States of Matter and Gases Unit 9

The States of Matter Solid: material has a definite shape and definite volume Solid: material has a definite shape and definite volume Liquid: material has a definite volume but a variable shape Liquid: material has a definite volume but a variable shape Gas: material has a variable shape and a variable volume Gas: material has a variable shape and a variable volume

Other States of Matter Plasma: Exists at extremely high temperatures Bose-Einstein Condensate: Exists at extremely low temperatures

Kinetic Molecular Theory  Kinetic energy is the energy an object has due to its motion.  Faster object moves = higher kinetic energy  According to the Kinetic Molecular Theory, ALL particles of matter are in constant motion.  This theory helps explain the behavior of solids, liquids, and gases.

Kinetic Energy and Temperature  Increase in kinetic energy results in an increase in temperature.  Temperature (in Kelvin) is directly proportional to the average kinetic energy.

Explaining the Behavior of Gases The kinetic theory of gases has 3 points: 1.Particles in a gas are in constant, random motion 2.The motion of one particle is unaffected by the motion of other particles unless they collide 3.Forces of attraction (intermolecular forces; IMF) among particles in a gas can be ignored under ordinary conditions

Behavior of Gases  Particles in a gas are never at rest.  Gaseous atoms travel in a straight line until it collides with either another atom or the wall of the container.  The constant motion of gas particles allow it to fill a container of any shape or size.

Explaining the Behavior of Liquids  Particles in a liquid are more closely packed than the particles in a gas.  Therefore, attractions (IMF) between the particles in a liquid do affect the movement of the particles. It slows them down – less kinetic energy It slows them down – less kinetic energy

Explaining the Behavior of Liquids  A liquid takes the shape of its container because particles can flow to new locations.  The volume is constant, because intermolecular forces of attraction keep the particles close together.

Explaining the Behavior of Solids  Solids have a definite volume and shape because their particles vibrate around fixed locations.  Strong attractions restrict motion and keep each atom in a fixed location relative to its neighbors.  Atoms vibrate around their locations but they do not exchange places with neighboring atoms.

Phase Changes  The reversible physical change that occurs when a substance changes from one state of matter to another.  How do we get from 1 phase to another?  It all deals with ENERGY!!!

Kinetic Theory and Gases This theory includes the following assumptions: 1. The particles in a gas are considered to be small, hard spheres with an insignificant volume. Relative to solids and liquids, the particles in gases are far apart. The particles are not attracted or repulsed by each other, and they move independently.

2. The motion of the particles in a gas is rapid, constant, and random. The particles travel in a straight-line path until they collide with an object or another particle. The particles change direction only when they rebound from a collision.

3. All collisions between particles in a gas are perfectly elastic. This means that during a collision the kinetic energy is transferred without loss from one particle to another. The total kinetic energy remains constant.

Pressure  Gas pressure results from the force exerted by a gas per unit surface area of an object.  Pressure is the result of the billions of collisions between gas particles & an object.  Atmospheric pressure results from the collisions of atoms and molecules in air.  More forceful collisions or more frequent collisions mean higher gas pressure.

Units of Pressure P = F/A  N/m 2  1 Pa  1 atm = 760 mm Hg = kPa  Other units:  1 atm = 760. mm Hg = 760. torr = in Hg = 101,300 Pa = kPa = 14.7 psi = 76 cm Hg.

 Calculate the pressure in mm Hg, when p = 1.42 atm  Calculate the pressure in kPa, when p = 0.93 atm.

Measuring Pressure of a Trapped Gas Manometer – device used to measure gas pressure Manometer – device used to measure gas pressure Open-armed manometer Open-armed manometer if gas end lower than open end, P gas = P air + diff. in height of Hg if gas end lower than open end, P gas = P air + diff. in height of Hg if gas end higher than open end, P gas = P air – diff. in height of Hg if gas end higher than open end, P gas = P air – diff. in height of Hg Closed-armed manometer Closed-armed manometer P gas = difference in height of mercury P gas = difference in height of mercury Barometer – special closed-armed manometer designed to measure air pressure. Barometer – special closed-armed manometer designed to measure air pressure.

Factors Affecting Gas Pressure 1. Amount of gas = more gas particles results in more collisions which increases the pressure. 2. Volume = compressing a gas into a container results in more collisions which increases the pressure. 3. Temperature = Gas particles will move more with a temperature increase resulting in more collisions which increases the pressure.

