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## Gases

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**Gases**Revision history: 10/5/01 2/20/03 5/21/03 6/24/04 12/27/06 12/29/06 01/05/10 01/09/10 050212 Pisgah High School M. Jones**The Properties of Gases**Part I**Properties of Gases**• Gases expand to fill the container. • Gases take on the shape of the container. • Gases are highly compressible. (Can be liquefied at high pressures). • Gases have low densities. • Gases mix uniformly.**The Kinetic Molecular Theory**The kinetic molecular theory describes the behavior of ideal gases. An ideal gas is one that conforms to the KMT.**1. Molecules are in constant random motion**Temperature is proportional to the average kinetic energy of the molecules. KE = ½ mv2 KE = ½ mass times speed squared The speed is proportional to the absolute temperature (Kelvin).**2. A gas is mostly empty space**Molecules are far apart from each other. This accounts for the low density and high compressibility. The volume of the individual molecules is negligible compared to the volume of the gas.**3. No intermolecular forces**There are no attractive or repulsive forces between gas molecules. Adjacent molecules do not attract or repel each other.**4. Collisions are elastic**When gas molecules collide with each other they may speed up or slow down, BUT … The net (total) energy of the gas molecules does not change.**Kinetic Molecular Theory**• Gases in constant motion, speed depends on temperature. • Molecules have negligible volume. • No intermolecular forces. • Elastic collisions. No change in energy.**Temperature reminder**When doing calculations, temperature must always be in an absolute temperature scale … … where the lowest possible temperature is zero degrees. Use Kelvin degrees!**Temperature conversion**K = C + 273**Pressure**1. Pressure is the force per unit area exerted by the gas molecules. 2. Pressure is proportional to the number of collisions between the gas molecules and the walls of the container.**Pressure**P = 1. Pressure is a measure of the force per unit area. force Pressure can be in pounds per square inch (PSI), or … area … newtons per square meter (N/m2) pascal (Pa) = N/m2**Pressure**P = At sea level, air pressure holds up a column of mercury 760 mm high. 1. Pressure is a measure of the force per unit area. force area Glass tube with Hg Torricelli Bowl of Hg**Pressure Measurements**Standard sea level pressure is… 1.00 atmospheres (atm) 760 mm Hg 760 torr (from Torricelli) 101.3 kilopascals (kPa) 14.7 lb/in2**Pressure Measurements**Standard sea level pressure is… 1.00 atmospheres (atm) 760 mm Hg 760 torr (from Torricelli) 101.3 kilopascals (kPa) 14.7 lb/in2 Exact**Pressure**2. Pressure is proportional to the number of collisions between the gas molecules and the walls of the container. If you change the number of collisions, you change the pressure.**The Gas Laws**Part II**The Gas Laws**Boyle’s Law Amonton’s Law Charles’s Law Combined Gas Law Gay-Lussac’s Law Avogadro’s Law Dalton’s Law**Boyle’s Law**At a constant temperature, pressure is inversely proportional to volume. Pressure Volume**Boyle’s Law**At a constant temperature, pressure is inversely proportional to volume. 1/Pressure Volume**Boyle’s Law**1 P µ V At a constant temperature, pressure is inversely proportional to volume. PV = k P1V1 = P2V2 Year: 1662**Amonton’s Law**P µ T P1 P2 = T1 T2 “Air thermometer”, 1695. This is not Gay-Lussac’s law. Diagram from http://chemed.chem.purdue.edu/genchem/topicreview/bp/ch4/gaslaws3.html**Amonton’s Law**P µ T P1 P2 = T1 T2 This is why you measure your tire pressure when the tire is cold. Tire pressures vary with temperature.**Amonton’s Law**Amonton’s air thermometer was used to find the value of absolute zero. Measure the pressures of a gas at various temperatures at a constant volume.