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## Chapter 6

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**Chapter 6**Gas Laws**The Gas Phase**• Gases have no distinct volume or shape. • Gases expand to fill the volume of their container. • Gas particles are miscible with each other. • Evidence for gas particles being far apart : • We can see through gases • We can walk through gases • Gases are compressible • Gases have low densities**Kinetic Theory of a Gas**• Gas particles are sizeless relative to their volume. • Gas particles are in constant random motion. • Gas particles have elastic collisions. • Gas particles do not have attractive forces with each other. • The Average kinetic energy of a gas is directly proportional to absolute temperature.**Kinetic Theory of a Gas**• Sizeless particles relative to the volume means that most of a gas is empty space. • We can see through a gas • We can walk through a gas • Elastic collision means that no kinetic energy is lost on impact. • If gas particles had attractive forces then they would not be mostly empty space, and be in the solid or liquid state. • Since gas particles are in constant rapid motion, then they must possess kinetic energy**Parameters Affecting Gases**• Pressure (P) • Volume (V) • Temperature (T) • Number of Moles (n)**Pressure**Pressure is equal to force/unit area (P =F/A) • On earth the force related to gravity • From physics the F=ma, where m is kg and a=9.8m/s2 • The units kgm/s2 is called a Newton (N) • Since P = F/A, then pressure unit is Kgm/s2m2, or N/m2 • Pascal is the abbreviation of N/m2 called Pa**Pressure**The atomosphere is pushing with a force of 14.7 lbs/in2 on every surface in this room. For example each square inch on the whiteboard has 17.7 lbs of air pushing on each square inch, which is probably several tons. Why is the white board not pushed into the next room????**Pressure Units**• SI units = Newton/meter2 = 1 Pascal (Pa) • 1 standard atmosphere (atm) = 101,325 Pa • 1 atm =760 mm Hg • 1 atm = 760 torr (torr is abbreviation of mmHg) • 1 atm = 14.7 lbs/in2 • 1 atm = 1.013 barr • Barr = 100 kPa**Measurement of Pressure**What is above mercury?**Measurement of Pressure**760 mm Hg**Measurement of Pressure**How many pounds of mercury are in the tube if its opening is 1.0 in2, assuming 14.7 psi pressure? How about if the opening is 2.0 in2? 760 mm Hg**Measurement of Pressure**How many pounds of mercury are in the tube if its opening is 1.0 in2, assuming 14.7 psi pressure? How about if the opening is 2.0 in2? How high would the column of Hg be in the 2.0in2 device? 760 mm Hg**Pressure Measurement**Is the atmosphere or the gas in the canister pushing harder? Open Tube Manometer = 15 mm**Pressure Measurement**Is the atmosphere or the gas in the canister pushing harder? Gas in the canister If the atmospheric pressure is 766 mm, then what is the pressure of the canister? Open Tube Manometer = 15 mm**Pressure Measurement**Is the atmosphere or the gas in the canister pushing harder? Gas in the canister If the atmospheric pressure is 766 mm, then what is the pressure of the canister? P = 766 + 15 = 781 mm (torr) Open Tube Manometer = 15 mm gas**Pressure Measurement**Open Tube Manometer Is the atmosphere or the gas in the canister pushing harder? gas**Pressure Measurement**Open Tube Manometer Is the atmosphere or the gas in the canister pushing harder? The atmosphere What is the pressure of the gas if the atmosphere is 766 mm? = 13 mm gas**Pressure Measurement**Open Tube Manometer Is the atmosphere or the gas in the canister pushing harder? The atmosphere What is the pressure of the gas if the atmosphere is 766 mm? 753 mm = 13 mm gas**Pressure Measurement**Open Tube Manometer Now what is pushing harder, the gas or the atomosphere? gas**Pressure Measurement**Open Tube Manometer Now what is pushing harder, the gas or the atmosphere? Neither, both the same. gas**Pressure Measurement**Open Tube Manometer Now what is pushing harder, the gas or the atmosphere? Neither, both the same. Is the gas canister empty? gas**Pressure Measurement**Open Tube Manometer Now what is pushing harder, the gas or the atmosphere? Neither, both the same. Is the gas canister empty? No, completely full of gas! gas**Boyles Law**Consider a gas in a closed system