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# III. Ideal Gas Law - PowerPoint PPT Presentation

Gases. III. Ideal Gas Law. A. Ideal Gas Law. = k. V n. Merge the Combined Gas Law with Avogadro’s Principle:. PV T. PV nT. = R. UNIVERSAL GAS CONSTANT R=0.0821 L atm/molK R=8.315 dm 3 kPa/molK. You don’t need to memorize these values!. A. Ideal Gas Law. PV=nRT.

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### III. Ideal Gas Law

= k

V

n

Merge the Combined Gas Law with Avogadro’s Principle:

PV

T

PV

nT

= R

UNIVERSAL GAS CONSTANT

R=0.0821 Latm/molK

R=8.315 dm3kPa/molK

You don’t need to memorize these values!

PV=nRT

UNIVERSAL GAS CONSTANT

R=0.0821 Latm/molK

R=8.315 dm3kPa/molK

You don’t need to memorize these values!

• Calculate the pressure in atmospheres of 0.412 mol of He at 16°C & occupying 3.25 L.

GIVEN:

P = ? atm

n = 0.412 mol

T = 16°C = 289 K

V = 3.25 L

R = 0.0821Latm/molK

WORK:

PV = nRT

P(3.25)=(0.412)(0.0821)(289)

L mol Latm/molK K

P = 3.01 atm

WORK:

85 g 1 mol = 2.7 mol

32.00 g

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

GIVEN:

V=?

n=85 g

T=25°C = 298 K

P=104.5 kPa

R=8.315dm3kPa/molK

= 2.7 mol

PV = nRT

(104.5)V=(2.7) (8.315) (298)

kPa mol dm3kPa/molKK

V = 64 dm3

• Moles  Liters of a Gas:

• STP - use 22.4 L/mol

• Non-STP - use ideal gas law

• Non-STP

• Given liters of gas?

• Looking for liters of gas?

C. Johannesson

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

CaCO3 CaO + CO2

5.25 g

? Lnon-STP

5.25 g

CaCO3

1 mol

CaCO3

100.09g

CaCO3

1 mol

CO2

1 mol

CaCO3

= 1.26 mol CO2

Plug this into the Ideal Gas Law to find liters.

C. Johannesson

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

GIVEN:

P=103 kPa

V = ?

n=1.26 mol

T=25°C = 298 K

R=8.315dm3kPa/molK

WORK:

PV = nRT

(103 kPa)V=(1mol)(8.315dm3kPa/molK)(298K)

V = 1.26 dm3 CO2

C. Johannesson

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

4 Al + 3 O2 2 Al2O3

15.0 L

non-STP

? g

GIVEN:

P=97.3 kPa

V = 15.0 L

n=?

T=21°C = 294 K

R=8.315dm3kPa/molK

WORK:

PV = nRT

(97.3 kPa) (15.0 L)= n (8.315dm3kPa/molK) (294K)

n = 0.597 mol O2

Given liters: Start with Ideal Gas Law and calculate moles of O2.

NEXT 

C. Johannesson

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

4 Al + 3 O2 2 Al2O3

15.0L

non-STP

? g

Use stoich to convert moles of O2 to grams Al2O3.

0.597

mol O2

2 mol Al2O3

3 mol O2

101.96 g Al2O3

1 mol

Al2O3

= 40.6 g Al2O3

C. Johannesson

C. Dalton’s Law

Ptotal = P1 + P2 + ...

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

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

C. Johannesson

C. Dalton’s Law

• 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.

The total pressure in the collection bottle is equal to atmospheric pressure and is 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

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

Sig Figs: Round to least number of decimal places.

C. Johannesson

C. Dalton’s Law

• 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?

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

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

Sig Figs: Round to least number of decimal places.

C. Johannesson