Ideal Gas Law Describing a sample of a
![Ideal Gas Law Ideal Gas Law](https://slidetodoc.com/presentation_image/06dbda923abe2cc658929d9c42fa4e42/image-1.jpg)
Ideal Gas Law
![Describing a sample of a gas • 4 variables are needed to completely describe Describing a sample of a gas • 4 variables are needed to completely describe](http://slidetodoc.com/presentation_image/06dbda923abe2cc658929d9c42fa4e42/image-2.jpg)
Describing a sample of a gas • 4 variables are needed to completely describe a sample of a gas: • • Temperature Pressure Volume Amount (number of moles) of gas
![Equation of State • An equation relating the macroscopic variables that describe some type Equation of State • An equation relating the macroscopic variables that describe some type](http://slidetodoc.com/presentation_image/06dbda923abe2cc658929d9c42fa4e42/image-3.jpg)
Equation of State • An equation relating the macroscopic variables that describe some type of matter. • The ideal gas law is an equation of state for gases.
![Boyle’s Law Graphs Pressure vs. Volume vs. 1/Pressure Boyle’s Law Graphs Pressure vs. Volume vs. 1/Pressure](http://slidetodoc.com/presentation_image/06dbda923abe2cc658929d9c42fa4e42/image-4.jpg)
Boyle’s Law Graphs Pressure vs. Volume vs. 1/Pressure
![Charles’ Law Graph Charles’ Law Graph](http://slidetodoc.com/presentation_image/06dbda923abe2cc658929d9c42fa4e42/image-5.jpg)
Charles’ Law Graph
![Gay-Lussac’s Law Graph Gay-Lussac’s Law Graph](http://slidetodoc.com/presentation_image/06dbda923abe2cc658929d9c42fa4e42/image-6.jpg)
Gay-Lussac’s Law Graph
![Avogadro’s Law Avogadro’s Law](http://slidetodoc.com/presentation_image/06dbda923abe2cc658929d9c42fa4e42/image-7.jpg)
Avogadro’s Law
![Recall Boyle’s Law Charles’ Law V 1/P Avogadro’s Law V T (Kelvin) V n Recall Boyle’s Law Charles’ Law V 1/P Avogadro’s Law V T (Kelvin) V n](http://slidetodoc.com/presentation_image/06dbda923abe2cc658929d9c42fa4e42/image-8.jpg)
Recall Boyle’s Law Charles’ Law V 1/P Avogadro’s Law V T (Kelvin) V n Constant T, n Constant P, n Constant T, P So V 1/P X n X T
![Ideal Gas Law • To turn a proportionality into an equation, insert a constant: Ideal Gas Law • To turn a proportionality into an equation, insert a constant:](http://slidetodoc.com/presentation_image/06dbda923abe2cc658929d9c42fa4e42/image-9.jpg)
Ideal Gas Law • To turn a proportionality into an equation, insert a constant: V = Rn. T/P • Or multiply both sides by P: • PV = n. RT where R is the ideal gas law constant. If three of the variables are known, the 4 th can be determined. • The units of R depend on the units used for P, T, and V.
![Units of R • Two common values of R: • 0. 08206 Liter Atm Units of R • Two common values of R: • 0. 08206 Liter Atm](http://slidetodoc.com/presentation_image/06dbda923abe2cc658929d9c42fa4e42/image-10.jpg)
Units of R • Two common values of R: • 0. 08206 Liter Atm Mole K • 8. 314 Joules or 8. 314 Liter KPa Mole K
![Problem-Solving • Most commonly used value of R: • 0. 08206 Liter Atm Mole Problem-Solving • Most commonly used value of R: • 0. 08206 Liter Atm Mole](http://slidetodoc.com/presentation_image/06dbda923abe2cc658929d9c42fa4e42/image-11.jpg)
Problem-Solving • Most commonly used value of R: • 0. 08206 Liter Atm Mole K • • Note: Pressure must be in atm Volume must be in liters Temperature must be in Kelvins
![Ideal Gas Law Problems • What pressure is exerted by 0. 75 moles of Ideal Gas Law Problems • What pressure is exerted by 0. 75 moles of](http://slidetodoc.com/presentation_image/06dbda923abe2cc658929d9c42fa4e42/image-12.jpg)
Ideal Gas Law Problems • What pressure is exerted by 0. 75 moles of a gas at 25 C in a container with a volume of 1. 5 L? • Find the volume of 0. 85 moles of gas at a pressure of 520 torr and a temperature of 15 C. • How many moles of gas are present in a sample at 700 torr, 333 C, and occupying a volume of 452 m. L?
