Ideal Gas Laws

Pressure is defined as force per unit area  The fundamental (S.I.) unit for pressure is the Pascal (Pa), (1Pa = 1N/m 2 ).  Normal (or standard) atmospheric pressure (1atm) 1 atm= x 10 5 Pa Or 1 atm = 760 torr (where 1 torr = 1mmHg)  Standard temperature and pressure, s.t.p. = 1 atm and 0°C. F = the magnitude of the force A = the area over which it is spread

The Kinetic Theory of Matter - Reviewed microscopic definition of temperature. The basic ideas of the kinetic theory are  all matter consists of particles (atoms or molecules) in motion  as the temperature increases, the average speed of the movement increases. the temperature of a body is a measure of the average kinetic energy of it particles. explain the differences between the different states (or phases) of matter.

Why a Gas Exerts a Pressure Assumptions Molecules of a gas move at random in a container Molecules continually collide with each other and with the container walls All collisions are elastic Pressure Results from: When a molecule collides with the wall, a change of momentum occurs. change in momentum is caused by the force exerted by the wall on the molecule The molecule exerts an equal but opposite force on the wall The pressure exerted by the gas is due to the sum of all these collision forces.

Why the Pressure Exerted by a Gas Increases as the Temperature Increases Gas Temperature Average Kinetic Energy of its molecules Molecules hit the wall harder and more frequently Total force due to collisions is greater Pressure increases

Why the Temperature of a Gas Increases when it is Compressed A molecule elastically colliding with a stationary wall will rebound at the same speed. A molecule colliding with a moving piston (which is compressing the gas) will rebound moving faster than before the collision. Average speed of the molecules will increase Temperature will increase. If the piston is moving the opposite way, the average speed (temperature) will decrease.

Clicker Understanding A mass sits on top of a piston that is free to slide in a cylinder of gas. The pressure in the gas in the cylinder is A. greater than the pressure of the atmosphere outside the cylinder. B. equal to the pressure of the atmosphere outside the cylinder. C. less than the pressure of the atmosphere outside the cylinder.

The Gas Laws Experimentally found relations between the pressure, volume and temperature of a fixed mass of gas. These results do not depend on the type of gas.

Charles’ Law Consider a quantity of gas in a container of variable volume Changing the temperature while allowing it to change volume at constant pressure Extrapolating, we find Suggests that the volume occupied by the gas because of the motion of its molecules would be zero at -273°C. Jacques Charles Frenchman who invented the hydrogen balloon in 1783.

Charles’ Law The volume of a fixed mass of gas at constant pressure is directly proportional to the absolute temperature. If a fixed mass of gas has initial (absolute) temperature T 1 and initial volume V 1 and final (absolute) temperature and volume T 2 and V 2 respectively, then we can write V 1 /T 1 =V 2 /T 2

The Pressure Law (Gay-Lussac’s Law) The pressure of a fixed mass of gas at constant volume is directly proportional to the absolute temperature. P 1 /T 1 =P 2 /T 2

The Boyle/Marriotte Law Varying the pressure and volume of a sample of gas at constant temperature. The pressure of a fixed mass of gas at constant temperature is inversely proportional to the volume. P 1 V 1 = P 2 V 2 Changes of pressure and volume which take place at constant temperature are called isothermal changes.

Ideal GAS From A to B  Energy supplied to increase T and V at constant P. Apply Charles’ law – From B to C  Compress the gas slowly to change V and P at constant T. Apply the Boyle/Marriotte law - an imaginary gas which obeys the gas laws perfectly for any temperature and pressure P 1 V’ = P 2 V 2 V 1 /T 1 =V’/T 2

Ideal GAS Eliminating V’ This is called the equation of state of an ideal gas and is usually written in the following form pV = (a constant)×T Animation

Ideal GAS limitations PV = (a constant)×T Applies to real gases for limited temperature and pressure ranges. Between 0°C and 100°C and between about ½ to 2 atmospheres of pressure, real gases give the results described above. If gases are compressed to extreme pressures at low temperature, their behavior is very different.

Universal Gas Constant The "constant" in the equation depends  on the quantity of gas in the container  the type of gas  given mass of gas we have a different number of particles for different gases. Avogadro’s law states that at a given temperature and pressure, equal volumes of any gas contain equal numbers of particles. Avogadro’s number, N A = 6.02×10 23 molecules/mol where n = # of moles; N = total # of molecules With a given number of particles of any gas in our cylinder we have a constant called the universal gas constant, R. R= 8.31 J/(mol K) n = N/N A

Ideal GAS Laws where n is the number of moles of gas. To consider individual molecules of a gas, we define the gas constant per molecule (or Boltzmann’s constant), k, or k = 1.38 x J/K where N = number of molecules PV = nRT PV = NkT k = R/N A

Ideal vs. Real Gases Ideal Gas An (imaginary) gas which obeys the gas laws perfectly for all temperatures and pressures. In order for a gas to be considered ideal  there must be negligible forces of attraction between its molecules  the total volume of its molecules must be negligible compared with the volume occupied by the gas. Real Gases Real gases near s.t.p. behave like an ideal gas. Real gas molecules:  attract each other  do not occupy negligible volume when the gas is at high pressure.  Decreasing the temperature and increase the pressure of a real gas will eventually change its state.

Clicker Understanding The two identical cylinders shown both have the same mass on the piston and the same volume. One contains hydrogen, the other nitrogen. Both gases are at the same temperature. The number of moles of hydrogen is A. greater than the number of moles of nitrogen. B. equal to the number of moles of nitrogen. C. less than the number of moles of nitrogen.

Absolute Temperature Using ideal gas assumptions, laws of mechanics, and equation of state, derive: Where v is the root mean square speed k is Boltzman’s constant, k=1.380 ×10 −23 J/K Average kinetic energy of the molecules is proportional to the absolute temperature

Evaporation Vaporization in a liquid Equilibrium vapor pressure – pressure of the vapor that coexists in equilibrium Cooling process

Evaporation – Kinetic Theory Molecules pick up energy from collisions with neighboring molecules. When energy equals the latent heat of vaporization, these fast moving particles become vapor. As the vapor particles, move the total kinetic energy of the liquid particles remaining decreases.

Evaporation Rate of Evaporation depends on: Surface Area Temperature of the liquid Pressure of the air above the liquid Movement of air (convection current) Humidity (depends on temperature and pressure)

Clicker Understanding Suppose you have a sample of gas at 10°C that you need to warm up to 20°C. Which will take more heat energy: raising the temperature while keeping the pressure constant or raising the temperature while keeping the volume constant? A. It takes more energy to raise the temperature while keeping the volume constant. B. It takes more energy to raise the temperature while keeping the pressure constant. C. The heat energy is the same in both cases.

Question Thinking in terms of kinetic energy, explain the processes of evaporation, boiling, and vaporization of water.

Constant Volume & Mass Increasing Temperature

Constant Volume & Mass Increasing Pressure

Constant Pressure & Mass Decreasing Volume

Constant Pressure & Mass Increasing Temperature

Constant Temp. & Mass Decreasing Volume

Constant Temp. & Mass Increasing Pressure

Constant Volume & Temp. Increasing Mass

Constant Volume & Press. Increasing Mass

Constant Pressure & Temp Increasing Mass