Physical Chemistry I (TKK-2246) 13/14 Semester 2 Instructor: Rama Oktavian Office Hr.: M.13-15, Tu , W , Th , F

Outlines 1. Gas structure 2. Kinetic theory of gas 3. Calculation of the gas pressure 4. Dalton’s law in kinetic theory of gas 4. Dalton’s law in kinetic theory of gas

Learning check Molar mass of gas In an experiment to measure the molar mass of a gas, 250 cm3 of the gas was confined in a glass vessel. The pressure was 152 Torr at 298 K and, after correcting for buoyancy effects, the mass of the gas was 33.5 mg. What is the molar mass of the gas?

Learning check Dalton’s partial pressure A gas mixture consists of 320 mg of methane, 175 mg of argon, and 225 mg of neon. The partial pressure of neon at 300 K is 8.87 kPa. Calculate (a) the volume and (b) the total pressure of the mixture.

Learning check Dalton’s partial pressure A vessel of volume 22.4 dm 3 contains 2.0 mol H 2 and 1.0 mol N 2 at K initially. All the H 2 reacted with sufficient N 2 to form NH 3. Calculate the partial pressures and the total pressure of the final mixture.

Gas structure 1.In gases, the particles are very spread out 2.They are moving very quickly in different directions 3.They are not arranged in any pattern 4.They are changing places all of the time.

Gas structure 1.A gas will fill the whole volume of its container. 2.A gas is easily compressed. 3.The speed of the particles in a gas increases as the temperature increases

Kinetic theory of gases Kinetic theory of gas observes molecular motion in gases In the kinetic model of gases we assume that the only contribution to the energy of the gas is from the kinetic energies of the molecules The pressure that a gas exerts is caused by the collisions of its molecules with the walls of the container.

Kinetic theory of gases 1. Gases are made of tiny particles far apart relative to their size: Volume occupied by the molecules is inconsequential Volume is mostly space Explains why gases are compressible

Kinetic theory of gases 2. Gas particles are in continuous, rapid, random motion As a result there are collisions with other molecules or with the wall of the container Creates pressure Increase in temperature increases the movement of the molecules and thus the pressure exerted by the gas

Kinetic theory of gases 3. There are no attractive forces between molecules under normal conditions of temperature and pressure Gas molecules are moving too fast Gas molecules are too far apart Intermolecular forces are too weak

Kinetic theory of gases 4. Collisions between gas particles and between particles and container walls are elastic collisions.  Collisions in which there is no net loss of total kinetic energy  Kinetic energy can be transferred between two particles during collisions  Total kinetic energy remains the same as long as temperature remains the same

Kinetic theory of gases 5. All gases at the same temperature have the same average kinetic energy. The energy is proportional to the absolute temperature. Absolute temperature = Kelvin temp scale K e = ½ mv 2 Ke = the kinetic energy m = mass v = the velocity

Kinetic theory of gases Pressure and molecular speed relation (1) Where M = mN A, the molar mass of the molecules, and c is the root mean square speed of the molecules, the square root of the mean of the squares of the speeds, v, of the molecules: (2)

Kinetic theory of gases Pressure and molecular speed relation Justification Consider the movement of gas the momentum before collision is the momentum after collision is the change in momentum is the difference between final and initial momentum

Kinetic theory of gases Pressure and molecular speed relation Justification The distance that molecule can travel along the x-axis in an interval ∆t is written as if the wall has area A, then all the particles in a volume will reach the wall

Kinetic theory of gases Pressure and molecular speed relation Justification The number density of particles is where n is the total amount of molecules in the container of volume V and N A is Avogadro’s constant The number of molecules in the volume x

Kinetic theory of gases Pressure and molecular speed relation Justification At any instant, half the particles are moving to the right and half are moving to the left Therefore the number of molecules will become The total momentum change within interval Δt is x

Kinetic theory of gases Pressure and molecular speed relation Justification The total momentum change within interval Δt is x Where M = mN A

Kinetic theory of gases Pressure and molecular speed relation Justification Rate of change of momentum can be written as total momentum divided by time interval rate of change of momentum is equal to the force (by Newton’s second law of motion)

Kinetic theory of gases Pressure and molecular speed relation Justification the pressure, the force divided by the area, is rate of change of momentum is equal to the force (by Newton’s second law of motion) Not all the molecules travel with the same velocity, so the detected pressure, p, is the average (denoted ) of the quantity just calculated

Kinetic theory of gases Pressure and molecular speed relation Justification To write an expression of the pressure in terms of the root mean square speed, c, we begin by writing the speed of a single molecule, v, as because the molecules are moving randomly, all three averages are the same, it follows

Kinetic theory of gases Pressure and molecular speed relation Justification

Kinetic theory of gases Pressure and molecular speed relation Using Boyle’s Law and ideal gas Law the root mean square speed of the molecules in a gas at a temperature T must be the higher the temperature, the higher the root mean square speed of the molecules, and, at a given temperature, heavy molecules travel more slowly than light molecules

Kinetic theory of gases Pressure and kinetic energy relation Kinetic energy of molecule is defined as M = mN A N = nN A

Kinetic theory of gases Pressure and kinetic energy relation Using Boyle’s Law and ideal gas Law k is Boltzmann constant k = × m 2 kg s -2 K -1

Kinetic theory of gases The Speed of Molecules in Air Air is primarily a mixture of nitrogen N 2 (molecular mass = 28.0 g/mol) and oxygen O 2 (molecular mass = 32.0 g/mol). Assume that each behaves as an ideal gas and determine the speeds of the nitrogen and oxygen molecules when the temperature of the air is 293 K and determine the kinetic energy contained in that molecule

Kinetic theory of gases Dalton’s law of partial pressure In a mixture of gases the total pressure is the sum of the forces per unit area produced by the impacts of each kind of molecule on a wall of a container