Combined Gas Law

How can you combine all three laws into one equation?

•Boyle’s Law P x V•Charles’s Law V / T•Gay-Lussac’s Law P / T

Combined Gas Law

• relates pressure, temperature, and volume in a single statement

Equation:

P₁V₁ = P₂V₂T₁ T₂

Using Combined Gas Law

• Lets you solve problems if more than one variable changes at a time

• Helps you remember all the other equations

Try Using the Combined Gas Law

• Find what you know and plug it in. Remember to change °C to K!

P₁V₁ = P₂V₂T₁ T₂

.58 L

Worksheet Practice of the 3 Gas Laws and

Combined Gas Law

The particles that make up different gases can come in all different sizes

Particles in a gas are far enough apart from each other that size has very little influence on the volume occupied by the gas

Avogadro’s principle

• equal volumes of gas at the same temperature and pressure contain equal numbers of particles

Avogadro’s Principle

• Why does this work with gases but not with liquids or solids?

Remember 1 mole = 6.02 x 10²³

•Molar volume of a gas – the volume that 1 mol occupies at 0°C and 1 atm pressure

0°C and 1 atm pressure are known as…

STP (Standard Temperature &

Pressure)

After many experiments…

•1 mol of gas at STP has a volume of 22.4 L

Using molar volume in calculations

• Because the volume of 1 mol of any gas at STP is 22.4 L, you can use 22.4/mol as a conversion factor when a gas is at STP.

How many moles are in a sample of gas that has a volume of 3.72 L at STP?

Question?

• What is the volume of 4.59 mol of CO₂ gas at STP?

4.59 x 22.4 = 102.8

What is the equation for the Combined Gas Law?

How do they relate to each other?

How can Avogadro’s principle fit into the equation?

• The volume and temp. of this tire stay the same as air is added. However, the pressure in the tire increases as the amount of air increases

PV = constantnT

Experiments using known values of P, T, V, and n have determined the value of this

constant

• Ideal Gas Constant = R

The unit used for pressure determines that value

Ideal Gas Constant

R = 0.0821 if pressure is in atmR = 8.314 if pressure is in kPaR = 62.4 if pressure is in mmHg

Plugging R into the equation gives you…

• Ideal Gas Law – relates the number of particles to pressure, temperature, and volume

Equation:

RP =V =n =R =T =

PressureVolumeMolesIdeal Gas ConstantTemperature

Calculations

• Calculate the number of moles of ammonia gas (NH₃) contained in a 3.0 L vessel at 3.00x10² K with a pressure of 1.5 atm.

• Determine the Kelvin temp. required for 0.014 mol of gas to fill a balloon to 1.20 L under 0.988 atm pressure.

Calculations

Ideal Gases vs. Real Gases

• Particles take up no space

Ideal Gases vs. Real Gases

• No intermolecular attractive forces

Ideal Gases vs. Real Gases

• Particles are in constant, random motion, moving in straight lines until colliding with walls or each other

Ideal Gases vs. Real Gases

• Follows gas laws under all conditions of temperature and pressure

• All gases have volume and are subject to intermolecular interactions• Collisions are not perfectly elastic

However…

No gas is truly ideal

Most gases will behave like ideal gases at a wide range of temperatures and pressures.

Calculations can be made using gas laws that closely approximate experimental measurements

When will a real gas not follow the Ideal gas law?

High Pressure

Low Temperature

High Pressure Example:

• propane gas will liquefy if enough pressure is applied

Low Temperature Example:

• Nitrogen gas turns to a liquid at -196°C

• http://phet.colorado.edu/en/simulation/gas-properties