Gas laws  The factors affecting gases are expressed and used in several “gas laws”  The gas laws allow us to take situations involving gases and solve them mathematically.  The gas laws we will learn are: Boyle’s Law, Charles’s Law, Gay-Lussac’s Law, Combined Gas Law, Ideal Gas Law, Avogadro’s Law, Dalton’s Law, & Graham’s Law.

Boyle’s Law  Robert Boyle proposed this law in 1662  If the temperature is constant, as the pressure of a gas increases, the volume decreases and vice versa.  The law states that for a given mass of gas at constant temperature, the volume of the gas varies inversely with pressure. P 1 x V 1 = P 2 x V 2 P 1 x V 1 = P 2 x V 2

Charles’s Law  Jacques Charles in 1787  As the temperature of an enclosed gas increases, the volume increases, if the pressure is constant.  The law states that the volume of a fixed mass of gas is directly proportional to its Kelvin temperature if the pressure is constant. V 1 V 2 V 1 V = --- T 1 T 2  T: K = °C  STP = 0°C kPa

Gay-Lussac’s Law  Joseph Gay-Lussac in  As the temperature of an enclosed gas increases, the pressure increases, if the volume is constant.  This law states that the pressure of a gas is directly proportional to the Kelvin temperature if the volume remains constant. P 1 P 2 P 1 P = --- T 1 T 2

Example

Practice

The Combined Gas Law  This is a single expression that combines Boyle’s, Charles’s, and Gay-Lussac’s laws.  This law allows you to do calculations for situations in which only the amount of gas is constant. P 1 x V 1 P 2 x V 2 P 1 x V 1 P 2 x V = T 1 T 2 T 1 T 2

Practice  The temperature of 4.5 L of a gas at 1.2 atm is decreased from 350 K to 300 K, while the volume increases to 5.5 L. Calculate the new pressure of the gas.

Avogadro’s Law  As volume increases, the number of gas molecules increases (constant p and T)  Count number of gas molecules by moles  One mole of any ideal gas occupies 22.4 L at standard conditions - molar volume  Equal volumes of gases contain equal numbers of molecules It doesn’t matter what the gas is! It doesn’t matter what the gas is!

Ideal Gas Law  To calculate the number of moles of a contained gas requires an expression with the variable n. PV = nRT R is the ideal gas constant = R is the ideal gas constant = 8.31 (L* kPa) / (K * mol) 8.31 (L* kPa) / (K * mol)  Pressure in kPa or atmVolume in L  Temperature in Kn in moles  When pressure is in atm:  R = (L * atm) / (K * mol)

Example  What volume will 3.15 mol of hydrogen gas occupy at STP?  pV = nRT  x V = 3.15 x 8.31 x 273  V = 3.15 x 8.31 x 273 / = 70.5 L

Practice  What pressure is exerted by 1.24 moles of a gas stored in a 15.0 L container at 22 o C?  If you wish to collect 10.0 L of nitrogen gas at 15 o C and atm, what mass of gas will you need to have?

Stoichiometry  At STP, 1 mole of any gas occupies 22.4 L  Practice:  5.6 L N 2 reacts with excess H 2 at STP. How many L of NH 3 will form? And how many grams?

Practice  12.5 g of methane (CH 4 ) burns with O 2. How many L of CO 2 will be formed at STP?

Dalton’s Law  In a mixture of gases, the total pressure is the sum of the partial pressures of the gases.  This law states that at constant volume and temperature, the total pressure exerted by a mixture of gases is equal to the sum of the partial pressures of the component gases. P total = P 1 + P 2 + P 3 + …….

Graham’s Law  Thomas Graham during the 1840’s  Gases of lower molar mass diffuse and effuse faster than gases of higher molar mass. 1.Diffusion – particles move from an area of higher particle concentration to an area of lower particle concentration. Diffusion 2. Effusion – same as diffusion except the gas particles escape through small holes (pores) in a container. Effusion

Real Gases  The ideal gas law holds closely at high temperatures (above 0 o C) and low pressure (below 1 atm).  Under these conditions particles are far enough apart that they display ideal behavior (no interaction and no volume).

Real gases  Under high pressure particles are pushed close enough together to allow particle interactions, lowering the pressure to some extent (kinetic energy becomes less, so collisions happen with less force).  At lower temperatures the results are similar to when there is high pressure: Less kinetic energy and particle interaction.