Chapter 11 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.

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Presentation transcript:

Chapter 11 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

Composition of Earth’s Atmosphere Compound%(Volume)Mole Fraction a Nitrogen Oxygen Argon Carbon dioxide Methane2 x x Hydrogen5 x x a. mole fraction = mol component/total mol in mixture. The Air We Breathe

Kinetic Theory of Gases Kinetic Theory Postulates: Gas particles are sizeless relative to the volume of the gas Gas particles are in constant rapid motion Gas particles have elastic collisions; means no kinetic energy is lost on impact. The absolute temperature is directly proportional to the kinetic energy of a gas. Gas particles have no attraction to each other; i.e. no inter particle froces.

Parameters Affecting Gases Pressure (P); atm, mmHg, torr, lbs/in 2 Volume (V); L, mL Temperature (T); K (only) Number of Moles (n)

Pressure Pressure is equal to force/unit area (P =F/A) lbs/in 2 Force is a push which comes from gas particles striking a container wall

Pressure Units SI units = Newton/meter 2 = 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/in 2  1 atm = barr  Barr = 100 kPa

Measurement of Pressure What is above mercury?

Measurement of Pressure

Elevation and Atmospheric Pressure

Units for Expressing Pressure UnitValue Atmosphere1 atm Pascal (Pa)1 atm = x 10 5 Pa Kilopascal (kPa)1 atm = kPa mmHg1 atm = 760 mmHg Torr1 atm = 760 torr Bar1 atm = bar mbar1 atm = mbar psi1 atm = 14.7 psi

Pressure Measurement Open Tube Manometer Is the atmosphere or the gas in the canister pushing harder? = 15 mm

Pressure Measurement Open Tube Manometer 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? = 15 mm

Pressure Measurement Open Tube Manometer 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 = = 781 mm (torr) = 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 gas Now what is pushing harder, the gas or the atomosphere?

Pressure Measurement Open Tube Manometer gas Now what is pushing harder, the gas or the atmosphere? Neither, both the same.

Pressure Measurement Open Tube Manometer gas Now what is pushing harder, the gas or the atmosphere? Neither, both the same. Is the gas canister empty?

Pressure Measurement Open Tube Manometer gas Now what is pushing harder, the gas or the atmosphere? Neither, both the same. Is the gas canister empty? No, completely full of gas!

Dalton’s Law of Partial Pressures For a mixture of gases in a container P Total = P 1 + P 2 + P

Boyles Law Atm ● ● ● ● 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?

Boyles Law Atm ● ● ● ● 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? ● ● ●

Boyles Law Atm ● ● ● ● 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? ● ● ●

Boyles Law Atm ● ● ● ● 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? ● ● ●

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 P  1/V (T and n fixed) P  V = Constant P 1 V 1 = P 2 V 2 Pressure and volume are inversely proportional.

Charles’s Law The volume of a gas is directly proportional to Kelvin temperature, and extrapolates to zero at zero Kelvin. V  T (P & n are constant) V 1 = V 2 T 1 T 2

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. Volume: L, mL, cm 3, … Pressure: Atm, mmHg, Torr, PSI, KPa Temperature, K (only)

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? 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? (1.35 atm) (2.54 L) T1T1 = (2.50atm)V 2 T1T1 Constant Temp. means T 1 =T 2 (1.35 atm ) (2.54 L ) (2.50atm) V 2 = V 2 = 1.37 L

Example A sample of oxygen gas is at atm and occupies a volume of 11.2 L at 0 0 C, what volume will the gas occupy at 6.00 atm at room temperature (25 0 C)?

Ideal Gas Law PV = nRT R = universal gas constant = L atm K -1 mol -1 P = pressure in atm V = volume in liters n = moles T = temperature in Kelvin

STP “STP” means standard temperature and standard pressure  P = 1 atmosphere  T = 0  C  The molar volume of an ideal gas is liters at STP (put 1 mole, 1 atm, R, and 273 K in the ideal gas law and calculate V)

Example Calculate the pressure of a 1.2 mol sample of methane gas in a 3.3 L container at 25°C. Calculate the pressure of a 1.2 mol sample of methane gas in a 3.3 L container at 25°C.

