atm)

V= volume (L)n= Mole Gas (mol) T= temperature (K)

R= universal gas constant

Ex: H2 has a volume of 8.56 L at 0oC and 1.5 atm. Calculate the moles of H2 present.

PV = nRT

R = 0.08206 L* atm mol * K

Given

V= 8.56 L

T = 0oC + 273 = 273 K

P = 1.5 atm

n = ?

R = 0.08206 atm L/mol K

n = PV

RT____ n = (1.5 atm)(8.56 L)_______________________

(0.08206 atm L/mol K)(273 K)

n = 0.57 mol

Learning Check

• Ideal Gas Law formula:

• Unit for P:

• Unit for V:

• Unit for n:

• Value & unit of R:

• Unit for T:

Dalton’s Law of Partial Pressures

Partial Pressure – pressure that a gas would exert if it alone in the container.

Ptotal = P1 + P2 + P3…Ex: A container holds three gases: oxygen, carbon dioxide,

and helium. The partial pressures of the three gases are 2.00 atm, 3.00 atm, and 4.00 atm, respectively. What is the total pressure inside the container?

Given

P1= 2.00 atm

P2= 3.00 atm

P3= 4.00 atm

Ptotal= ?

Ptotal = P1 + P2 + P3

Ptotal = 2.00 atm + 3.00 atm + 4.00 atm

Ptotal = 9.00 atm

A common method of collecting gas samples in the laboratory is to bubble the gas into a bottle filled with water and allow it to displace the water. When this technique is used, however, the gas collected in the bottle contains a small but significant amount of water vapor. As a result, the pressure of the gas that has displaced the liquid water is the sum of the pressure of the gas plus the vapor pressure of water at that temperature. The vapor pressures of water at various temperatures are given in Table.

PTotal - Pvapor = PGas

Given

T = 16°C

Pvapor =

V = 188 mL (doesn’t matter)

Ptotal = 92.3 kPa

Pgas= ?

PTotal - Pvapor = PGas

92.3 kPa – 1.82 kPa = PGas

Pgas = 90.5 kPa

Ex: A student collects oxygen gas by water displacement at a temperature of 16°C. The total volume is 188 mL at a pressure of 92.3 kPa. What is the pressure of oxygen collected?

1.82 kPa

Given

T = 17°C + 273 = 290. K

Pvapor =

V = 0.461 L

Ptotal = 0.989 atm

Pgas= ?

ngas =

PTotal - Pvapor = PGas

99.7 kPa – 1.94 kPa = PGas

Pgas = 97.8 kPa

Ex: Hydrogen gas is collected by water displacement. Total volume collected is 0.461 L at a temperature of 17°C and a pressure of 0.989 atm. What is the pressure of dry hydrogen gas collected? How many moles of hydrogen are present?

1.94 kPa

x ________

atm

kPa

1

101.3= 99.7 kPa

n = PV

RT____

n = (0.965 atm)(0.461 L)_______________________(0.08206 atm L/mol K)(290. K)

n = 0.0187 mol

x ________

kPa

atm

101.3

1= 0.965 atm

Learning Check

• Dalton’s Law formula:

• In a sentence summarize how Dalton’s Law works.

• What does it mean to collect gas over water?

Gas Stoichiometry

STP = Standard Temperature and Pressure• Standard Temperature = 0oC• Standard Pressure = 1 atm• Molar Volume 1.00 molgas = 22.4 Lgas

Ex 1: A sample of N2 has a volume of 1.75 L at STP. How many moles of N2 are present?

x ________L

mol

22.4

1= 0.0781 mol1.75 L

or

use PV = nRT

Ex 2: Calculate the volume of O2 produced at 1.00 atm and 25 oC by the decomposition of 10.5g KClO3.

2KClO3 2KCl + 3O2

Given

V= ?

T = 25oC + 273 = 298 K

P = 1.00 atm

R = 0.08206 atm L/mol K

n = 10.5 g KClO3

V = nRT

P____

V = (0.128 mol) (0.08206 atm L/mol K)(298 K)_______________________________ 1.00 atm

V = 3.13 L

x __________mol KClO3

mol O2

2

3= 0.128 mol x ___________

g KClO3

mol KClO3

122.6

1

Ex 3: Calculate the volume of CO2 produced at STP from 152g of CaCO3.

CaCO3 CaO + CO2

mol CaCO3

mol CO2

1

1=

34.0 L

x ___________

g CaCO3

mol CaCO3

100.1

1152 g CaCO3 x _______x __________ L

mol

22.4

1

or

use PV = nRT

Learning Check

• What does STP mean?

 

• STP Temperature =

• STP Pressure =

• 1 mole of gas = ______ L of gas