Gas Laws

Chapters 13.1 and 14Pre-AP Chemistry

Nature and Properties of Gases• Gases are easily compressible

– Easily compressible– Flow easily (fluids)– Assume the shape and volume of container

• Gases are described by four variables: – Amount of gas (n)– Volume (V)– Pressure (P)– Temperature (T)

• Kinetic theory – all particles are in constant motion …one exception

Kinetic Molecular Theory

1. Particles have insignificant volume– Large distance between particles– No attractive or repulsive forces

2. Motion is rapid and random– Travel in straight line path until collisions

3. Collisions are completely elastic– KE is transferred without loss

Temperature

• When heating a gas, most energy goes into motion

• Average KE is related to temperature (K)• All particles same average KE at room temp• All motion stops at absolute zero– 0 K or -273⁰C

Temperature Conversions

• Celsius to Kelvin: K = 273 + ⁰C

• Kelvin to Celsius: ⁰C = K - 273

[E1] Convert 924.8 K to Celsius.

[E2] The hottest planet in the solar system measured a temperature of 480 K on a certain

day. What is this temperature in Celsius?

[E3] The Rhinovirus reproduces especially well at nostril temperatures of 32.8⁰C. What is this

temperature in Kelvin?

Gas Pressure

• Force exerted by gas per unit surface area• Result of billions of simultaneous collisions• Ex: Helium balloon• Vacuum – No pressure– no gas particles

• Barometer – device used to measure atmospheric pressure

Pressure Conversions

• Standard Temperature and Pressure (STP)– 0⁰C = 273 K– 1 atm

• 1 atm = 760 mm Hg = 760 torr = 101.3 kPa (SI)• These are conversion factors

[E4] Convert 25.3 atm to mm Hg.

[E5] The air pressure for a certain tire is 109 kPa. What is this pressure in atmospheres?

[E6] The weather news gives the atmospheric pressure as 1.07 atm. What is this atmospheric pressure in mm Hg?

Practice• An experiment at Sandia National Labs in

New Mexico is performed at 758.7 torr. What is this pressure in atm?

• A bag of potato chips is sealed in a factory near sea level. The atmospheric pressure at the factory is 761.3 mm Hg. The pressure inside the bag is the same. What is the pressure inside the bag of potato chips in Pa?

Practice Solutions• An experiment at Sandia National Labs in

New Mexico is performed at 758.7 torr. What is this pressure in atm? (Answer: 0.998 atm)

• A bag of potato chips is sealed in a factory near sea level. The atmospheric pressure at the factory is 761.3 mm Hg. The pressure inside the bag is the same. What is the pressure inside the bag of potato chips in Pa?(Answer: 1.01 x 105 Pa)

The Empirical Gas Laws (14.2)

• There are four empirical gas laws• These laws relate the gas variables• Empirical – based on observation

Boyle’s Law

• Relates Pressure and Volume

• Law: P1 V1 = P2 V2

• Inverse relationship

• If V then P

[E7] If the volume of the lungs is 2.400 L during exhalation and the pressure is 101.70 KPa, and the pressure during inhalation is 101.01 KPa,

what is the volume of the lungs during inhalation?

Charles’s Law

• Relates Temp and Volume

• Law:

• Direct relationship

• If T then V

Gay-Lussac’s Law

• Relates Pressure and Temp

• Law:

• Direct relationship

• If T then P

Combined Gas Law

• Combination of the previous empirical laws

Key Terms

• Isothermal – constant temperature

• Isobaric – constant pressure

• Isochoric – constant volume

Avogadro’s Law

• Relates Moles and Volume

• Law:

• Direct relationship

• If n then V

𝑽𝟏𝒏𝟏 = 𝑽𝟐𝒏𝟐

The Empirical Laws

• The previous laws are useful when only two variables are changing…everything else is constant.

• They are laws for specific scenarios.• It is possible to use the laws to create a law

that is general in nature – not specific.

Ideal Gas Law• Combines the previous observations.• One of the most fundamental and important

laws in chemistry. • Describes a SINGLE gas.𝑷𝑽= 𝒏𝑹𝑻 PRESSURE

VOLUMEMOLES

GAS CONSTANT

TEMPERATURE

Ideal Gases

• This is for ideal gases…not real gases.

• Many real gases behave as ideal gases.

• An ideal gas completely follows all the tenants of the Kinetic Molecular Theory.

Gas Constant – R

• This is a universal constant.• It is important to memorize the value of this

number with the CORRECT units.• The value changes based on the units.

R =

Implications of R on PV=nRT

• Previous laws – we could use any units as long as we were consistent.

• The units used in the ideal gas law are determined by our choice of R.

• If R = 0.0821 atm L∙/mol K∙ is used:– P must be in atm– V must be in L– T must be in K

Tips on Solving Gas Law Problems

1. Write down all the variables that are known.2. Determine which variable you are looking for.3. Convert all variables to the correct units.4. Write down the correct law/equation.5. Rearrange equation.6. Plug in values and solve.7. See if your answer makes sense.

Real vs. Ideal Gases

• Ideal gases follow Kinetic Molecular Theory– Particles have insignificant volume– No attractive/repulsive forces

• Ideal gases become real gases when:– High pressure Molecule volume is important– Low temperature Molecules become sticky– All about intermolecular forces

van der Waals Equation

• This equation described real gases.• It takes into account the stickiness of gases

and the volume significance

ቆ𝑷+ 𝒂∙𝒏𝟐𝑽𝟐 ቇሺ𝑽− 𝒏∙𝒃ሻ= 𝒏𝑹𝑻

[E8] The gas in a spray can has a pressure of 103 kPa at 25 ⁰C. The can is heated to 928 ⁰C.

What is the resulting pressure?

[E9] A balloon has a volume of 30.0L at 313K and a pressure of 1147.9 mmHg. What is the

volume at 0 ⁰C and 1 atm?

[E10] The temperature of a gas is 300.K and the volume is 821 L. The temperature of the gas is

raised by 35.0 K. What is the new volume?

[E11] The volume of a sealed, rigid cylinder is 20.0L. The pressure in the cylinder is 985 torr

at 31 ⁰C. What is the effect when the temperature is lowered to 3.1 ⁰C?

[E12] An isothermal system contains CO2 gas at 900 K with a pressure of 5.31 kPa. What is the

volume of the gas?

[E13] At a pressure of 1.00 atm, one mole of a gas is at 0⁰C. What volume does it occupy?

[E14] A container with a volume of 3000. mLholds 32.0 g CH4 gas at 25.0⁰C. What is the

pressure within the container?

[E15] In a 3.05L bottle, CO2 gas is heated to 298K at a pressure of 225.1 kPa. How many grams

of carbon dioxide gas are in the bottle?