Example Calculate the pressure of a 1.2 mol sample of methane gas in a 3.3 L container at 25°C. Calculate the pressure of a 1.2 mol sample of methane gas in a 3.3 L container at 25°C L-atm Mole-K

Example Calculate the pressure of a 1.2 mol sample of methane gas in a 3.3 L container at 25°C. Calculate the pressure of a 1.2 mol sample of methane gas in a 3.3 L container at 25°C L-atm Mole-K 3.3 L

Example Calculate the pressure of a 1.2 mol sample of methane gas in a 3.3 L container at 25°C. Calculate the pressure of a 1.2 mol sample of methane gas in a 3.3 L container at 25°C L-atm Mole-K 3.3 L 298 K

Example Calculate the pressure of a 1.2 mol sample of methane gas in a 3.3 L container at 25°C. Calculate the pressure of a 1.2 mol sample of methane gas in a 3.3 L container at 25°C L-atm Mole-K 3.3 L 298 K 1.2 mole

Example Calculate the pressure of a 1.2 mol sample of methane gas in a 3.3 L container at 25°C. Calculate the pressure of a 1.2 mol sample of methane gas in a 3.3 L container at 25°C L-atm Mole-K 3.3 L 298 K 1.2 mole = 8.9 atm

Example An experiment shows that a g sample of an unknown gas occupies 127 mL at 98°C and 754 torr pressure. Calculate the molar mass of the gas. An experiment shows that a g sample of an unknown gas occupies 127 mL at 98°C and 754 torr pressure. Calculate the molar mass of the gas.

Example An experiment shows that a g sample of an unknown gas occupies 127 mL at 98°C and 754 torr pressure. Calculate the molar mass of the gas. An experiment shows that a g sample of an unknown gas occupies 127 mL at 98°C and 754 torr pressure. Calculate the molar mass of the gas. mole-K L-atm

Example An experiment shows that a g sample of an unknown gas occupies 127 mL at 98°C and 754 torr pressure. Calculate the molar mass of the gas. An experiment shows that a g sample of an unknown gas occupies 127 mL at 98°C and 754 torr pressure. Calculate the molar mass of the gas. mole-K L-atm0.495 g

Example An experiment shows that a g sample of an unknown gas occupies 127 mL at 98°C and 754 torr pressure. Calculate the molar mass of the gas. An experiment shows that a g sample of an unknown gas occupies 127 mL at 98°C and 754 torr pressure. Calculate the molar mass of the gas. mole-K L-atm0.495 g L mL

Example An experiment shows that a g sample of an unknown gas occupies 127 mL at 98°C and 754 torr pressure. Calculate the molar mass of the gas. An experiment shows that a g sample of an unknown gas occupies 127 mL at 98°C and 754 torr pressure. Calculate the molar mass of the gas. mole-K L-atm0.495 g L mL 127 mL

Example An experiment shows that a g sample of an unknown gas occupies 127 mL at 98°C and 754 torr pressure. Calculate the molar mass of the gas. An experiment shows that a g sample of an unknown gas occupies 127 mL at 98°C and 754 torr pressure. Calculate the molar mass of the gas. mole-K L-atm0.495 g L mL 127 mL 760 torr atm

Example An experiment shows that a g sample of an unknown gas occupies 127 mL at 98°C and 754 torr pressure. Calculate the molar mass of the gas. An experiment shows that a g sample of an unknown gas occupies 127 mL at 98°C and 754 torr pressure. Calculate the molar mass of the gas. mole-K L-atm0.495 g L mL 127 mL 760 torr atm 754 torr

Example An experiment shows that a g sample of an unknown gas occupies 127 mL at 98°C and 754 torr pressure. Calculate the molar mass of the gas. An experiment shows that a g sample of an unknown gas occupies 127 mL at 98°C and 754 torr pressure. Calculate the molar mass of the gas. mole-K L-atm0.495 g L mL 127 mL 760 torr atm 754 torr 371 K

Example An experiment shows that a g sample of an unknown gas occupies 127 mL at 98°C and 754 torr pressure. Calculate the molar mass of the gas. An experiment shows that a g sample of an unknown gas occupies 127 mL at 98°C and 754 torr pressure. Calculate the molar mass of the gas. mole-K L-atm0.495 g L mL 127 mL 760 torr atm 754 torr 371 K = 120 g/mole

Collecting a Gas Over Water

A sample of KClO 3 is heated and decomposes to produce O 2 gas. The gas is collected by water displacement at 25°C. The total volume of the collected gas is 229 mL at a pressure of 755 torr. How many moles of oxygen formed? Hint: The gas collected is a mixture so use Dalton’s Law to calculate the pressure of oxygen then the ideal gas law to find the number of moles oxygen. Hint: The gas collected is a mixture so use Dalton’s Law to calculate the pressure of oxygen then the ideal gas law to find the number of moles oxygen. P T = P + P Practice O2O2 H2OH2O

