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States of Matter The Solid State Particles are tightly packed, very close together (strong cohesive forces) Low kinetic energy (energy of motion) Fixed shape and volume Crystalline or amorphous structure

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The Liquid State Particles are close to each other (making them mostly incompressible) Attractive forces keep molecules close, but not so close to restrict movement

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**Gas particles move randomly and rapidly.**

The Gas State Gas particles move randomly and rapidly. Size of gas particles is small compared to the space between the particles. Gas particles exert no attractive forces on each other. Kinetic energy of gas particles increases with increasing temperature. 3

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**a The symbol “~” means approximately.**

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**Pressure (P) is the force (F) exerted per unit area (A).**

Gases and Pressure When gas particles collide with the walls of a container, they exert a pressure. Pressure (P) is the force (F) exerted per unit area (A). Force F Pressure = = Area A 760. mm Hg 760. torr 1 atmosphere (atm) = 14.7 psi 101,325 Pa 5

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Gas Laws Mathematical relationships describing the behavior of gases with regard to mixing, diffusion, changes in pressure, changes in temperature Boyle’s Law: Describes the relation between pressure and volume of a gas, under a constant temperature PiVi = PfVf where i = initial condition and f = final condition

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**Boyle’s Law: Inverse relation between Pressure and Volume**

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Example: Freon-12, CCl2F2, is used in refrigeration systems. What is the new volume (L) of a 8 L sample of Freon gas initially at 50 mm Hg after its pressure is changed to 200 mm Hg at constant T? Set up a data table Conditions 1 Conditions 2 P1 = 50 mm Hg P2 = 200 mm Hg V1 = 8 L V2 = ?

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**2. Solve Boyle’s Law for V2:**

P1V1 = P2V2 V = V1P1 P2 V2 = 8 L x 50 mm Hg = L 200 mm Hg

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Learning Check A sample of helium gas has a volume of 6.4 L at a pressure of atm. What is the new volume when the pressure is increased to 1.40 atm (T constant)?

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**Solution P1V1 = P2V2 Solve for V2: V2 = V1P1 P2**

V2 = L x atm = L 1.40 atm Volume decreases when there is an increase in the pressure (Temperature is constant).

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Learning Check A sample of oxygen gas has a volume of 12.0 L at 600. mm Hg. What is the new pressure when the volume changes to 36.0 L? (T and n constant.)

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**Solution Conditions 1 Conditions 2 P1 = 600. mm Hg P2 = ?**

V1 = L V2 = L P2 = P1 V1 V2 600. mm Hg x L = mm Hg L

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**Charles’ Law: Describes relation between temperature and volume of a gas, under constant pressure**

Vi/Ti = Vf/Tf Charles’s Law: Direct relationship between Volume and Temperature

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Charles’ Law

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Example: A balloon has a volume of 785 mL at 21°C. If the temperature drops to 0°C, what is the new volume of the balloon (P constant)? Set up data table: Conditions 1 Conditions 2 V1 = 785 mL V2 = ? T1 = 21°C = 294 K T2 = 0°C = 273 K Be sure that you always use the Kelvin (K) temperature in gas calculations!

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**2. Solve Charles’ law for V2**

V1 = V2 T T2 V2 = V1 T2 T1 V2 = 785 mL x K = 729 mL 294 K

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Learning Check A sample of oxygen gas has a volume of 420 mL at a temperature of 18°C. At what temperature (in °C) will the volume of the oxygen be 640 mL (P and n constant)?

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**Solution T2 = T1V2 V1 T2 = 291 K x 640 mL = 443 K 420 mL**

= 443 K – 273 K = 170°C

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**Combined Gas Law: Describes relation between pressure, temperature and volume of a gas**

PiVi/Ti = PfVf/Tf

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Example: A sample of helium gas has a volume of L, a pressure of atm and a temperature of 29°C. At what temperature (°C) will the helium have a volume of 90.0 mL and a pressure of 3.20 atm (n constant)? 1. Set up Data Table Conditions 1 Conditions 2 P1 = atm P2 = atm V1 = L (180 mL) V2 = 90.0 mL T1 = 29°C = 302 K T2 = ?

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2. Solve for T2 P1 V1 = P2 V2 T1 T2 T2 = T1 P2V2 P1V1 T2 = 302 K x atm x mL = K 0.800 atm mL T2 = 604 K – = °C

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Learning Check A gas has a volume of 675 mL at 35°C and atm pressure. What is the volume(mL) of the gas at –95°C and a pressure of 802 mm Hg (n constant)?

