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## CHAPTER 10

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**CHAPTER 10**• GASES**Characteristics of Gases**• There are three phases for all substances: solid, liquid and gases. • Gases are highly compressible and occupy the full volume of their containers. • When a gas is subjected to pressure, its volume decreases. • Gases always form homogeneous mixtures with other gases. • Gases only occupy about 0.1 % of the volume of their containers.**Pressure**• Pressure is the force acting on an object per unit area: • Units: psi pounds per square inch**Pressure**SI Units: 1 N = 1 kg.m/s2; 1 Pa = 1 N/m2. • Atmospheric pressure is measured with a barometer. • If a tube is inserted into a container of mercury open to the atmosphere, the mercury will rise 760 mm up the tube. • Standard atmospheric pressure is the pressure required to support 760 mm of Hg in a column.**Pressure**• force per unit area • standard pressure • 76 cm Hg • 760 mm Hg • 760 torr • 1 atmosphere • 101.3 kPa • Units: 1 atm = 760 mmHg = 760 torr = 1.01325 105 Pa = 101.325 kPa. density = 13.6 g/mL**Pressure**• The pressures of gases not open to the atmosphere are measured in manometers. • A manometer consists of a bulb of gas attached to a U-tube containing Hg.**Pressure**If the U-tube is closed, then the pressure of the gas is the difference in height of the liquid (usually Hg). • If the U-tube is open to the atmosphere, a correction term needs to be added: • If Pgas < Patm then Pgas + Ph2 = Patm. • If Pgas > Patm then Pgas = Patm + Ph2.**The Gas Laws**Weather balloons are used as a practical consequence to the relationship between pressure and volume of a gas. • As the weather balloon ascends, the volume decreases. • As the weather balloon gets further from the earth’s surface, the atmospheric pressure decreases. • Boyle’s Law: the volume of a fixed quantity of gas is inversely proportional to its pressure.**Boyle’s Laws**• Mathematically: • A plot of V versus P is a hyperbola. • Similarly, a plot of V versus 1/P must be a straight line passing through the origin.**Boyle’s Law**• Vµ 1/P • V= k (1/P) or PV = k • P1V1 = k1 P2V2 = k2 • k1 = k2 (for same sample of gas @ same T) • P1V1 = P2V2 Boyle’s Law (math form) • think in terms of balloons!!!**Boyle’s Law**• Example At 250C a sample of He has a volume of 400 mL under a pressure of 760 torr. What volume would it occupy under a pressure of 2.00 atm at the same T?**Boyle’s Law**• Example At 250C a sample of He has a volume of 400 mL under a pressure of 760 torr. What volume would it occupy under a pressure of 2.00 atm at the same T?**Boyle’s Law**• Example At 250C a sample of He has a volume of 400 mL under a pressure of 760 torr. What volume would it occupy under a pressure of 2.00 atm at the same T?**The Gas Laws**We know that hot air balloons expand when they are heated. • Charles’ Law: the volume of a fixed quantity of gas at constant pressure increases as the temperature increases. • Mathematically:**Charles’ Law**A plot of V versus T is a straight line. • When T is measured in C, the intercept on the temperature axis is -273.15C. • We define absolute zero, 0 K = -273.15C. • Note the value of the constant reflects the assumptions: amount of gas and pressure.**Charles’ Law**• volume of a gas is directly proportional to the absolute temperature at constant pressure**Charles’ Law**• volume of a gas is directly proportional to the absolute temperature at constant pressure**Charles’ Law**• volume of a gas is directly proportional to the absolute temperature at constant pressure**Charles’ Law**• Example A sample of hydrogen, H2, occupies 100 mL at 250C and 1.00 atm. What volume would it occupy at 500C under the same pressure? T1 = 25 + 273 = 298 T2 = 50 + 273 = 323**Charles’ Law**• Example A sample of hydrogen, H2, occupies 100 mL at 250C and 1.00 atm. What volume would it occupy at 500C under the same pressure?