Vapor Pressure of Water

A sample of KClO 3 is heated and decomposes to produce O 2 gas. The gas is collected by water displacement at 25°C. The total volume of the collected gas is 229 mL at a pressure of 755 torr. How many moles of oxygen formed? Hint: The gas collected is a mixture so use Dalton’s Law to calculate the pressure of oxygen then the ideal gas law to find the number of moles oxygen. Hint: The gas collected is a mixture so use Dalton’s Law to calculate the pressure of oxygen then the ideal gas law to find the number of moles oxygen. P T = P + P Practice O2O2 H2OH2O 755 torr = P O2O torr P = 755 – 23.8 = 731 torr O2O2

Practice A sample of KClO 3 is heated and decomposes to produce O 2 gas. The gas is collected by water displacement at 25°C. The total volume of the collected gas is 229 mL at a pressure of 755 torr. How many moles of oxygen formed? mole-K L-atm

Practice A sample of KClO 3 is heated and decomposes to produce O 2 gas. The gas is collected by water displacement at 25°C. The total volume of the collected gas is 229 mL at a pressure of 755 torr. How many moles of oxygen formed? mole-K L-atm atm 760 torr

Practice A sample of KClO 3 is heated and decomposes to produce O 2 gas. The gas is collected by water displacement at 25°C. The total volume of the collected gas is 229 mL at a pressure of 755 torr. How many moles of oxygen formed? mole-K L-atm atm 760 torr 731 torr

Practice A sample of KClO 3 is heated and decomposes to produce O 2 gas. The gas is collected by water displacement at 25°C. The total volume of the collected gas is 229 mL at a pressure of 755 torr. How many moles of oxygen formed? mole-K L-atm atm 760 torr 731 torr 298 K

Practice A sample of KClO 3 is heated and decomposes to produce O 2 gas. The gas is collected by water displacement at 25°C. The total volume of the collected gas is 229 mL at a pressure of 755 torr. How many moles of oxygen formed? mole-K L-atm atm 760 torr 731 torr 298 KmL L

Practice A sample of KClO 3 is heated and decomposes to produce O 2 gas. The gas is collected by water displacement at 25°C. The total volume of the collected gas is 229 mL at a pressure of 755 torr. How many moles of oxygen formed? mole-K L-atm atm 760 torr 731 torr 298 KmL L 229 mL = 9.00 X mole

Stoichiometry and Gases Calculate the volume of hydrogen gas at 25°C and 766 torr from 13.4 g of zinc and an excess of hydrochloric acid. Zn (s) + 2 HCl (aq) ZnCl 2 (aq) + H 2 (g) 13.4 g Zn

Stoichiometry and Gases Calculate the volume of hydrogen gas at 25°C and 766 torr from 13.4 g of zinc and an excess of hydrochloric acid. Zn (s) + 2 HCl (aq) ZnCl 2 (aq) + H 2 (g) 13.4 g Zn g Zn mole Zn

Stoichiometry and Gases Calculate the volume of hydrogen gas at 25°C and 766 torr from 13.4 g of zinc and an excess of hydrochloric acid. Zn (s) + 2 HCl (aq) ZnCl 2 (aq) + H 2 (g) 13.4 g Zn g Zn mole Zn mole H 2

Stoichiometry and Gases Calculate the volume of hydrogen gas at 25°C and 766 torr from 13.4 g of zinc and an excess of hydrochloric acid. Zn (s) + 2 HCl (aq) ZnCl 2 (aq) + H 2 (g) 13.4 g Zn g Zn mole Zn mole H L-atm mole H 2 -K

Stoichiometry and Gases Calculate the volume of hydrogen gas at 25°C and 766 torr from 13.4 g of zinc and an excess of hydrochloric acid. Zn (s) + 2 HCl (aq) ZnCl 2 (aq) + H 2 (g) 13.4 g Zn g Zn mole Zn mole H L-atm mole H 2 -K K

Stoichiometry and Gases Calculate the volume of hydrogen gas at 25°C and 766 torr from 13.4 g of zinc and an excess of hydrochloric acid. Zn (s) + 2 HCl (aq) ZnCl 2 (aq) + H 2 (g) 13.4 g Zn g Zn mole Zn mole H L-atm mole H 2 -K K 760 torr

Stoichiometry and Gases Calculate the volume of hydrogen gas at 25°C and 766 torr from 13.4 g of zinc and an excess of hydrochloric acid. Zn (s) + 2 HCl (aq) ZnCl 2 (aq) + H 2 (g) 13.4 g Zn g Zn mole Zn mole H L-atm mole H 2 -K K 760 torr atm 766 torr

Stoichiometry and Gases Calculate the volume of hydrogen gas at 25°C and 766 torr from 13.4 g of zinc and an excess of hydrochloric acid. Zn (s) + 2 HCl (aq) ZnCl 2 (aq) + H 2 (g) 13.4 g Zn g Zn mole Zn mole H L-atm mole H 2 -K K 760 torr atm 766 torr = 4.97 L

The End