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## The Gas Laws

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**The Gas Laws**• The gas laws describe HOW gases behave. • They can be predicted by theory. • The amount of change can be calculated with mathematical equations.**Standard Atmospheric Pressure**• Oneatmosphereis equal to 760 mm Hg, 760 torr, or 101.3 kPa (kilopascals).**Standard Atmospheric Pressure**• Perform the following pressure conversions. a) 144 kPa = _____ atm (1.42) b) 795 mm Hg = _____ atm (1.05)**Standard Atmospheric Pressure**• Perform the following pressure conversions. c) 669 torr = ______ kPa (89.2) d) 1.05 atm = ______ mm Hg (798)**Standard Atmospheric Pressure**• Air pressure at higher altitudes, such as on a mountaintop, is slightly lower than air pressure at sea level.**Standard Atmospheric Pressure**• Air pressure is measured using abarometer.**Pressure and the Number of Molecules**• More molecules mean more collisions between the gas molecules themselves and more collisions between the gas molecules and the walls of the container. • Number of molecules is DIRECTLY proportional to pressure.**Pressure and the Number of Molecules**• Doublingthe number of gas particles in a basketball doubles the pressure.**Pressure and the Number of Molecules**• Gases naturally move from areas of high pressure to low pressure because there is empty space to move in.**If you double the number of molecules, you double the**pressure. 2 atm**4 atm**• As you remove molecules from a container,**2 atm**• As you remove molecules from a container, the pressure decreases.**1 atm**• As you remove molecules from a container, the pressure decreases until the pressure inside equals the pressure outside.**Changing the Size (Volume) of the Container**• In a smaller container, molecules have less room to move. • The molecules hit the sides of the container more often, striking a smaller area with the same force.**Changing the Size (Volume) of the Container**• As volume decreases, pressure increases. • Volume and pressure are INVERSELY proportional.**1 atm**• As the pressure on a gas increases, 4 Liters**As the pressure on a gas increases, the volume decreases.**2 atm 2 Liters**Temperature and Pressure**• Raising the temperature of a gas increases the pressure if the volume is held constant. • At higher temperatures, the particles in a gas have greater kinetic energy.**Temperature and Pressure**• They move faster and collide with the walls of the container more often and with greater force, so the pressure rises.**300 K**• If you start with 1 liter of gas at 1 atm pressure and 300 K and heat it to 600 K, one of 2 things happens.**600 K**300 K • Either the volume will increase to 2 liters at 1 atm,**600 K**300 K • or the pressure will increase to 2 atm while the volume remains constant.**Ideal Gases**• In this unit we will assume the gases behave ideally. • Ideal gases do not really exist, but this makes the math easier and is a close approximation.**Kinetic Molecular Theory of Gases**• Gas particles are much smaller than the spaces between them. The particleshave negligible volume. • There are no attractive or repulsive forces between gas molecules.**Kinetic Molecular Theory of Gases**• Gas particles are in constant, random motion. Until they bump into something (another particle or the side of a container), particles move in a straight line.**Kinetic Molecular Theory of Gases**• No kinetic energy is lost when gas particles collide with each other or with the walls of their container. • All gases have the same kinetic energy at a given temperature.**Temperature**• Temperature is a measure of the average kinetic energy of the particles in a sample of matter.**Ideal Gases**• There are no gases for which this is true. • Real gases behave more ideally at high temperature and low pressure.**Ideal Gases**• At low temperature, the gas molecules move more slowly, so attractive forces are no longer negligible. • As the pressure on a gas increases, the molecules are forced closer together and attractive forces are no longer negligible. • Therefore, real gases behave more ideally at high temperature and low pressure.**Avogadro’s Law**• Avogadro’s law states that equal volumes of different gases (at the same temperature and pressure) contain equal numbers of atoms or molecules.**Avogadro’s Law**• has the same number of particles as .. 2 Liters of Helium 2 Liters of Oxygen**Avogadro’s Law**• The molar volume for a gas is the volume that one mole occupies at 0.00ºC and 1.00 atm. • 1 mole = 22.4 L at STP (standard temperature and pressure). • As a result, the volume of gaseous reactants and products can be expressed as small whole numbers in reactions.**Problem**• How many moles are in 45.0 L of a gas at STP? 2.01 moles**Problem**• How many liters are in 0.636 moles of a gas at STP? 14.2 L**Avogadro’s Law**• V = K xn (K is some constant) • V / n = K • Easier to use: V1 V2 = n1 n2**Example**• Consider two samples of nitrogen gas. Sample 1 contains 1.5 mol and has a volume of 36.7 L. Sample 2 has a volume of 16.5 L at the same temperature and pressure. Calculate the number of moles of nitrogen in sample 2.**Example**V1 • Sample 1 contains 1.5 mol and has a volume of 36.7 L. Sample 2 has a volume of 16.5 L. Calculate the number of moles of nitrogen in sample 2. V2 36.7 L 16.5 L = n1 n2 1.5 mol n2 = 0.67 mol**Problem**• If 0.214 mol of argon gas occupies a volume of 652 mL at a particular temperature and pressure, what volume would 0.375 mol of argon occupy under the same conditions? V2 = 1140 mL**Problem**• If 46.2 g of oxygen gas occupies a volume of 100. L at a particular temperature and pressure, what volume would 5.00 g of oxygen gas occupy under the same conditions? V2 = 10.8 L**Boyle’s Law**• At Boyle’s lawstates that the pressure and volume of a gas at constant temperature are inversely proportional. • Inversely proportional means as one goes up the other goes down.**Boyle’s Law**• P x V = K (K is some constant) • P1 V1 = P2 V2**Boyle’s Law**• The P-V graph for Boyle’s law results in a hyperbola because pressure and volume are inversely proportional.**P**V**Example**• A balloon is filled with 25 L of air at 1.0 atm pressure. If the pressure is changed to 1.5 atm, what is the new volume?**Example**• First, make sure the pressure and volume units in the question match. • A balloon is filled with 25 L of air at 1.0 atm pressure. If the pressure is changed to 1.5 atm, what is the new volume? THEY DO!**Example**P1 • A balloon is filled with 25L of air at 1.0atm pressure. If the pressure is changed to 1.5atm, what is the new volume? V1 = P2 V2 V2 1.0 atm (25 L) 1.5 atm V2 = 17 L