Gas MixturesBecause the gas laws apply to ideal gases, they also apply to gas mixtures. Laws frequently used:

• Ideal gas law

• Dalton’s Law for partial pressures(including mole fraction)

Collection of Gases By Water Displacement

Example: 2KClO3(g) 2KCl(s) + 3O2(g)

Dalton’s Law of Partial Pressures

Dalton’s Law (based on Avogadro’s Law)

For two gases in a mixture:

Ptotal = total gas pressure

PA = partial pressure of gas ‘A’ (etc.)

Ptotal = PA + PB + ....

The total pressure of a gas mixture is the sum of the partial pressures of the components of the gas.

Dalton’s Law

PN2 = 0.78 atm

PO2 = 0.21 atm

Example:• air is 78% N2, 21% O2, and 1% other gases. At 1 atm:

Example - 1

A mixture of gases in scuba diving tank: (at 25oC, 1atm)He...... 46 L O2...... 12 L tank

volume = 5.0 L

¿

(a)partial pressure of each gas?

(b)total pressure inside tank?

Strategy – for (a)

(i) to use PV = nRT, we need the number of moles of each.

(ii) then we can determine the partial pressure for each

A mixture of gases in scuba diving tank: (at 25oC, 1atm)He...... 46 L O2...... 12 L tank volume = 5.0 L

¿

(i) number of moles of each gas?

(ii) partial pressure of each gas?

(a) partial pressure of each gas?

A mixture of gases in scuba diving tank: (at 25oC, 1atm)He...... 46 L O2...... 12 L tank volume = 5.0 L

¿

(b) total pressure inside tank?

Ptotal = PA + PB + ....

Ptotal = 9.3 atm + 2.4 atm = 11.7 atm

Example - 2Potassium chlorate (KClO3) was heated in a test tube and decomposed by the following reaction:

¿Question:

a. What is the partial pressure of O2 in the gas collected?

b. What was the mass of KClO3 in the original sample?

2KClO3(s) 2KCl(s) + 3O2(g)

The oxygen is collected by water displacement at 22oC, at a total pressure of 754 torr, for a total volume of 0.650 L. (PH2O = 21 torr.)

¿

2KClO3(s) 2KCl(s) + 3O2(g)

(a) What is the PO2?

Ptotal = PO2 + PH2O

PO2 = 754 torr – 21 torr = 733 torr

¿

2KClO3(s) 2KCl(s) + 3O2(g)

(b) What was the mass of KClO3 in the original sample?

iii. Number of moles of O2

ii. Number of moles of KClO3 / i. Grams KClO3

Example - 3Two bulbs are separated by a valve.

¿

Bulb Gas Pinit Vinit

A Ne 1.09 atm 1.12 LB CO 0.773 atm 2.18 L

When the valves are opened, and the gases are allowed to reach equilibrium, what is the final pressure inside the bulbs?

(Assume constant temperature.)

¿

Strategy

(iv) Final pressure

(iii) pressure from PV = nRT (Ttotal = VA + VB + VC)

(ii) total number of moles (ntotal = nA + nB + nC)

(i) mole of each gas

¿

(i) mole of each gas:

(ii) total moles:

(We don’t know Temp, but RT will cancel when calculating Ptotal)

¿

(iii) PTotal:

Mole Fraction

The ratio of the number of moles of given component in a mixture to the total number of moles in the mixture.

for component gas, A:

Combining ideal gas laws for both, and cancelling out R, V and T, and rearrange:

The fraction is called the mole fraction of A (= XA)

PA = Xa

Ptotal