III. Ideal Gas Law Gases Gases. V n A. Avogadro’s Principle b Equal volumes of gases contain equal numbers of moles at constant temp & pressure true for

III. Ideal Gas LawIII. Ideal Gas Law

GasesGases

kn

VV

n

A. Avogadro’s PrincipleA. Avogadro’s PrincipleA. Avogadro’s PrincipleA. Avogadro’s Principle

Equal volumes of gases contain equal numbers of moles• at constant temp & pressure• true for any gas

PV

TVn

PVnT

A. Ideal Gas LawA. Ideal Gas LawA. Ideal Gas LawA. Ideal Gas Law

= kUNIVERSAL GAS

CONSTANTR=0.0821 Latm/molK

R=8.315 dm3kPa/molK

= R

You don’t need to memorize these values!

Merge the Combined Gas Law with Avogadro’s Principle:

A. Ideal Gas LawA. Ideal Gas LawA. Ideal Gas LawA. Ideal Gas Law

UNIVERSAL GAS CONSTANT

R=0.0821 Latm/molKR=8.315

dm3kPa/molK

PV=nRT

You don’t need to memorize these values!

GIVEN:

P = ? Atm

V = 3.25 L

n = 0.412 molR = 0.0821 L atm/molK

T = 16°C = 289 K

WORK:

PV = nRT

P(3.25)=(0.412)(0.0821)(289) L mol Latm/molK K

P = 3.01 atm

C. Ideal Gas Law ProblemsC. Ideal Gas Law ProblemsC. Ideal Gas Law ProblemsC. Ideal Gas Law Problems Calculate the pressure in atmospheres of

0.412 mol of He at 16°C & occupying 3.25 L.

GIVEN:

P = 104.5 kPa

V = ?

n = 85 gR=8.315 dm3kPa/molK

T = 25°C = 298 K

C. Ideal Gas Law ProblemsC. Ideal Gas Law ProblemsC. Ideal Gas Law ProblemsC. Ideal Gas Law Problems

Find the volume of 85 g of O2 at 25°C and 104.5 kPa.

= 2.7 mol

WORK:

85 g 1 mol = 2.7 mol

32.00 g

PV = nRT(104.5)V=(2.7) (8.315) (298) kPa mol dm3kPa/molK K

V = 64 dm3

B. Dalton’s LawB. Dalton’s LawB. Dalton’s LawB. Dalton’s Law

The total pressure of a mixture of gases equals the sum of the partial pressures of the individual gases.

Ptotal = P1 + P2 + ...When a H2 gas is collected by water displacement, the gas in the collection bottle is actually a mixture of H2 and water vapor.

GIVEN:

PH2 = ?

Ptotal = 94.4 kPa

PH2O = 2.72 kPa

WORK:

Ptotal = PH2 + PH2O

94.4 kPa = PH2 + 2.72 kPa

PH2 = 91.7 kPa


Hydrogen gas is collected over water at 22.5°C. Find the pressure of the dry gas if the atmospheric pressure is 94.4 kPa.

Look up water-vapor pressure on p.899 for 22.5°C.

Sig Figs: Round to least number of decimal places.

The total pressure in the collection bottle is equal to atmospheric pressure and is a mixture of H2 and water vapor.

GIVEN:

Pgas = ?

Ptotal = 742.0 torr

PH2O = 42.2 torr

WORK:

Ptotal = Pgas + PH2O

742.0 torr = PH2 + 42.2 torr

Pgas = 699.8 torr

A gas is collected over water at a temp of 35.0°C when the barometric pressure is 742.0 torr. What is the partial pressure of the dry gas?

Look up water-vapor pressure on p.899 for 35.0°C.

Sig Figs: Round to least number of decimal places.


The total pressure in the collection bottle is equal to barometric pressure and is a mixture of the “gas” and water vapor.

- Gases - Gases

IV. Gas Stoichiometry at Non-STP ConditionsIV. Gas Stoichiometry at Non-STP Conditions

A. Gas StoichiometryA. Gas StoichiometryA. Gas StoichiometryA. Gas Stoichiometry Moles Moles Liters of a Gas: Liters of a Gas:

• STP - use 22.4 L/mol • Non-STP - use ideal gas law

Non-Non-STPSTP• Given liters of gas?

start with ideal gas law• Looking for liters of gas?

start with stoichiometry conv.

1 molCaCO3

100.09g CaCO3

B. Gas Stoichiometry B. Gas Stoichiometry ProblemProblemB. Gas Stoichiometry B. Gas Stoichiometry ProblemProblem

What volume of CO2 forms from 5.25 g of CaCO3 at 103 kPa & 25ºC?

5.25 gCaCO3 = 1.26 mol CO2

CaCO3 CaO + CO2

1 molCO2

1 molCaCO3

5.25 g ? Lnon-STPLooking for liters: Start with stoich

and calculate moles of CO2.

Plug this into the Ideal Gas Law to find liters.

WORK:

PV = nRT

(103 kPa)V=(1mol)(8.315dm3kPa/molK)(298K)

V = 1.26 dm3 CO2


What volume of CO2 forms from 5.25 g of CaCO3 at 103 kPa & 25ºC?

GIVEN:

P = 103 kPaV = ?

n = 1.26 molT = 25°C = 298 KR = 8.315 dm3kPa/molK

WORK:

PV = nRT

(97.3 kPa) (15.0 L)= n (8.315dm3kPa/molK) (294K)

n = 0.597 mol O2


How many grams of Al2O3 are formed from 15.0 L of O2 at 97.3 kPa & 21°C?

GIVEN:

P = 97.3 kPaV = 15.0 L

n = ?T = 21°C = 294 KR = 8.315 dm3kPa/molK

4 Al + 3 O2 2 Al2O3 15.0 L

non-STP ? gGiven liters: Start with

Ideal Gas Law and calculate moles of O2.

NEXT

2 mol Al2O3

3 mol O2


How many grams of Al2O3 are formed from 15.0 L of O2 at 97.3 kPa & 21°C?

0.597mol O2 = 40.6 g Al2O3

4 Al + 3 O2 2 Al2O3

101.96 g Al2O3

1 molAl2O3

15.0Lnon-STP

? gUse stoich to convert moles of O2 to grams Al2O3.

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III. Ideal Gas Law Gases Gases. V n A. Avogadro’s Principle b Equal volumes of gases contain equal numbers of moles at constant temp & pressure true for