**Finding Absolute Zero**-273 C Pressure Extrapolate to the x-axis -300 -150 0 100 200 300 Temperature (C)**Charles’s Law**Volume Temperature At constant pressure, volume is directly proportional to temp.**Charles’s Law**V µ T V V1 V2 = k = T T1 T2 At constant pressure, volume is directly proportional to temperature.**Charles’s Law**• Studied gases during 1780’s. • Hydrogen balloon assents, 3000 m, in 1783. • Collaborated with the Montgolfier brothers on hot air balloons, 1783. • Charles’s gas studies published by Gay-Lussac in1802.**Charles’s Law**Hydrogen balloon assent, 3000 m, 1783.**Combined Gas Law**T 1 P µ T P µ P µ V V gives**Combined Gas Law**T P µ V kT P = V to an Next we convert equation by adding a constant.**Combined Gas Law**PV = k kT T P = V Rearranging the equation gives:**Combined Gas Law**PV = k T Combining the laws of Boyle, Amonton and Charles produces the combined gas law.**Combined Gas Law**P2V2 P1V1 k k = = T2 T1 Consider a confined gas at two sets of conditions. Since the number of molecules is the same and the values of k are the same, then we can combine the two equations.**Combined Gas Law**P2V2 P1V1 k k = = T2 T1 P1V1 P2V2 = T1 T2**Combined Gas Law**P1V1 P2V2 = T1 T2 Use the combined gas law whenever you are asked to find a new P, V or T after changes to a confined gas.**Sample Combined Gas Law Problem**Consider a confined gas in a cylinder with a movable piston. The pressure is 0.950 atm. Find the new pressure when the volume is reduced from 100.0 mL to 65.0 mL, while the temperature remains constant? 100 mL 65 mL**Sample Combined Gas Law Problem**Start with the equation for the combined gas law. 100 mL 65 mL**Sample Combined Gas Law Problem**P1V1 P2V2 = T1 T2 100 mL Since the temperature is constant, we can cancel out T1 and T2. 65 mL**Sample Combined Gas Law Problem**P1V1 = P2V2 P1V1 P2 = V2 This becomes Boyle’s Law 100 mL Next, solve for P2. 65 mL**Sample Combined Gas Law Problem**(0.950 atm)(100.0 mL) P2 = 65.0 mL P1V1 P2 = P2 = 1.46 atm V2 100 mL 65 mL**Combined Gas Law Problems**• 1. A sample of neon gas has a volume of 2.00 L at 20.0 C and 0.900 atm. What is the new pressure when the volume is reduced to 0.750 L and the temperature increases to 24.0 C? 2.43 atm The answer is**Combined Gas Law Problems**• 2. Some “left over” propane gas in a rigid steel cylinder has a pressure of 24.6 atm at a temperature of 20.C. When thrown into a campfire the temperature in the cylinder rises to 313C. What will be the pressure of the propane? 49.2 atm The answer is**Combined Gas Law Problems**• 3. Consider the fuel mixture in the cylinder of a diesel engine. At its maximum, the volume is 816 cc. The mixture comes in at 0.988 atm and 31 C. What will be the temperature (in C) when the gas is compressed to 132 cc and 42.4 atm? 1837 C The answer is**Gay-Lussac’s Law**Also known as the law of combining volumes. At a given temperature and pressure, the volumes of reacting gases are in a ratio of small, whole numbers. Year: 1802**Gay-Lussac’s Law**Gay-Lussac found that the volumes of gases in a reaction were in ratios of small, whole numbers. 2 H2(g) + O2(g) 2 H2O(g) 200 mL of hydrogen reacts with 100 mL of oxygen. 2:1**Gay-Lussac’s Law**2 H2(g) + O2(g) 2 H2O(g) The ratio of volumes of gases come from the ratios of the coefficients in the balanced equation.**Avogadro’s Law**V µ n V V1 V2 = k = n n1 n2 Avogadro’s law followed Dalton’s atomic theory and Gay-Lussac’s law. Year: 1811. Equal volumes of gases at the same temperature and pressure have equal numbers of molecules.**Dalton’s Law**Dalton’s law of partial pressures deals with mixtures of gases. The total pressure is the sum of the partial pressures: Ptotal = P1 + P2 + P3 … Use when dealing with the pressure of H2O(g) when collecting a gas over water.