S1.5 Ideal Gases

S1.5 Ideal Gases

​Ideal Gases

​To simplify the math when working with gases, we assume the gases are ideal gases.

​Ideal Gases

​At low temperatures and high pressures, gases do NOT behave like ideal gases because the particles are close enough that intermolecular forces become too strong to disregard. In other words, we would need to use more advanced equations in these conditions.

​Explore the simulation on the next slide to understand pressure and temperature in relation to gases.

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​Pressure

​The pressure of a gas is the force of gas collisions against the container walls divided by the surface area of the container walls. It is usually measured in Pascals (Pa) or kilopascals (kPa).

​Reminder, in S1.1 we covered Temperature:
The average kinetic energy of the particles in a sample.

​Review: Avogadro's Law

​Equal volumes of all gases at the same temperature and pressure contain equal number of molecules/moles.
The mass will differ as each molecule has a different mass.

​Standard Temperature & Pressure

​Temperature of 273.15 K and pressure of 100 kPa & is listed in the data booklet.

Note: Much older IB Syllabus and other non-IB sources define STP as 273.15 K and 101.3 kPa (instead of 100 kPa).

​Molar Volume

​As a result of Avogadro’s Law, one mole of any gas at STP (273.15 K & 100 kPa) occupies a volume of 22.7 dm³.
Vm = 22.7 dm³ mol^-1.

Note: As the current IB syllabus defines STP as 100 kPa and older/other sources define it as 101.3 kPa, online you will see other sources use 22.4 dm³ mol^-1.

​Connecting to Mole Map

​Mass

​x Molar Mass

​÷ Molar Mass

​x 6.02 x 10²³

​÷ 6.02 x 10²³

x Volume

÷ Volume

Concentration

Gas Volume at STP

÷ V_m

x V_m

​Mass

​x Molar Mass

​÷ Molar Mass

​x 6.02 x 10²³

​÷ 6.02 x 10²³

x Volume

÷ Volume

Concentration

Gas Volume at STP

÷ V_m

x V_m

​Mass

​x Molar Mass

​÷ Molar Mass

​x 6.02 x 10²³

​÷ 6.02 x 10²³

x Volume

÷ Volume

Concentration

Gas Volume at STP

÷ V_m

x V_m

Effects of Changing Conditions

If a gas has changing conditions (for example, does not stay at STP), we can predict the effects of the changes.

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Multiple Choice

It the temperature of a gas triples, what happens to its volume?

• Triples

• Doubles

• Remains Constant

• Halves (becomes 1/2 of original volume)

• Becomes a third (1/3) of its original volume

Multiple Choice

If the pressure of a gas doubles when its temperature changes (while other variables remain constant), what must have happened to the temperature?

• Doubled

• Halved

• Remained Constant

Multiple Choice

If a gas is compressed to a quarter of its original volume, what happens to the pressure (other variables remaining constant)?

• Becomes 1/4 of original pressure

• Quadruples (4 times larger)

• Remains Constant

Multiple Choice

The the pressure of a gas is doubled while other variables remain constant, what must happen to the volume?

• Doubles

• Halves

• Remains Constant

• Triples

• Becomes 1/3 (one third) of original.

​Linearizing Data

​In some cases, it is helpful to linearize data by manipulating the variables. In the case of inverse relationships (like volume and pressure), inversing one of the variables leads to a straight line:

​Combined Gas Law

​From the results above, we can just make one combined gas law instead of 3 separate gas laws.

​Alternative Method:
From your investigation, you know that P and V are inversely proportional when T is constant. So when you halve the pressure, the volume doubles.
Double of 2.0 dm³ is 4.0 dm³.

​Qualitative Solving

​Sometimes we are asked to solve without measurements.

​Example: What happens to the volume of a fixed mass of gas when its pressure and its absolute temperature are both doubled?

​Method 1:
Conceptually we know that:

• P & V are inversely proportional, so if we double pressure, volume halves.

• V & T are proportional, so if we double temperature, the volume doubles.

So if we halve the volume and then double it, we end up with the original answer. So volume does not change.

​Mixing Gases

​When gases are mixed together, their individual pressures add up to the total pressure of the gas mixture.

​Example: Two containers are connected by a stopcock as shown. Gas "A" is at a pressure of 202 kPa while gas "B" is at a pressure of 140 kPa. What will the resultant pressure be when the stopcock is opened? Assume temperature remains constant.

​Mixing Gases

​Ideal Gas Law

​The ideal gas law allows us to calculate moles of gases at non-STP conditions. Let’s add this to our Mole Map.

​Note: You can also use pressure in kPa if the volume is in dm³. 

​Connecting to Mole Map

​Mass

​x Molar Mass

​÷ Molar Mass

​x 6.02 x 10²³

​÷ 6.02 x 10²³

x Volume

÷ Volume

Concentration

Gas Volume at STP

÷ V_m

x V_m

Gas Volume

PV/RT

nRT/P

​Molar Mass and Ideal Gas Law

​Since n is in both n = m/M and PV=nRT, we can substitute m/M into the ideal gas law equation. This allows us to solve for the molar mass of a gas:

​Experimental Data

​Sometimes we are given experimental data to solve the problem with.

​Connecting to Empirical / Molecular Formulas

​As we progress through chemistry, different units can start to interact with one another (which is why retention is important).

​Additional Graphs

​It does come up that they will ask for a graph of relationships between variables in the Ideal Gas Law in relation to n. When we make n the subject we see that: