The Combined & Ideal Gas Laws

The Combined Gas Law The combined gas law takes the relationships described by Boyle’s, Charles’ and Gay-Lussac’s Laws and expresses them together in one formula. The combined gas law takes the relationships described by Boyle’s, Charles’ and Gay-Lussac’s Laws and expresses them together in one formula. It is important to note that the amount of the gas (moles) is held constant throughout any calculations involving the combined gas law. It is important to note that the amount of the gas (moles) is held constant throughout any calculations involving the combined gas law. The formula for the combined gas law is: The formula for the combined gas law is: P 1 V 1 = P 2 V 2 T 2 T 1 If you cross multiply, you can rearrange the formula into the following which may be easier to manipulate when finding a missing value. If you cross multiply, you can rearrange the formula into the following which may be easier to manipulate when finding a missing value. P 1 V 1 T 2 = P 2 V 2 T 1

Molar Volume of Ideal Gases We have discussed two sets of conditions that act as standards when describing gases – STP and SATP. We have discussed two sets of conditions that act as standards when describing gases – STP and SATP. STP = 101.3kPa & 273K (0 ° C) STP = 101.3kPa & 273K (0 ° C) SATP = 100kPa & 298K (25 ° C) SATP = 100kPa & 298K (25 ° C) Each of these sets of standards has a standard molar volume associated with it. The molar volume is the amount of space that one mole of the gas would take up if it were in one of the sets of conditions- STP or SATP. Each of these sets of standards has a standard molar volume associated with it. The molar volume is the amount of space that one mole of the gas would take up if it were in one of the sets of conditions- STP or SATP. For STP, any gas will take up 22.4L/mol. A single morel takes up 22.4L of space. For STP, any gas will take up 22.4L/mol. A single morel takes up 22.4L of space. For SATP, any gas will take up 24.8L/mol. A single mole takes up 24.8L of space. For SATP, any gas will take up 24.8L/mol. A single mole takes up 24.8L of space.

The Ideal Gas Law The ideal gas law illustrates the relationship between pressure, volume, temperature and moles. Remember, moles was always held at a constant previous to this. The ideal gas law illustrates the relationship between pressure, volume, temperature and moles. Remember, moles was always held at a constant previous to this. The formula for the ideal gas law is: The formula for the ideal gas law is: PV = nRT In this formula: In this formula: –P = Pressure –V = Volume –n = Moles –T = Temperature –R = The Ideal Gas Constant The “R” is new to you – it is the Ideal Gas Constant and it has a value of 8.31 kPa·L/K·mol. The “R” is new to you – it is the Ideal Gas Constant and it has a value of 8.31 kPa·L/K·mol.

The Ideal Gas “R” Value The “R” in the Ideal Gas Law is a constant and has a value of 8.31 kPa·L/K·mol. Notice it has all of the units of the other four parts of the law – this is so it can be used to cancel out three of those parts when solving for the fourth. (You’ll see what I mean shortly.) The “R” in the Ideal Gas Law is a constant and has a value of 8.31 kPa·L/K·mol. Notice it has all of the units of the other four parts of the law – this is so it can be used to cancel out three of those parts when solving for the fourth. (You’ll see what I mean shortly.) Where does it come from? Where does it come from? When this formula was developed, the chemists used SATP values as the starting point. When this formula was developed, the chemists used SATP values as the starting point. –P = 100kPa –T = 298K (25 ° C) –V = 24.8L/mol (This value is the molar volume of 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” Value Using the combined gas law we know that the relationship between P, V & T is… Using the combined gas law we know that the relationship between P, V & T is…P1V1T1 If we plug in our SATP values in this formula, we will get… If we plug in our SATP values in this formula, we will get…(100kPa)(24.8L/mol)(298K) We will work the rest of this out on the board – watch carefully and the Ideal Gas Constant will magically appear before your eyes. We will work the rest of this out on the board – watch carefully and the Ideal Gas Constant will magically appear before your eyes. Now…go forth and solve the many issues concerning ideal gases everywhere. Now…go forth and solve the many issues concerning ideal gases everywhere.

THE END