Unit 5: States of Matter

Content Outline: Density of Gases, Gay-Lussac’s and Avogadro’s Laws (5.7)

  1. The Ideal Gas according to the Kinetic Molecular Theory of Matter
  1. Gases consist of large numbers of tiny particles that are far apart relative to their size.
  2. Collisions between gas particles and/or between particles and the container walls are Elastic collisions.
  3. Gas particles are in continuous, rapid, random motion. They possess Kinetic Energy.
  4. The Kinetic Energy allows the individual atoms/molecules to overcomeallattractive forces.
  5. The temperature of a gas depends on the mass and velocity(speed) of the atoms/molecules in the gas.

II. The Ideal Gas Lawsmathematical equation is:

A. PV = nRT

  1. R is the Ideal Gas Constant – its value is (0.0821 L*Atm/Mol* K)
  2. V is volume – It is measured in Liters.
  3. T is Temperature – It is measured in Kelvins
  4. P is pressure – It is measured in Atmospheres
  5. n is amount of a substance measured in moles
  1. Kinetic-Molecular Theory of Real Gases
  1. Density (the amount of matter within a given area… howclose are the atoms/molecules)
  1. Real gases usually occupy 1/1000 the amount of space, as the same substance does as a liquid or solid, if the containers, pressure, temperature for comparing elements/molecules are unified.
  1. The gas atoms/molecules are very far apart, but they can be affected by the volumeof the container, flexibility of the container (pressure), and the Temperature (Heat =Kinetic Energy)of the gas… but the amount of matter/gas(n)must remain the same, unless you add or take away atoms/molecules… in which case you will change the density(mass) of the gas in the container.
  2. Again, because of these variable we use STP (1 atmosphereand 0OC) to state that 1 moleof a gas will occupy 22.4 Liters for the comparison for density (mass/volume).
  1. Avogadro’s Law for gases (Amount of a substance measured in moles)
  1. Proposed by Amedeo Avogadro in 1811.
  2. His gas law states: Equal volumes (22.4 L) of gases at the same temperature (0OC) and pressure (1 atm.) will contain equal numbers of atoms/molecules (1 mole…6.022 x 1023). These values look like STP and the Ideal Gas Law…how about that? Can you begin to see how this all ties together. Just add R.
  3. Mathematically expressed as:

V = kn it can also be thought of as: V/n = k

k = gas constant (rate of the reaction)

  1. For Ideal Gases and Real gases, these can be thought of as the same value, as units for V and n are defined, as above.
  1. These standardized values are called the Standard Molar Volume of a Gas.
  2. This means you can use the same methods as you learned in Unit 4 for Composition and Reaction Stoichiometry.

Unit Given X Unit Wanted = Unit Wanted

Unit Given

  1. Therefore the equation can also be thought of as:

V1 = V2 at constant T and P

n1 n2

  1. This proves that volume is not related to particle size or mass. Important concept!
  2. Solve these problems just like Charles’ Law PROCESS, not UNITS.
  1. Must know 3 variables, make units appropriate, cross-multiply…and then divide.

D. This law also helped prove that elemental gases (H2, O2, F2, Cl2, Br2, I2) are diatomic (two atoms) and not monatomic (one atom) like the Noble gases. (Think Hydrogen and Diatomic 7-look at a Periodic Table.)

  1. Gay-Lussac’s Law of Gases (Temperature- Pressure relationship)
  1. Joseph Gay-Lussac, a French chemist, proposed this Law in 1802.
  2. The Law basically states: The pressure (P)of a fixed mass of gas (n) at a constant volume (V) is directly proportional to the temperature (T)in K.
  1. Simply put: if V and n stay constantP is directly related (it does what the other does) to T.

So if P increases ...so does T.

So if P decreases…so does T.

  1. This can be Mathematically expressed as:

P = kT or as P/T = k (the gas constant…rate of the reaction)

  • For every 1 K = 1/273 change in Pressure for a confined volume and at 0OC.

VeryInteresting, wouldn’t you say? KE = T and affects P.

Therefore, this can be thought of as:

P1 = P2(P1and T1 are the first situation.)

T1 T2(P1 and T2 are the second situation.)

  1. Solve these problems just like above too. How easy can it be?
  1. Gay-Lussac’s Law of Combining Volumes of gases
  1. This law states that at constantT and P, the volume of reactants = volume of products.
  2. It can be thought of as just adding the coefficients (# of moles):

For example the following reaction: H2+ Cl2= 2HCl

  1. You would solve these just like the reaction stoichiometry problems from Unit 4.

Unit Given X Unit Wanted= Unit Wanted

Unit Given