Gases

General Characteristics of Gases Highly compressible. Occupy the full volume of their containers. When gas is subjected to pressure, its volume decreases. Gases always form homogeneous mixtures with other gases. Gases only occupy about 0.1 % of the volume of their containers.

Four Physical Quantities for Gases Phys. Qty. Symbol SI unit Other common units pressure P Pascal (Pa) atm, mm Hg, torr, psi volume V m3 dm3, L, mL, cm3 temp. T K °C, °F moles n mol

Figure 10.2: Pressure Atmosphere Pressure and the Barometer Standard atmospheric pressure = 760 mm of Hg 1 atm = 760 mmHg = 760 torr = 101.325 kPa.

Units: Force and Pressure

Units: Force and Pressure – F12

Figure 10.3: Pressure Closed Systems => manometers

The Empirical Gas Laws Figure 10.7: The Pressure-Volume Relationship: Boyle’s Law

The Empirical Gas Laws The Pressure-Volume Relationship: Boyle’s Law Mathematically: A sample of gas contained in a flask with a volume of 1.53 L and kept at a pressure of 5.6x103 Pa. If the pressure is changed to 1.5x104 Pa at constant temperature, what will be the new volume?

A sample of gas contained in a flask with a volume of 1 A sample of gas contained in a flask with a volume of 1.53 L and kept at a pressure of 5.6x103 Pa. If the pressure is changed to 1.5x104 Pa at constant temperature, what will be the new volume?

The Empirical Gas Laws The Temperature-Volume Relationship: Charles’s Law Charles’s Law: the volume of a fixed quantity of gas at constant pressure increases as the temperature increases. Mathematically: A sample of gas at 15°C and 1 atm has a volume of 2.58 L. What will be the new volume if temp. is increased to 38°C at constant pressure?

Example Calculation A sample of gas at 15°C and 1 atm has a volume of 2.58 L. What will be the new volume if temp. is increased to 38°C at constant pressure?

Figure 10.9

The Empirical Gas Laws The Quantity-Volume Relationship: Avogadro’s Law Avogadro’s Law: the volume of gas at a given temperature and pressure is directly proportional to the number of moles of gas. Mathematically:

The Ideal Gas Equation Boyle’s Law: We can combine these into a general gas law: Boyle’s Law: Charles’s Law: Avogadro’s Law:

The Ideal Gas Equation R = gas constant, then The ideal gas equation is: R = 0.08206 L·atm/mol·K = 8.3145 J/mol·K J = kPa·L = kPa·dm3 = Pa·m3 Real Gases behave ideally at low P and high T.

Gas Examples A sample of H2 gas has a volume of 8.56 L at a temperature of 0°C and a pressure of 1.5 atm. Calculate the moles of H2 present. At a constant temperature of 25°C and a pressure of 1 atm, a 12.2 L sample containing 0.50 moles of O2 gas was converted to ozone ( O3 ). What would be the volume of ozone? A sample of diborane gas ( B2H6 ), a substance that bursts into flames when exposed to air, has a pressure of 345 torr at a temperature of -15°C and a volume of 3.48 L. If temp. and pressure are changed to 36°C and 468 torr; what will be the new volume of the gas? What is the molar volume of an ideal gas at STP? [STP stands for Standard Temperature and Pressure: 0°C and 1 atm. STP is only applied to gases.]

A sample of H2 gas has a volume of 8 A sample of H2 gas has a volume of 8.56 L at a temperature of 0°C and a pressure of 1.5 atm. Calculate the moles of H2 present.

At a constant temperature of 25°C and a pressure of 1 atm, a 12 At a constant temperature of 25°C and a pressure of 1 atm, a 12.2 L sample containing 0.50 moles of O2 gas was converted to ozone ( O3 ). What would be the volume of ozone?

A sample of diborane gas ( B2H6 ), a substance that bursts into flames when exposed to air, has a pressure of 345 torr at a temperature of -15°C and a volume of 3.48 L. If temp. and pressure are changed to 36°C and 468 torr; what will be the new volume of the gas? V2 = 3.07 L n = 0.07457 mol

What is the molar volume of an ideal gas at STP What is the molar volume of an ideal gas at STP? [STP stands for Standard Temperature and Pressure: 0°C and 1 atm. STP is only applied to gases.] Key – F14

Density of an Ideal-Gas Gas Densities and Molar Mass The molar mass of a gas can be determined as follows: The density of a gas was measured at 1.50 atm and 27°C and found to be 1.95 g/L. Calculate the molecular weight of the gas? If the gas is a homonuclear diatomic, what is this gas?

Density of an Ideal-Gas

Density of an Ideal-Gas – F12

Density Calculation The density of a gas was measured at 1.50 atm and 27°C and found to be 1.95 g/L. Calculate the molecular weight of the gas? If the gas is a homonuclear diatomic, what is this gas? HW 11-9-11 - Key

Gas Mixtures and Partial Pressures Dalton’s Law: in a gas mixture the total pressure is given by the sum of partial pressures of each component: Each gas obeys the ideal gas equation:

Gas Mixtures and Partial Pressures Partial Pressures and Mole Fractions Let ni be the number of moles of gas i exerting a partial pressure Pi, then where i is the mole fraction (ni/nt). CyberChem Diving video

Kinetic Molecular Theory Assumptions: Gases consist of a large number of molecules in constant random motion. Volume of individual molecules negligible compared to volume of container. Intermolecular forces (forces between gas molecules) negligible.

How fast can gas molecules move?

Kinetic Molecular Theory Graham’s Law of Effusion Effusion is the escape of a gas through a tiny hole (a balloon will deflate over time due to effusion). Figure 10.20

Kinetic Molecular Theory Diffusion Diffusion of a gas is the spread of the gas through space and the mixing through other gases. Diffusion is faster for light gas molecules. Diffusion is slowed by gas molecules colliding with each other.

Kinetic Molecular Theory Graham’s Law of Effusion Consider two gases with molar masses M1 and M2, the relative rate of effusion is given by: Also works for Comparison of Diffusion rates

Kinetic Molecular Theory Figure 10.19: Molecular Effusion and Diffusion The lower the molar mass, M, the higher the rms.

Why Low Pressure?...Ideal Figure 10.23 Real Gases behave ideally at low P and high T. Why Low Pressure?...Ideal Figure 10.23

Why High Temperature?...Ideal Real Gases behave ideally at low P and high T. Why High Temperature?...Ideal Figure 10.24

Real Gases: Deviations from Ideal Behavior The van der Waals Equation General form of the van der Waals equation: Corrects for molecular volume Corrects for molecular attraction

Gases