Chapter 5 – Gases

In Chapter 5 we will explore the relationship between several properties of gases:

Pressure: Pascals (Pa)

Volume: m3 or liters

Amount: moles

Temperature: Kelvin

Pressure Measurements

Pressure Measurements

A barometer

a near perfect vacuum

760 mm Hg = 1 atm

Pressure Measurements

A manometer

Ideal Gasses

For an ideal gas (all gasses for now):

PV = nRT

An ideal gas: we assume that the gas molecules occupy zero volume and have no interaction with each other (except elastic collisions). These assumptions are good approximations under most conditions for all common gases.

A 3.00-L bulb containing neon gas at 3.85 atm is connected to an evacuated 5.00-L flask. The valve connecting the flasks is opened, and the pressure is allowed to equilibrate. If the temperature remains constant, what is the final pressure in the system?

How many molecules are present in a sample of hydrogen gas having a volume of 8.56 L at 0ºC and 1.5 atm pressure?

What volume of oxygen (at standard temperature and pressure - STP) is needed to fully oxidize (rust) a cube of solid iron that measures 10 cm on each side?

At 1.50 atm pressure and 27ºC, a gasis found to have a density of 1.95 g/L. What is the molar mass of the gas?

Each component of a gas mixture exerts a pressure that it would exert if it were in the container alone.

Partial pressure

The atmospheric pressure is 743 mm Hg.If the partial pressure of oxygen is 156Torr, what is the mol fraction of oxygenin air?

A mixture of 1.00 g of H2 and 1.00 g of He is placed in a 1.00 L container at standard temperature and pressure (STP). What is the total pressure of the gas?

Gas Collection Over Water

Ptotal = Pgas + PH2O

Gas Collection Over Water

A sample of nitrogen (N2) is present in a container with liquid water present. The sample has a total pressure of 763 mmHg at 27°C. The vapor pressure of water at 27°C is 26.7 mmHg. What is the density of the gas mixture?

A mixture of CH4 at 0.500 atm and O2 at 0.750 atm is present in a 3.00 L container at 28°C. The mixture is ignited by a spark and reacts according to the equation below. What is the total pressure in the container, now at 44°C, after the reaction is complete? The vapor pressure of water at 44°C is 68.26 mmHg.

A gaseous mixture consists of 50.0% O2, 25.0% N2, and 25.0% Cl2, by weight. At standard temperature and pressure, What is the partial pressure of Cl2?

Kinetic Molecular Theory

• Particles are point masses in constant, random,

straight line motion.

• Particles are separated by great distances.

• Collisions are rapid and elastic.

• No force between particles.

• Total energy remains constant.

Pressure and Molecular Speed

um is the modal speed

uav is the simple average

urms

Distribution of Molecular Speeds

Gas Properties

Diffusion

•Effusion

Graham’s Law

• Only for gases at low pressure (natural escape, not a jet).

• Tiny orifice (no collisions)

• Does not apply to diffusion.

• Ratio used can be:– Rate of effusion (as above)

– Molecular speeds

– Effusion times

– Distances traveled by molecules

– Amounts of gas effused.

Rank the following gasses in order of increasing rate of effusion:

N2, O2, Cl2, Ar

An equimolar mixture of nitrogen and carbon dioxide in a container are allowed to effuse through a hole. After a certain period of time, 0.5 mol of N2 has escaped the container. How much carbon dioxide has escaped?

Kinetic Molecular Theory

• Particles are point masses in constant, random,

straight line motion.

• Particles are separated by great distances.

• Collisions are rapid and elastic.

• No force between particles.

• Total energy remains constant.

Real Gases

PV/nRT = 1 for an ideal gas

Deviations occur for real gases:

• If PV/nRT > 1 , then molecular volume is significant.

• If PV/nRT < 1 , then intermolecular forces of attraction are significant.

Ideal Cl2N2 CO2H2He

22.41L 22.40L22.06L

22.42L 22.31L22.41L

Real Gases at STP

The van der Waals Equation

These effects are usually only seen at high pressure (gasses behave as ideal at low pressure)

Real Gases

A sample of 1.00 mol O2 is in a 100 mL container at 27°C. Assuming that the van der Waals equation is a better representation of a real gas under the conditions of this problem, how much does the ideal-gas equation overestimate the pressure compared to the van der Waals equation?

For oxygen, a = 1.360 L2-atm/mol2 and b = 0.03183 L/mol