Applying the ideal gas equation

Copyright © 2011 Pearson Canada Inc. Slide 1 of 19General Chemistry: Chapter 6

Copyright © 2011 Pearson Canada Inc. Slide 2 of 19General Chemistry: Chapter 6

Using the Gas Laws

Avogadro’ Hypothesis:

• Equal volumes of different gases at the same T and P contain equal numbers of molecules (or, equal numbers of moles of gas). Neglecting history (Avogadro’s elegant experiments!), we can apply the Ideal Gas Law Equation to two gases (Gas 1 and Gas 2).

• n1 = P1V1/RT1 and n2 = P2V2/RT2

• If P1=P2 and V1=V2 and T1=T2 then n1=n2

Class Example – Avogadro’s Hypothesis:

• At a given T and P, 8.00 g of oxygen gas (O2(g)) has a volume of 8.00 L. At the same T and P 10.0 L of a gas having the molecular formula XO2 has a mass of 20.0 g. Identify element X.

Partial Solution: Apply Avogadro’s HypothesisHere: Number of moles of = Number of moles of

O2(g) per liter XO2(g) per liter

# Moles O2(g) per liter = 0.250 mol/8.00L

= 0.0313 mol L∙ -1

“Aside”: Moles O2 = 8.00g/(32.0 g.mol-1) = 0.250mol

Completion of “XO2 example” in class

Ideal Gas Law and Molecular Formulas:

• In high school you used % composition data for compounds to derive corresponding empirical formulas. The Ideal Gas Law Eqtn can be used to determine molar masses. Combining an empirical formula with a molar mass allows a molecular formula to be determined. Empirical formulas specify relative numbers of atoms of each element. Knowing “too much chemistry” Can lead you astray. How?

Molecular Formulas using PV=nRT• Elemental analysis shows that a compound

containing carbon, hydrogen and fluorine , CxHyFz, is 63.17 % carbon, 3.53 % hydrogen and 33.30 % fluorine by mass. At 44.2 oC a 2.400 g sample of this substance is completely evaporated in a previously empty 2.50 L container and a gas pressure of 22.2 kPa is observed. Determine (a) the empirical formula of the compound and (b) the molecular formula of the compound.

A Step at a Time?

• One possible strategy is:• Step 1: Use mass % composition data to

determine the empirical formula for CxHyFz. • Step 2: Use the ideal gas law equation to get

(a) the number of moles of CxHyFz in 2.400g of compound and (b) the molar mass of CxHyFz.

• Step 3: Combine the results to Step 1 and Step 2 to find the molecular formula of CxHyFz.

Empirical Formula of CxHyFz •

• “Knowing too much chemistry” one might be tempted to use 2.016 g.mol-1 for the molar mass of H. Why is this absolutely wrong? We’ll complete this problem in class.

Mass of C atomsMass of H atomsMass of F atoms

Moles of C atomsMoles of H atomsMoles of F atoms

6-5 Gases in Chemical Reactions

Copyright © 2011 Pearson Canada Inc. General Chemistry: Chapter 6 Slide 10 of 41

•Stoichiometric factors relate gas quantities to quantities of other reactants or products.

•Ideal gas equation relates the amount of a gas to volume, temperature and pressure.

•Law of Combining Volumes can be developed using the gas law.

Copyright © 2011 Pearson Canada Inc. General Chemistry: Chapter 6 Slide 11 of 41

6-6 Mixtures of Gases•Partial pressure–Each component of a gas mixture exerts a pressure that it would exert if it were in the container alone.

• Gas laws apply to mixtures of gases.

• Simplest approach is to use ntotal, but....

Dalton’s law of partial pressures illustratedFigure 6-12

Copyright © 2011 Pearson Canada Inc. General Chemistry: Chapter 6 Slide 12 of 41

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

Partial Pressure

Copyright © 2011 Pearson Canada Inc. General Chemistry: Chapter 6 Slide 13 of 41

Ptot = Pa + Pb +…

Va = naRT/Ptot and Vtot = Va + Vb+…

Va

Vtot

naRT/Ptot

ntotRT/Ptot= =

na

ntot

Pa

Ptot

naRT/Vtot

ntotRT/Vtot= =

na

ntot

na

ntot

= aRecall