**Standard Temperature & Pressure**• STP • P = 1.00000 atm or 101.3 kPa • T = 273 K or 00C**The Gas Laws**• Avogadro’s Hypothesis: equal volumes of gas at the same temperature and pressure will contain the same number of molecules. • Avogadro’s Law: the volume of gas at a given temperature and pressure is directly proportional to the number of moles of gas.**Avogadro’s Law**Mathematically: V = constant n. • We can show that 22.4 L of any gas at 0C contain 6.02 1023 gas molecules.**The Ideal Gas Equation**• Summarizing the Gas Laws Boyle: (constant n, T) Charles: V T (constant n, P) Avogadro: V n (constant P, T). • Combined: • Ideal gas equation:**The Ideal Gas Equation**• Ideal gas equation: PV = nRT. • R = gas constant = 0.08206 L•atm/mol-K. • We define STP (standard temperature and pressure) = 0C, 273.15 K, 1 atm. • Volume of 1 mol of gas at STP is 22.4 L.**Ideal Gas Law**• R has several values depending upon the choice of units R = 8.314 J/mol K R = 8.314 kg m2/s2 K mol R = 8.314 dm3 kPa/K mol R = 1.987 cal/K mol**Ideal Gas Law**• Example: What volume would 50.0 g of ethane, C2H6, occupy at 140oC under a pressure of 1820 torr?**Ideal Gas Law**• Example: What volume would 50.0 g of ethane, C2H6, occupy at 140oC under a pressure of 1820 torr? T = 140 + 273 = 413 K P = 1820 torr (1 atm/760 torr) = 2.39 atm 50 g (1 mol/30 g) = 1.67 mol**Ideal Gas Law**• Example: Calculate the number of moles in, and the mass of, an 8.96 L sample of methane, CH4, measured at standard conditions.**Ideal Gas Law**• Example: Calculate the pressure exerted by 50.0 g of ethane, C2H6, in a 25.0 L container at 25oC.**The Ideal Gas Law**If PV = nRT and n and T are constant, then PV = constant and we have Boyle’s law. • Other laws can be generated similarly. • In general, if we have a gas under two sets of conditions, then**Ideal Gas Law**• Example: A sample of nitrogen gas, N2, occupies 750 mL at 750C under a pressure of 810 torr. What volume would it occupy at standard conditions?**Example: A sample of nitrogen gas, N2, occupies 750 mL at**750C under a pressure of 810 torr. What volume would it occupy at standard conditions?**Ideal Gas Laws**• A sample of methane, CH4, occupies 260 mL at 32oC under a pressure of 0.500 atm. At what temperature would it occupy 500 mL under a pressure of 1200 torr?**Molar Mass and Density**• Density has units of mass over volume. • Rearranging the ideal-gas equation with M as molar mass we get**Molar Mass and Density**The molar mass of a gas can be determined as follows: Volumes of Gases in Chemical Reactions • The ideal-gas equation relates P, V, and T to number of moles of gas. • The n can then be used in stoichiometric calculations.**Molar Mass and Density**• Example: One mole of a gas occupies 36.5 L and its density is 1.36 g/L at a given T & P. (a)What is its molar mass? (b)What is its density at STP?**Molar Mass and Density**• Example: One mole of a gas occupies 36.5 L and its density is 1.36 g/L at a given T & P. (a)What is its molar mass? (b)What is its density at STP?**Molar Mass and Density**• Example: One mole of a gas occupies 36.5 L and its density is 1.36 g/L at a given T & P. (a)What is its molar mass? (b)What is its density at STP?**Determination of Molar Mass & Formulas of Gaseous Compounds**• Example: A compound that contains only carbon & hydrogen is 80.0% C and 20.0% H by mass. At STP 546 mL of the gas has a mass of 0.732 g . What is the molecular (true) formula for the compound? 100 g of compound contains: 80 g of C & 20 g of H