Dalton’s Law of Partial PressuresJust simply states that the total pressure of a mixed gas is equal to the sum of the individual pressures

For example, suppose you had three gases, nitrogen, oxygen, and hydrogen, all mixed in a container.

Now assume that their pressures were the following:

- Oxygen = 1.0atm

- Nitrogen = 5.0atm

- Hydrogen = 3.0 atm

What would the total pressure of the gas in the container be?

Dalton’s Law of Partial PressuresJust simply states that the total pressure of a mixed gas is equal to the sum of the individual pressures

Ptotal = Poxygen + PHydrogen + Pnitrogen

Ptotal = 1.00 + 3.00 + 5.00

Ptotal = 9atm

Dalton’s Law of Partial PressuresIf you have a mixture of pressure units, you must convert to one or the other!

Lets try another example. Assume the following mixture of gases had the following pressure…

Now assume that their pressures were the following:

- Helium= 1.00atm

- Xenon= 5.00atm

- Nitrogen= 780mmHg

- What would the total pressure of the gas in the container be?

Dalton’s Law of Partial PressuresJust simply states that the total pressure of a mixed gas is equal to the sum of the individual pressures

Ptotal = PHelium + PXenon + PNitrogen

Ptotal = 1.00 + 5.00 + (780/760)

Ptotal = 1.00 + 5.00 + 1.03

Ptotal = 7.03atm

Dalton’s Law of Partial PressuresLikewise, the pressure of a gas in a mixture is equivalent to the percentage it is found. Therefore, assume that air is 70% nitrogen, 28% oxygen, and 2% hydrogen. Now assume that air pressure in this room is 101.325kPa. What would be the pressure of the individual gases?

Nitrogen: 101.325 x 0.70 = 70.93kPa

Oxygen: 101.325 x 0.28 = 28.37kPa

Hydrogen: 101.325 x 0.02 = 2.03kPa

Dalton’s Law of Partial PressuresSimilarly, given the number of moles of a gas, we can determine the percentage each gas represents in the mixture. For example, suppose we have a mixture of hydrogen, oxygen, nitrogen, and xenon gas in a container pressurized to 50.0atm. The number of moles of each gas in the container are as follows:

Hydrogen = 15.0mol

Oxygen = 20.0mol

Nitrogen = 35.0mol

Xenon = 12.5mol

Dalton’s Law of Partial PressuresFirst, determine the total number of moles in the container by adding the moles of each individual gas.

Hydrogen = 15.0mol

Oxygen = 20.0mol

Nitrogen = 35.0mol

Xenon = 12.5mol

Total Moles = 15.0 + 20.0 + 35.0 + 12.5

Or equal to 82.5moles

Dalton’s Law of Partial PressuresThen, use the divide the moles of each gas into the total mole count to determine the percentage of each in the container.

Hydrogen = 15.0mol

Oxygen = 20.0mol

Nitrogen = 35.0mol

Xenon = 12.5mol

15.0mol / 82.5mol = 0.1818 or 18.18%

20.0mol / 82.5mol = 0.2424 or 24.24%

35.0mol / 82.5mol = 0.4242 or 42.42%

12.5.0mol / 82.5mol = 0.1515 or 15.15%

Dalton’s Law of Partial PressuresFinally, use the percentage and total pressure in the container to determine the partial pressure of each gas. Remember, the problem stated the total pressure in the container was 50.0atm. Therefore…

Hydrogen = 18.18%

Oxygen = 24.24%

Nitrogen = 42.42%

Xenon = 15.15%

0.1818 x 50.0atm = 9.09atm

0.2424 x 50.0atm = 12.12atm

0.4242 x 50.0atm = 21.21atm

0.1515 x 50.0atm = 7.58atm

Ideal Gas LawUnlike the previous gas laws, the ideal gas law can be

used to determine the pressure, volume, temperature, or number of moles of a single gas at a given environmental condition.

Ideal Gas LawPV = nRT

P = Pressure

V = Volume

n = Number of Moles in the Gas

R = Constant (next slide)

T = Temperature (in Kelvins)

Ideal Gas LawPV = nRT

With the ideal gas law, there is a constant value known as “R”. This constant can have the following values:

0.0821 (L x atm/mol x K)

8.314 (L x kPa/mol x K)

Which one you use depends on the units of pressure in your problem

Ideal Gases vs. Real GasesNote, all gas laws, including the ideal gas law, can only

be used on the assumption a gas is an ideal gas. Ideal gases have the following properties:

Elastic collisions – When two gas molecules collide, energy is transferred from one particle to another completely

Random motion and movement (a property of a gas)

Ideal Gases

Ideal Gas LawUsing the ideal gas law is similar to those of the previous

four gas laws. Simply find your variables, put them into the ideal gas law equation, and then solve for the unknown.

Ideal Gas LawHow many moles of a gas are contained in 22.41L at 101.325kPa at 273K?

1. Identify Givens P = 101.325kPa T1 = 273K V1 = 22.41Ln = unknown R = 8.314 (LxkPa/molxK)

2. Substitute Into the Equation

PV = nRT

(101.325kPa)(22.41L)=(n)(8.314 LxkPa/molxK)(273K)

3. Solve For The Unknown Variable

(2270) = (n)(8.314)(273)2270 = 2269n1.00mol = n

Ideal Gas LawHow many moles of air molecules are contained in a 2.00L flask at 98.8kPa at 298K?

1. Identify Givens P = 98.8kPa T1 = 298K V1 = 2.00Ln = unknown R = 8.314 (LxkPa/molxK)

2. Substitute Into the Equation

PV = nRT

(98.8kPa)(2.00L)=(n)(8.314 LxkPa/molxK)(298K)

3. Solve For The Unknown Variable

(197.6) = (n)(8.314)(298)197.6= 2478n0.080mol= n

Ideal Gas LawWhat would be the volume of 135mol of nitrogen in the stratosphere where the temperature is -57C and the pressure is 0.072atm?

1. Identify Givens P = 0.072atm T1 = 216K V1 = unknownn = 135mol R = 0.0821 (Lxatm/molxK)

2. Substitute Into the Equation

PV = nRT

(0.072atm)(V)=(135mol)(0.0821 Lxatm/molxK)(216K)

3. Solve For The Unknown Variable

(0.072)(V) = (135)(0.0821)(216)0.072V= 2394V = 33250L