![Extensions of Ideal Gas Law Problems • PV = n. RT • n = Extensions of Ideal Gas Law Problems • PV = n. RT • n =](http://slidetodoc.com/presentation_image/06dbda923abe2cc658929d9c42fa4e42/image-13.jpg)
Extensions of Ideal Gas Law Problems • PV = n. RT • n = mass formula mass • Density = mass volume
![Memorize three fundamental equations. • Substitute and rearrange as problem demands. • PV = Memorize three fundamental equations. • Substitute and rearrange as problem demands. • PV =](http://slidetodoc.com/presentation_image/06dbda923abe2cc658929d9c42fa4e42/image-14.jpg)
Memorize three fundamental equations. • Substitute and rearrange as problem demands. • PV = n. RT or PV = mass RT formula mass • Rearrange to solve for mass or density volume • (P formula mass) = mass/volume = density RT
![Formula mass (Identity) of gas • Formula mass = mass RT PV • Or Formula mass (Identity) of gas • Formula mass = mass RT PV • Or](http://slidetodoc.com/presentation_image/06dbda923abe2cc658929d9c42fa4e42/image-15.jpg)
Formula mass (Identity) of gas • Formula mass = mass RT PV • Or formula mass = density RT P
![Density of a gas • At STP, density of a gas = molar mass/22. Density of a gas • At STP, density of a gas = molar mass/22.](http://slidetodoc.com/presentation_image/06dbda923abe2cc658929d9c42fa4e42/image-16.jpg)
Density of a gas • At STP, density of a gas = molar mass/22. 4 L • This is an easy relationship but it is only true at STP!!!
![Dalton’s Law of Partial Pressures Dalton’s Law of Partial Pressures](http://slidetodoc.com/presentation_image/06dbda923abe2cc658929d9c42fa4e42/image-17.jpg)
Dalton’s Law of Partial Pressures
![Dalton’s Law of Partial Pressures • For a mixture of gases: • Ptot = Dalton’s Law of Partial Pressures • For a mixture of gases: • Ptot =](http://slidetodoc.com/presentation_image/06dbda923abe2cc658929d9c42fa4e42/image-18.jpg)
Dalton’s Law of Partial Pressures • For a mixture of gases: • Ptot = P 1 + P 2 + P 3 + … • The total pressure of a gas mixture is the sum of the partial pressures of the component gases. The pressure exerted by each gas in an unreactive mixture is independent of the other gases in the mixture.
![Addition or Subtraction Problems • Three gases, He, N 2, and Ar are present Addition or Subtraction Problems • Three gases, He, N 2, and Ar are present](http://slidetodoc.com/presentation_image/06dbda923abe2cc658929d9c42fa4e42/image-19.jpg)
Addition or Subtraction Problems • Three gases, He, N 2, and Ar are present in a gas mixture. The partial pressure of He is 360 torr, of N 2 is 400 torr, and of Ar is 250 torr. Find the total pressure. • Ar is added to the above mixture until the total pressure is 1200 torr. Find the new pressure of the Argon.
![Collecting Gas by Water Displacement When the water levels inside and outside the inverted Collecting Gas by Water Displacement When the water levels inside and outside the inverted](http://slidetodoc.com/presentation_image/06dbda923abe2cc658929d9c42fa4e42/image-20.jpg)
Collecting Gas by Water Displacement When the water levels inside and outside the inverted container are the same, the total pressure inside the container above the water is equal to the atomspheric pressure.
![Sometimes gases are collected by water displacement C H (g) + H O(g) 2 Sometimes gases are collected by water displacement C H (g) + H O(g) 2](http://slidetodoc.com/presentation_image/06dbda923abe2cc658929d9c42fa4e42/image-21.jpg)
Sometimes gases are collected by water displacement C H (g) + H O(g) 2 2 2
![Line up the water levels! Line up the water levels!](http://slidetodoc.com/presentation_image/06dbda923abe2cc658929d9c42fa4e42/image-22.jpg)
Line up the water levels!
![Ptot = Pgas + Pwater • The volume of gas collects above the water, Ptot = Pgas + Pwater • The volume of gas collects above the water,](http://slidetodoc.com/presentation_image/06dbda923abe2cc658929d9c42fa4e42/image-23.jpg)
Ptot = Pgas + Pwater • The volume of gas collects above the water, but some of the water molecules evaporate and go into the gas phase as well. • The vapor pressure of water depends only on the temperature. Look it up in a reference table and then subtract it from the total pressure.
