The CombinedThe Combined& &

Ideal Gas LawsIdeal Gas Laws

The Combined Gas LawThe Combined Gas Law• The combined gas law takes the relationships The combined gas law takes the relationships

described by Boyle’s, Charles’ and Gay-Lussac’s described by Boyle’s, Charles’ and Gay-Lussac’s Laws and expresses them together in one formula.Laws and expresses them together in one formula.

• It is important to note that the amount of the gas It is important to note that the amount of the gas (moles) is held constant throughout any (moles) is held constant throughout any calculations involving the combined gas law.calculations involving the combined gas law.

• The formula for the combined gas law is:The formula for the combined gas law is:

PP11VV11 = = PP22VV22

TT22 T T11

• If you cross multiply, you can rearrange the If you cross multiply, you can rearrange the formula into the following which may be easier to formula into the following which may be easier to manipulate when finding a missing value.manipulate when finding a missing value.

PP11VV11TT2 2 = P= P22VV22TT11

Molar Volume of Ideal GasesMolar Volume of Ideal Gases• We have discussed two sets of conditions that We have discussed two sets of conditions that

act as standards when describing gases – STP act as standards when describing gases – STP and SATP.and SATP.

• STP = 101.3kPa & 273K (0STP = 101.3kPa & 273K (0°°C)C)• SATP = 100kPa & 298K (25SATP = 100kPa & 298K (25°°C)C)• Each of these sets of standards has a Each of these sets of standards has a

standard molar volume associated with it. The standard molar volume associated with it. The molar volumemolar volume is the amount of space that is the amount of space that one mole of the gas would take up if it were one mole of the gas would take up if it were in one of the sets of conditions- STP or SATP.in one of the sets of conditions- STP or SATP.

• For For STPSTP, any gas will take up , any gas will take up 22.4L/mol22.4L/mol. A . A single morel takes up 22.4L of space.single morel takes up 22.4L of space.

• For For SATPSATP, any gas will take up , any gas will take up 24.8L/mol24.8L/mol. A . A single mole takes up 24.8L of space.single mole takes up 24.8L of space.

The Ideal Gas LawThe Ideal Gas Law• The ideal gas law illustrates the relationship between The ideal gas law illustrates the relationship between

pressure, volume , temperature and moles. pressure, volume , temperature and moles. Remember, moles was always held at a constant Remember, moles was always held at a constant previous to this.previous to this.

• The formula for the ideal gas law is:The formula for the ideal gas law is:

PV = nRTPV = nRT• In this formula:In this formula:

– P = PressureP = Pressure– V = VolumeV = Volume– n = Molesn = Moles– T = TemperatureT = Temperature– R = The Ideal Gas ConstantR = The Ideal Gas Constant

• The The ““RR”” is new to you – it is the is new to you – it is the Ideal Gas Ideal Gas ConstantConstant and it has a value of and it has a value of 8.31 kPa8.31 kPa·L/K·mol·L/K·mol..

The Ideal Gas “R” ValueThe Ideal Gas “R” Value• The The ““RR”” in the Ideal Gas Law is a constant in the Ideal Gas Law is a constant

and has a value of and has a value of 8.31 kPa8.31 kPa·L/K·mol·L/K·mol. Notice . Notice it has all of the units of the other four parts of it has all of the units of the other four parts of the law – this is so it can be used to cancel the law – this is so it can be used to cancel out three of those parts when solving for the out three of those parts when solving for the fourth. (You’ll see what I mean shortly.)fourth. (You’ll see what I mean shortly.)

• Where does it come from?Where does it come from?• When this formula was developed, the When this formula was developed, the

chemists used chemists used SATPSATP values as the starting values as the starting point.point.– P = 100kPaP = 100kPa– T = 298K (25T = 298K (25°°C)C)– V = 24.8L/mol (This value is the molar volume of V = 24.8L/mol (This value is the molar volume of

any gas at SATP.)any gas at SATP.)• Now we need to use the combined gas law…Now we need to use the combined gas law…

Calculating the “R” ValueCalculating the “R” Value• Using the combined gas law we know that Using the combined gas law we know that

the relationship between P, V & T is…the relationship between P, V & T is…P1V1P1V1

T1T1• If we plug in our SATP values in this formula, If we plug in our SATP values in this formula,

we will get…we will get…(100kPa)(24.8L/mol)(100kPa)(24.8L/mol)

(298K)(298K)• We will work the rest of this out on the board We will work the rest of this out on the board

– watch carefully and the Ideal Gas Constant – watch carefully and the Ideal Gas Constant will magically appear before your eyes.will magically appear before your eyes.

• Now…go forth and solve the many issues Now…go forth and solve the many issues concerning ideal gases everywhere.concerning ideal gases everywhere.

THE ENDTHE END