containing a movable plunger. If the plunger is not moving up or down, what can be said about the pressure of the gas relative to the atmospheric pressure? Atm ● ● ● ●**Boyles Law**Suppose we add some red gas to the container, what would happen to the collisions of gas particles with container walls. Would they increase, decrease or stay the same? Atm ● ● ● ● ● ● ●**Boyles Law**Suppose we add some red gas to the container, what would happen to the collisions of gas particles with container walls. Would they increase, decrease or stay the same? More particles, more collisions, and more pressure. What happens to the plunger? Atm ● ● ● ● ● ● ●**Boyles Law**Suppose we add some red gas to the container, what would happen to the collisions of gas particles with container walls. Would they increase, decrease or stay the same? More particles, more collisions, and more pressure. What happens to the plunger? Atm ● ● ● ● ● ● ●**Boyles Law**The number of particles remain the same, but the surface area they have to strike increases, thus the number of collisions per square inch decrease as the plunger goes up exposing more surface area causing a decrease in pressure. ● ● ● ● ● ● ● ● ● ●**Boyle’s Law**Pressure and volume are inversely proportional. • P 1/V (T and n fixed) • P V = Constant • P1V1 = P2V2**Charles’s Law**The kinetic theory of gases states that absolute temperature and kinetic energy are directly proportional. As temperature increases then particle velocity increases and the particles reach the container wall sooner, thus increasing collisions per second. Since Charles law is for constant pressure, then the volume must expand to keep a constant pressure. The mathematical statement of Charles Law is below, showing pressure and volume directly proportional. V1 V2 = T1 T2**Avogadro’s Law**• For a gas at constant temperature and pressure, the volume is directly proportional to the number of moles of gas (at low pressures). V n V1 = V2 n1 n2**Amonton’s Law**• P T • P/T = Constant • P1 = P2 • T1 T2**Combined Gas Law**• Combining the gas laws the relationship P T(n/V) can be obtained. • If n (number of moles) is held constant, then PV/T = constant. Temperature, Kelvin, only Pressure, atm, torr, mmHg, Volume, L, mL, cm3, etc**Example**A balloon is filled with hydrogen to a pressure of 1.35 atm and has a volume of 2.54 L. If the temperature remains constant, what will the volume be when the pressure is increased to 2.50 atm?**Example**A sample of oxygen gas is at 0.500 atm and occupies a volume of 11.2 L at 00C, what volume will the gas occupy at 6.00 atm at room temperature (250C)?**Ideal Gas Law**PV = nRT R = universal gas constant = 0.08206 L atm K-1 mol-1 P = pressure in atm V = volume in liters n = moles T = temperature in Kelvin**Calculate the pressure of a 1.2 mol sample of methane gas**in a 3.3 L container at 25°C. This problem is not a “changing condition” problem, therefore use the ideal gas law. Example**Practice**A 1.22 g sample of a gas is contained in a 125 mL flask at 25⁰C and 766 torr. Find the molar mass.**Practice**A 1.22 g sample of a gas is contained in a 125 mL flask at 25⁰C and 766 torr. Find the molar mass. What are the units of molar mass?**Practice**A 1.22 g sample of a gas is contained in a 125 mL flask at 25⁰C and 766 torr. Find the molar mass. What are the units of molar mass? g/mole**Practice**0.0821 L-atm mole-K A 1.22 g sample of a gas is contained in a 125 mL flask at 25⁰C and 766 torr. Find the molar mass. What are the units of molar mass? g/mole**Practice**0.0821 L-atm 298.15 K mole-K A 1.22 g sample of a gas is contained in a 125 mL flask at 25⁰C and 766 torr. Find the molar mass. What are the units of molar mass? g/mole**Practice**760 torr 0.0821 L-atm 298.15 K mole-K atm A 1.22 g sample of a gas is contained in a 125 mL flask at 25⁰C and 766 torr. Find the molar mass. What are the units of molar mass? g/mole**Practice**760 torr 0.0821 L-atm 298.15 K mole-K atm A 1.22 g sample of a gas is contained in a 125 mL flask at 25⁰C and 766 torr. Find the molar mass. What are the units of molar mass? g/mole**Practice**760 torr 1000 mL 0.0821 L-atm 298.15 K mole-K atm L A 1.22 g sample of a gas is contained in a 125 mL flask at 25⁰C and 766 torr. Find the molar mass. What are the units of molar mass? g/mole