![Extension of Dalton’s Law • Since PV = n. RT then • Ptot = Extension of Dalton’s Law • Since PV = n. RT then • Ptot =](http://slidetodoc.com/presentation_image/06dbda923abe2cc658929d9c42fa4e42/image-24.jpg)
Extension of Dalton’s Law • Since PV = n. RT then • Ptot = ntot. RT & for each component, Pi = ni. RT V V Pi = ni. RT/V Ptot ntot. RT/V Which reduces to Pi / Ptot = ni / ntot
![Mole Fraction • ni / ntot is called the mole fraction = I • Mole Fraction • ni / ntot is called the mole fraction = I •](http://slidetodoc.com/presentation_image/06dbda923abe2cc658929d9c42fa4e42/image-25.jpg)
Mole Fraction • ni / ntot is called the mole fraction = I • Pi = (ni / ntot)Ptot
![Effusion gas vacuum Effusion gas vacuum](http://slidetodoc.com/presentation_image/06dbda923abe2cc658929d9c42fa4e42/image-26.jpg)
Effusion gas vacuum
![Effusion • Process where molecules of a gas confined in a container randomly pass Effusion • Process where molecules of a gas confined in a container randomly pass](http://slidetodoc.com/presentation_image/06dbda923abe2cc658929d9c42fa4e42/image-27.jpg)
Effusion • Process where molecules of a gas confined in a container randomly pass through a tiny opening in the container. • Rates of effusion can be used to determine the molar mass of a gas. • Kinetic energy of molecules in a gas depends only on temperature and equals ½ mv 2.
![Effusion Two gases at the same T have the same average KE: ½ M Effusion Two gases at the same T have the same average KE: ½ M](http://slidetodoc.com/presentation_image/06dbda923abe2cc658929d9c42fa4e42/image-28.jpg)
Effusion Two gases at the same T have the same average KE: ½ M 1 V 1 2 = ½ M 2 V 2 2 V 12 = M 2 V 22 M 1 Note: This V is the velocity of the molecules, NOT the volume of the container.
![Effusion Two gases at the same T have the same average KE: ½ M Effusion Two gases at the same T have the same average KE: ½ M](http://slidetodoc.com/presentation_image/06dbda923abe2cc658929d9c42fa4e42/image-29.jpg)
Effusion Two gases at the same T have the same average KE: ½ M 1 V 1 2 = ½ M 2 V 2 2
![Graham’s Law of Effusion • The rates of effusion of gases at the same Graham’s Law of Effusion • The rates of effusion of gases at the same](http://slidetodoc.com/presentation_image/06dbda923abe2cc658929d9c42fa4e42/image-30.jpg)
Graham’s Law of Effusion • The rates of effusion of gases at the same pressure and temperature are inversely proportional to the square roots of their molar masses. • The heavier gases move more slowly.
![Effusion • Recall: the faster you are going, the less time it takes you Effusion • Recall: the faster you are going, the less time it takes you](http://slidetodoc.com/presentation_image/06dbda923abe2cc658929d9c42fa4e42/image-31.jpg)
Effusion • Recall: the faster you are going, the less time it takes you to get somewhere.
![Diffusion • Gradual mixing of two or more molecules due to their spontaneous, random Diffusion • Gradual mixing of two or more molecules due to their spontaneous, random](http://slidetodoc.com/presentation_image/06dbda923abe2cc658929d9c42fa4e42/image-32.jpg)
Diffusion • Gradual mixing of two or more molecules due to their spontaneous, random motion. Gases are in constant, random motion and tend to move from regions of higher concentration to regions of lower concentration.
![Diffusion Diffusion](http://slidetodoc.com/presentation_image/06dbda923abe2cc658929d9c42fa4e42/image-33.jpg)
Diffusion
![Molecular speed and Temperature Molecular speed and Temperature](http://slidetodoc.com/presentation_image/06dbda923abe2cc658929d9c42fa4e42/image-34.jpg)
Molecular speed and Temperature
![Molecular speed and mass Molecular speed and mass](http://slidetodoc.com/presentation_image/06dbda923abe2cc658929d9c42fa4e42/image-35.jpg)
Molecular speed and mass
- Slides: 35