Physics 12

Objectives  Define pressure.  State the assumptions of the kinetic model of an ideal gas.  State that temperature is a measure of the average random kinetic energy of the molecules of an ideal gas.  Explain the macroscopic behavior of an ideal gas in terms of a molecular model.  State the equation of state for an ideal gas.  Describe the difference between an ideal gas and a real gas.  Describe the concept of the absolute zero temperature and the Kelvin scale of temperature  Solve problems using the equation of state of an ideal gas.

Activities  Lecture  Quiz  Computer simulation  Graphical analysis

Gases  Compared to solids and liquids, gases behave quite differently, particularly in the volume that they occupy.  What are some factors that might affect the volume that a gas occupies?  Explain this behavior from a microscopic perspective.

Gases  How would these factors affect the volume of a gas? FactorEffect on volume increase in pressure increase in temperature increase in number of gas molecules

Gases  Because of the myriad of factors that affect the behavior of gases, it is valuable to determine a relationship between them.  The relationship between the volume, pressure, temperature, and mass of a gas is called an equation of state.  By state, we mean the equilibrium state of the system.

Gases SI units for quantities involving gases QuantitySI unit volumem3m3 pressureNm -2 or Pascal (Pa) temperatureK **another unit for pressure, the atmosphere (atm) is often used: 1 atm = 1.01 x 10 5 Nm -2

Boyle’s law  What is the effect of pressure on the volume of a gas? FactorEffect on volume increase pressure decrease pressure

Boyle’s law  For a given quantity of gas, it is found experimentally that the volume of a gas is inversely proportional to the absolute pressure applied to it when the temperature is kept constant. V α 1/P  Why is it important that we state that temperature is constant? FactorEffect on volume increase pressuredecrease volume decrease pressureIncrease volume

Boyle’s law Graph of P vs. V (Boyle’s experiments) What are the implications of this relationship on the behavior of gases?

Charles’s law  A century later, Jacques Charles performed experiments on the effect of temperature on gases. FactorEffect on volume increase temperature decrease temperature What is the effect of temperature on the volume of a gas?

Charles’s law  The volume of a given amount of gas is directly proportional to the absolute temperature when the pressure is kept constant. V α T  Can you think of any applications / examples of this in the “real world”? FactorEffect on volume increase temperatureincrease volume decrease temperaturedecrease volume

Absolute zero  Recall the relationship between the Kelvin and Celsius scales.  What kind of relationship is this?

Gay-Lussac’s law  What is the effect of temperature on pressure? FactorEffect on pressure increase temperature decrease temperature

Gay-Lussac’s law  At constant volume, the absolute pressure of a gas is directly proportional to the absolute temperature. FactorEffect on pressure increase temperatureincrease pressure decrease temperaturedecrease pressure

The ideal gas law  The three laws can be combined into ONE general relationship between the three variables: PV α T  There is one more factor that might affect pressure or volume that is not present; what is it?

The ideal gas law  The amount of gas should also affect its volume: PV α mT  The amount of matter is expressed in moles.  1 mol of a substance contains 6.02 x atoms or molecules of the substance (Avogadro’s number).  Why don’t we use kilograms to express the amount of matter?

The ideal gas law  But an expression of proportionality is not nearly as useful as an equation, which brings us to the ideal gas law: PV = nRT Where: P is the pressure of the gas, V is the volume, n is the number of moles, and T is the temperature of the gas. R is the universal gas constant (the constant of proportionality between all four factors: R = Jmol -1 K -1

The ideal gas law Determine the volume of 1.00 mol of any gas at STP (standard temperature, 0C, and pressure, 1.00 atm).

The ideal gas law V = 22.4 L at STP

The ideal gas law A helium party balloon, assumed to be a perfect sphere, has a radius of 18.0 cm. At room temperature (20C), its internal pressure is 1.05 atm. Find the number of moles of helium in the balloon and the mass of the helium needed to inflate the balloon to these values. The atomic mass of helium is 4.00 gmol -1

The ideal gas law n = mol m = 4.26 g

Objectives  Define pressure.  State the assumptions of the kinetic model of an ideal gas.  State that temperature is a measure of the average random kinetic energy of the molecules of an ideal gas.  Explain the macroscopic behavior of an ideal gas in terms of a molecular model.  State the equation of state for an ideal gas.  Describe the difference between an ideal gas and a real gas.  Describe the concept of the absolute zero temperature and the Kelvin scale of temperature  Solve problems using the equation of state of an ideal gas.

Homework Giancoli pg 381 # 29, 31, 33, 35, 39 Quiz next class on gas laws Next lectures: Chapter 15-1 to 15-3