Combined Gas LawAvogadro’s Law

Write out the notes that are not in italics!

The Combined Gas Law

• The gas laws may be combined into a single law, called the combined gas law, that relates two sets of conditions of pressure, volume, and temperature by the following equation.

• With this equation, you can find the value of any one of the variables if you know the other five.

Applying the Combined Gas Law• A sample of nitrogen monoxide has a volume

of 72.6 mL at a temperature of 16°C and a pressure of 104.1 kPa.

• What volume will the sample occupy at 24°C and 99.3 kPa?

• Start by converting the temperatures to kelvins.

Applying the Combined Gas Law

• Next, solve the combined gas law equation for the quantity to be determined, the new volume, V2.

Applying the Combined Gas Law

• Substitute the known quantities and compute V2.

=(104.1 kPa)(72.6mL)(297K)

(99.3 kPa)(289K)

= 78.2mL

STP• At times a problem may say a

substance is at STP or standard temperature and pressure.

• Standard temperature is 0°C• Standard pressure is 1atm• When a problem occurs at STP, you

can put in the standard temp and pressure.

Avogadro’s Principle • In the early nineteenth century, Avogadro

proposed the idea that equal volumes of all gases at the same conditions of temperature and pressure contain the same number of particles.

• An extension of Avogadro’s principle is that one mole (6.02 x 1023 particles) of any gas at standard temperature and pressure (0°C and 1.00 atm pressure, STP) occupies a volume of 22.4 L.

Avogadro’s Law

• Avogadro’s Law This law relates volume with the number of

moles of a substance.

V1

n1

V2

n2

=

Practice avogadro’s law

• A 3.2mol sample of Helium is at 1.0atm. What is the pressure if the sample is increased to 7.6moles?

First solve the equation for P2

P2 =P1 n2

n1

Then plug in the numbers: P2 =(1.0atm)

(3.2mol)

(7.6mol)

P2 = 2.4atm

Worksheet time!

30 minutes

Worksheet time!

25 minutes

Worksheet time!

20 minutes

Worksheet time!

15 minutes

Worksheet time!

10 minutes

Worksheet time!

5 minutes

Worksheet time!

4 minutes

Worksheet time!

3 minutes

Worksheet time!

2 minutes

Worksheet time!

1 minutes

The Ideal Gas Law

• The pressure, volume, temperature, and number of moles of gas can be related in a simpler, more convenient way by using the ideal gas law.

• The following is the law’s mathematical expression, where n represents the number of moles.

PV = nRT

The Ideal Gas Law

• The ideal gas constant, R, already contains the molar volume of a gas at STP along with the standard temperature and pressure conditions.

Gases: Additional ConceptsGases: Additional Concepts \Gases: Additional ConceptsGases: Additional Concepts \

The Ideal Gas Law

• The constant R does the job of correcting conditions to STP.

• You do not have to correct STP in a separate step.

The Ideal Gas Law

• The Value of R depends on the units in which the pressure of the gas is measured, as shown below.

• These values are all equivalent. Use the one that matches the pressure units you are using.

Applying the Ideal Gas Law

• What pressure in atmospheres will 18.6 mol of methane exert when it is compressed in a 12.00-L tank at a temperature of 45°C?

• As always, change the temperature to kelvins before doing anything else.

Applying the Ideal Gas Law

• Next solve the ideal gas law equation for P.

• Substitute the known quantities and calculate P.

P =(18.6mol)(0.0821Latm/molK)(318K)

(12.00L)

P = 40.5 atm