Unit 10: Gases

Chemistry IMr. Patel

SWHS

Topic Outline• MUST have a scientific calculator (not graphing)!!• Properties of Gases (13.1, 14.1)• Kinetic Molecular Theory (13.1)• Temperature and Pressure Conversions (14.1)• Empirical Gas Laws (14.2)• Ideal Gases and Real Gases (14.3)• Dalton’s Law (14.4)• Graham’s Law (14.4)• Gas Law Stoichiometry

Nature and Properties of Gases• Gases are 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

Heat vs. Temperature• Heating Rise in Temperature

• Heat and Temperature are NOT the same thing!

• Heat (is energy)– Total energy of molecular motion– Depends on number, speed, and type of particle

• Temperature (measure of energy)– Measure of the average kinetic energy of a particle– Depends only on the speed of particle

• A bathtub full of water has more heat/thermal energy than a cup of water at the same temperature

• Energy transfers from hotter objects to cooler objects

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

Ex: Convert 924.8 K to Celsius.

Ex: The hottest planet in the solar system measured a temperature of 480 K on a certain

day. What is this temperature in Celsius?

Ex: 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

• Gas particles move from highpressure to low 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

Ex: Convert 25.3 atm to mm Hg.

Ex: The air pressure for a certain tire is 109 kPa. What is this pressure in atmospheres?

Ex: The weather news gives the atmospheric pressure as 1.07 atm. What is this atmospheric pressure in mm Hg?

Ex: Convert 1460 mm Hg to torr.

Practice1. An experiment at Sandia National Labs in New

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

2. 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 kPa?

Practice Solutions1. Answer: 0.998 atm

2. Answer: 1.01 kPa

The Empirical Gas Laws

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

Boyle’s Law• Relates

Pressure and Volume(Constant Temperature)

• Law: P1 V1 = P2 V2

• Inverse relationship

• If V then P

Ex: 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(Constant Pressure)

• Law:

• Direct relationship

• If T then V

Ex: If the volume of a gas at 25⁰C is 25.5 L, what is the temperature when the volume is 75.0 L?

Gay-Lussac’s Law

• Relates Pressure and Temp(Constant Volume)

• Law:

• Direct relationship

• If T then P

Ex: If the pressure of a gas at 75⁰C is 12.5atm, what is the temperature in Celsius when the

pressure is 3.75 atm?

Combined Gas Law

• Combination of the previous empirical laws

Avogadro’s Law

• Relates Moles and Volume

• Law:

• Direct relationship

• If n then V

𝑽𝟏𝒏𝟏 = 𝑽𝟐𝒏𝟐

Ex: If 3.75 moles of N2 gas are used to inflate a balloon to 0.250L, what is the volume when

the moles of gas are tripled?

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.

Ex: 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?

Ex: A balloon has a volume of 30.0L at 313K and a pressure of 1147.9 mmHg. What is the

volume at STP?

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.

PRESSURE

VOLUMEMOLES

GAS CONSTANT

TEMPERATURE𝑷𝑽= 𝒏𝑹𝑻

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 = 0.0821 atm L∙mol K ∙

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

Ex: A 5.78L container with a pressure of 1285 torr holds 7.50 moles of an ideal gas. What is

the temperature (in Celsius) within the container?

Ex: A container with a volume of 3.25L holds 32.0 g H2O gas at 25.0⁰C. What is the pressure

within the container?

Real Gases

• An ideal gas does not exist• Gas particles do have volume and

attraction/repulsion which is typically negligible

• Real Gases differ most from an ideal gas at:– Low Temperature– High pressure

• van der Waals Equation:

Dalton’s Law• Focuses on a mixture of different gases• Pressure depends on particle quantity – not

type of particle• Gases are independent of one another• Partial Pressure (PX) – pressure of a single gas

within a mixture of gases• Dalton’s Law of Partial pressure– Total pressure is the sum of the partial pressures

PTotal = P1 + P2 + P3 + …

Dalton’s Law

Dalton’s Law

Ex: A gas mixture containing carbon dioxide, oxygen, and nitrogen has a total pressure of 32.9 kPa. If the pressure due to O2 is 6.6 kPa and N2 is

23.0 kPa, what is the partial pressure of CO2?

Graham’s Law

• Diffusion – particles move from areas of high concentration to areas of low concentration– Spraying air freshener in the corner of a room

• Effusion – process of gas particles escaping a container through a single hole– Gas escaping from a balloon causing it to deflate

• Diffusion and Effusion depend on the type of particle

Graham’s Law

• Graham’s Law of Effusion– Gas particles with lower molar masses will

effuse/diffuse faster than gases with higher molar masses

Graham’s Law

• Consider: air vs. helium filled balloon– At the same temperature, the particles have the

same kinetic energy (KE=1/2 mv2)– The lower the molar mass gas particles will escape

at a faster rate– Helium atoms are much

smaller than nitrogen oroxygen• He balloon will deflate /

effuse much quicker (3 times faster)

Ex: Which gas effuses faster: CH4 or H2O?

Ex: How much faster do helium atoms effuse compared to argon atoms?

Ex: In a mixture of gases at the same temperature, at what rate do O2 molecules

effuse if Br2 molecules are effusing at a rate of 12.5 m/s?

Mixed Gas Law Problems

Ex: In a container, 2 mol of Ar gas is at a pressure of 760 torr and at 0⁰C. What volume does it

occupy?

Ex: 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?

Ex: 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?

Ex: An isothermal system contains 125g CO2 gas at 900 K with a pressure of 5.31 kPa. What is

the volume of the gas?

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

Ex: A container with a volume of 3000. mL holds 32.0 g CH4 gas at 25.0⁰C. What is the pressure

within the container?

Ex: 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?