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**Solution Data Table T1 = 308 K T2 = -95°C + 273 = 178K**

V1 = 675 mL V2 = ? P1 = 646 mm Hg P2 = 802 mm Hg Solve for V2 V2 = V1 P1 T2 P2T1 V2 = mL x 646 mm Hg x 178K = mL mm Hg x 308K

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**Pressure and temperature are directly related**

Gay–Lussac’s Law: Describes the relation between pressure and temperature of a gas, at a constant volume Pressure and temperature are directly related Pressure P = constant = k Temperature T P1 P2 = T1 T2 Note: Temperature must be expressed in kelvins. 26

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Avogadro’s Law: Equal volumes of gases measured at the same temperature and pressure contain equal number of molecules Vi/ni = Vf/nf where n = number of moles

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**Avogadro’s Law Example:**

If 0.75 mole of helium gas occupies a volume of 1.5 L, what volume will 1.2 moles of helium occupy at the same temperature and pressure? Conditions 1 Conditions 2 V1 = 1.5 L V2 = ? n1 = mole He n2 = 1.2 moles He V1/n1 =V2/n2 V2 = V1n2 n1 V2 = L x moles He = L 0.75 mole He

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Ideal Gas Law: Describes relation between pressure, volume, temperature and the number of molecules in an ideal gas sample PV = nRT where R = universal gas constant ( L atm/K mol)

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Ideal Gas Law Example: A cylinder contains 5.0 L of O2 at 20.0°C and 0.85 atm. How many grams of oxygen are in the cylinder? P = 0.85 atm, V = 5.0 L, T = 293 K, n (or g =?) PV = nRT n = PV RT = (0.85 atm)(5.0 L)(mole K) = mole O2 (0.0821atm L)(293 K) = mole O2 x g O2 = 5.8 g O2 1 mole O2

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Partial Pressure: Pressure an individual gas in a mixture would exert were it alone in the same container Dalton’s Law: Total pressure exerted by a mixture of gases equals the sum of the partial pressures P(total) = P(gas 1) + P(gas 2) + P(gas 3) etc.

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**Dalton’s Law of Partial Pressures**

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Summary of Gas Laws Boyle: PiVi = PfVf Charles: Vi/Ti = Vf/Tf Avogradro: Vi/ni = Vf/nf Gay-Lussac: Pi/Ti = Pf/Tf Dalton: P(total) = P(gas 1) + P(gas 2) + P(gas 3) *Combined: PiVi/Ti = PfVf/Tf *Ideal: PV = nRT * Memorize for exam

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**Intermolecular Forces**

Intermolecular forces: attractive forces that exist between molecules. In order of increasing strength, these are: London dispersion forces dipole–dipole interactions hydrogen bonding 35

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**London Dispersion Forces**

London dispersion forces: weak interactions due to the momentary changes in electron density in a molecule. Change in electron density creates a temporary dipole. The weak interaction between these temporary dipoles constitutes London dispersion forces. All covalent compounds exhibit London dispersion forces. The larger the molecule, the larger the attractive force, and the stronger the intermolecular forces. 36

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Dipole-dipole interaction: attraction between positive end of one polar molecule and negative end of a different polar molecule

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Hydrogen bonding: Specific type of dipole-dipole force, between the partial positive charge on H and partial negative charge on an electronegative element such as O, N, F

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**Intermolecular Forces: Boiling Point and Melting Point**

Boiling point: temperature at which a liquid is converted to a gas Melting point: temperature at which a solid is converted to a liquid The stronger the intermolecular forces on a substance, the higher its boiling point and melting point are. 40

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**Examples of Intermolecular Forces and Boiling, Melting Points:**

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**Both molecules have London dispersion forces and nonpolar bonds.**

In this case, the larger molecule will have stronger attractive forces. 42

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**Evaporation: the conversion of liquids into the gas phase.**

Vapor Pressure Evaporation: the conversion of liquids into the gas phase. Evaporation is endothermic—it absorbs heat from the surroundings. Condensation: the conversion of gases into the liquid phase. Condensation is exothermic—it gives off heat to the surroundings. 43

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**Viscosity and Surface Tension**

Viscosity: a measure of a fluid’s resistance to flow freely Compounds with strong intermolecular forces tend to be more viscous than compounds with weaker forces. Substances composed of large molecules tend to be more viscous, too, because large molecules do not slide past each other as freely. 44

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**Interior molecules in a liquid are surrounded by **

Surface tension: a measure of the resistance of a liquid to spread out. Interior molecules in a liquid are surrounded by intermolecular forces on all sides. Surface molecules only experience intermolecular forces from the sides and from below. 45

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**The Solid State: Types of Solids**

Crystalline solid: has a regular arrangement of particles—atoms, molecules, or ions—with a repeating structure. There are four different types of crystalline solids— ionic, molecular, network, and metallic. 46

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**Ionic solid: composed of oppositely charged ions**

Crystalline Solids Ionic solid: composed of oppositely charged ions Molecular solid: composed of individual molecules arranged regularly 47

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**Network solid: composed of a vast number of atoms covalently bonded together (SiO2).**

Metallic solid: a lattice of metal cations surrounded by a cloud of e− that move freely (Cu). 48 48

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**They can be formed when liquids cool too quickly **

Amorphous Solids Amorphous solid: has no regular arrangement of its closely packed particles. They can be formed when liquids cool too quickly for regular crystal formation. Very large covalent molecules tend to form amorphous solids, because they can become folded and intertwined. Examples: rubber, glass, and plastic. 49

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1 Lecture 6 Gases Properties of Gases Gas Pressure Copyright © 2007 by Pearson Education, Inc. Publishing as Benjamin Cummings.

1 Lecture 6 Gases Properties of Gases Gas Pressure Copyright © 2007 by Pearson Education, Inc. Publishing as Benjamin Cummings.

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