1. The Ideal Gas Law and Dalton’s Law of Partial Pressures
Gases Lecture III
The Ideal Gas Law and Dalton’s Law of Partial Pressures

2. The Ideal Gas Law
Is there a relationship between the following variables?
pressure
volume
YES
number of moles
temperature
they all have an affect on one another
the ideal gas law allows us to quantify this relationship by providing us an equation to evaluate the effects of one variable on another

3. PV=nRT In equation form, the ideal gas law looks like this
P is pressure in atmospheres
V is volume in liters
n is the number of moles of all gases present
T is the temperature in Kelvin
R is the ideal gas constant
R= atm x L/mol x K

4. Here’s a problem using this equation
What pressure, in atmospheres, is exerted by mol of nitrogen gas in a 6.10 L container at standard temperature?
1. Identify the variables
n=0.450 mol
V=6.10 L
T=273 K
R= atm x L/mol x K
2. Rearrange the equation
PV=nRT
P=nRT/V

5. 3. Solve the problem
P=(0.450 mol)(0.0821)(273 K)/(6.10 L)
P=1.65 atm

6. My lungs hold 6.30 L of air at normal body temperature (37 oC) and standard pressure. Assuming that air is made up of 20.9% oxygen, how many oxygen molecules are in my lungs after I take a breath?
1. Identify the variables
V=6.30 L
T=310 K
P=1.00 atm
R= atm x L/mol x K
2. Solve the equation
PV=nRT
n=PV/RT

7. 3. Solve the equation
n=(1.00 atm)(6.30 L)/( atm x L/mol x K)(310 K)
n= mol
4. Apply the percentage
n is the number of molecules of any gas, so each gas contributes the same to the total volume and pressure, regardless of molar mass
moles of oxygen= mol x 20.9%
moles of oxygen= mol

8. 5. Convert to molecules
mol X
6.022 x 1023 molecules =
1 mol
3.12 x 1022 molecules

9. Dalton’s Law of Partial Pressures
partial pressure is defined as the pressure of each individual gas in a mixture
remember ideal gases all behave the same way
Dalton’s law of partial pressures states that the total pressure of a mixture of gases is equal to the sum of the partial pressures of the gases in the mixture
In an equation, it looks like this. . .
Ptotal=P1+P2+P3. . .

10. + = barometer Poxygen=0.12 atm bulb with gas Pnitrogen=0.12 atm
Ptotal=0.24 atm

11. What does the pressure of a gas depend on?
Primarily the number of moles of gas present
The greater the number of moles of a particular gas present in a sample, the greater that gas contributes to the total pressure of the sample
if a gas makes up 3/5 of a sample, it accounts for 3/5 of the total pressure
if a gas makes up 64% of a sample, it accounts for 64% of the total pressure
the percentages and fractions refer to the number of moles, not the mass
IMPORTANT

12. let’s try an example
A 4.8 g sample of gas containing only nitrogen and oxygen contains 3.1 g of O2. The gas is sealed in a container and exerts a pressure of 940 mm Hg. What is the partial pressure of each gas in the container?
1. Find the number of moles of each gas
#mol=mass(g)/molar mass
#mol O2=(3.1 g)/(32.00g/mol) =
mol O2
#mol N2=(1.7 g)/(28.02g/mol) =
mol N2

13. 2. Determine the mole fraction of each gas
mole fraction=moles of individual gas
total moles of gas
total moles of gas= mol O mol N2 =
mol
mole fraction O2= mol/ mol =
0.6149
mole fraction N2= mol/ mol =
0.3851

14. 3. Multiply total pressure by the mole fraction to determine partial pressure of each gas
Poxygen=940 mm Hg x =
578 mm Hg
Pnitrogen=940 mm Hg x =
362 mm Hg
check: 578 mm Hg mm Hg = 940 mm Hg

15. When chemists want to collect a gas, they often do it with a technique known as water displacement
the reaction you are about to see makes hydrogen gas
H2O is present due to slight evaporation
reaction vessel
What factor could increase the amount of evaporated H2O?
temperature

16. the greater the temperature, the greater the number of water molecules present above the water
What will this do to the partial pressure of H2O?
Increased temperature will increase the partial pressure of H2O
this can be observed in chart 8 in the appendix of your book

17. The gas inside the water displacement chamber is at equilibrium with the gas outside the chamber
in other words, the gas inside is at the same pressure as the gas outside (Patm)
the atmospheric pressure is the same as the total pressure inside the chamber
Patm=Pgas+Pwater

18. Helium gas is collected over water at 25 oC
Helium gas is collected over water at 25 oC. What is the partial pressure of the helium if the atmospheric pressure outside the water collection bottle is 765 mm Hg?
1. Find the pressure of water at that temperature

19. 2. Rearrange the equation
Patm=Pgas+Pwater
Pgas=Patm-Pwater
3. Solve the equation
Pgas=765 mm Hg – 23.8 mm Hg =
741.2 mm Hg