Any Gas….. 4 Uniformly fills any container 4 Mixes completely with any other gas 4 Exerts pressure on its surroundings

Kinetic Molecular Theory of Gases  The particles are so small compared with the distances between them that the volume of the individual particles can be assumed to be negligible.  The particles are in constant motion. The collisions of the particles with the walls of the container are the cause of the pressure exerted by the gas.  The particles are assumed to exert no forces on each other; they are assumed neither to attract nor to repel each other.  The average kinetic energy of a collection of gas particles is assumed to be directly proportional to the Kelvin temperature of the gas.

KMT  Volume of individual particles is  zero  Collisions of particles with container walls cause pressure exerted by gas  Particles exert no forces on each other  Average kinetic energy  Kelvin temperature of a gas

Pressure and Volume

Pressure and volume (Boyle’s Law) Pressure ↓ Volume ↑ Inversely proportional Makes sense since a decrease in volume means that the gas particles will hit the wall more often, thus increasing pressure.

Pressure and Temperature

Pressure and Temperature (Gay-Lussac’s Law) pressure ↑ temperature ↑ or pressure ↓ temperature ↓ Directly proportional When the temperature of a gas increases,the speeds of its particles increase, the particles hitting the wall with greater particles increase, the particles hitting the wall with greater force and greater frequency. Since the volume remains force and greater frequency. Since the volume remains the same, this would result in increased gas pressure. the same, this would result in increased gas pressure.

Volume andTemperature

Volume and Temperature (Charles’ Law) pressure ↑ temperature↑ or temperature ↓ pressure ↓ Directly proportional When a gas is heated to a higher temperature, the speeds of its molecules increase thus they hit the walls more often of its molecules increase thus they hit the walls more often and with more force. The only way to keep the pressure constant is to increase the volume of the container. constant is to increase the volume of the container.

Increase Moles of Gas (T and P constant) Explain with the KMT

Volume and Number of Moles (Avogadro’s Law)  An increase in the number of particles at the same temperature would cause the pressure to increase if the volume were held constant. The only way to return the pressure to its original value is to increase the volume.  The volume of gas (at constant P and T) depends only on the number of gas particles present.

Dalton’s Law of Partial Pressures The total pressure of a gas sample is equal to the sum of the pressures that each gas exerts. P total = P 1 + P 2 + P 3 +……

Mole fraction The ratio of the number of moles of a given component in a mixture to the total number of moles in the mixture. Χ 1 = n 1 = n 1 Χ 1 = n 1 = n 1 n total n 1 + n 2 + n 3 n total n 1 + n 2 + n 3 Partial pressure of a particular component of a gaseous mixture is the mole fraction of that component times the total pressure. P 1 = χ 1 X P total P 1 = χ 1 X P total

Temperature  Kelvin temperature indicates the average kinetic energy of the gas particles.  Higher temperature means greater motion.-

Standard temperature and Pressure, STP Temperature = 0°C = 273 Kelvin mm Hg = torr = 1.00 atm = kPa ≈ 10 5 Pa

At a given temperature, not all molecules in a sample have the same velocity.

As temperature increases, how does the velocity of particles change?

Diffusion: describes the mixing of gases. The rate of diffusion is the rate of gas mixing.

Example: NH 3 + HCl  NH 4 Cl distance traveled by gas 1 = √M2 = √36. = 1.5 distance traveled by gas 2 √M1 √17.0 distance traveled by gas 2 √M1 √17.0

Effusion: describes the passage of gas into an evacuated chamber. What factor(s) influence the effusion rate of a gas?

Effusion Lighter –faster Larger-slower

Ideal/Real Gases Ideal gas is hypothetical. No gas exactly follows the ideal gas law. Two effects temperature and pressure temperature and pressure

PV/nRT Versus P (200 K) At what conditions do gases deviate most from ideal behavior?

PV/nRT Versus P for N 2 At what conditions do gases deviate most from ideal behavior?

Temperature  Temperature ↑ particles move faster  Temperature ↓ particles move slower and attractive forces become important. (attractive forces)  More attractive forces causes an apparent pressure increase.  As pressure increases, volume will decrease.

Pressure effects Low close to one atm volume observed ~ volume ideal volume observed ~ volume ideal Medium up to 150 atm volume observed ≤ volume ideal. volume observed ≤ volume ideal. High above 150 atm volume observed ≥ volume ideal. volume observed ≥ volume ideal.

Gas Density d = mass / volume mass = number of moles X molar mass a mole a mole moles = n, so mass = n MM Substituting into PV = nRT mm = dRT P

Substituting into PV = nRT  We find that mm = dRT P

Van der Waal’s Equation for Real Gases Used to modify the ideal gas law to address the problems associated with the assumptions made in the ideal gas law. Gas particles have no volume Attractive forces between gas particles do not exist  corrected pressure corrected volume P ideal V ideal