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Behavior of GASES

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Gases are made up of atoms and molecules just like all other compounds, but because they are in the form of a gas we can learn a great deal more about these molecules and compounds. It might seem a bit confusing because we can’t see most gases, but we know they exist.

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**Elements that exist as gases at 250C and 1 atmosphere**

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**I. Let’s look at some of the Nature of Gases:**

1. Expansion – gases do NOT have a definite shape or volume. 2. Fluidity – gas particles glide past one another, called fluid just like a liquid.

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Nature of Gases cont. 3. Compressibility – can be compressed because gases take up mostly empty space. 4. Diffusion – gases spread out and mix without stirring and without a current. Gases mix completely unless they react with each other.

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**Collisions of Gas Particles**

The word KINETIC refers to motion Kinetic energy= energy an object has because of its motion Collisions of Gas Particles

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**Collisions of Gas Particles**

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**II. Kinetic Molecular Theory of Gases**

Particles of matter (any type) are in constant motion! Because we know this we have a few assumptions that we make about gases, called the Molecular Theory of Gases:

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Kinetic theory: 1. Particles of a gas are in constant, straight-line motion, until they collide. They move independently from each other Molecular Motion

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Kinetic theory: 2. Gases consist of a large number of tiny particles (molecules or atoms) ; these particles are very far apart, therefore gas is mostly empty space. There are no forces of attraction or repulsion between particles of gases.

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Kinetic theory: 3. Collisions between particles of a gas and the container wall are elastic. Which means there is no loss of energy. Total Kinetic energy remains constant. elastic collisions inelastic collisions

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Kinetic theory: The average kinetic energy of gas particles depends on the temperature of the gas. (It is directly proportional) KE=1/2 mv2 (m=mass in kg and v=velocity is m/sec) Calories (cal) ..Joules (j) measure Enegy 1 cal= 4.18 J 1Cal = 1000 cal

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**Volume (V) 1. Volume – refers to the space matter (gas) occupies.**

III. Volume, Pressure, Temperature, Number of Moles (Descriptions of Gases) Volume (V) 1. Volume – refers to the space matter (gas) occupies. Measured in liters (L). 1.00 dm3 = 1.00L = 1000 cm3 = 1000mL

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Pressure (P) 2. Pressure(P) – the number of times particles collide with each other and the walls of the container (force exerted on a given area). A vacuum is empty space= It has no pressure Pressure Simulation

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Atmospheric Pressure The gases in the air are exerting a pressure called atmospheric pressure Atmospheric pressure is a result of the fact that air has mass and is colliding with everything under the sun with a force.

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Atmospheric Pressure

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**Atmospheric Pressure Atmospheric pressure varies with altitude**

The lower the altitude, the longer and heavier the column of air above an area of the earth. Check the back of a box of cake mix for the difference in baking times based on the atmospheric pressure in your region.

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Atmospheric Pressure Knowing atmospheric pressure is how forecasters predict the weather. Low pressure or dropping pressure = a change of weather from fair to rain. High pressure = clear skies & sun.

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**Pressure is measured with a device called a barometer**

Pressure is measured with a device called a barometer (They operate on the change of pressure due to the weather)

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Barometer At 1 atm (one atmospheric pressure) a column of mercury 760 mm high. 1 atm Pressure Column of Mercury Dish of Mercury

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**Barometer At 1 atm a column of mercury 760 mm high. 1 atm Pressure**

A 2nd unit of pressure is mm Hg (mercury) atm = 760 mm Hg A 3rd unit & the SI unit is the Pascal (Pa) atm = kPa 1 atm Pressure 760 mm

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**Measured in atmospheres (atm).**

1atm = 760 millimeters Hg (Barometers use Hg) 1atm = 760 torr (Named after Torricelli for the invention of the barometer) 1atm = kPa – kilopascals 1 atm = 760 mm Hg = kPa

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**Practice: Convert 4.40 atm to mmHg.**

Convert 212.4kPa to mmHg.

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Temperature (T) 3. Temperature (T) – as temperature increases gas particles move faster, as temperature decreases gas particles move slower. measured with a thermometer in Celsius. calculations involving gases are made after converting the Celsius to Kelvin temperature. Measured in Kelvin (K). Kelvin = C Celsius = K - 273

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**Practice: Convert 32.0°C to K.**

Convert 400. K to °C.

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**4. Number of Moles – tells you how much of a certain gas you have**

1 mole = number of grams of the compound or element (molar mass) 6.02 x 1023 molecules per mole of the gas. Amount (n)

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**STP – “standard temperature and pressure”. ( Measured at Sea Level)**

Standard Temperature C= 273 K Standard Pressure atm= 760 torr = 760 mmHg = kPa

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**Gas Laws - How do all of pressure, temperature, volume, and amount of a gas relate to each other?**

Combined GAS Law (Initial) (Final) Peas x Vegetables P1 x V1 = P2 x V2 Table T T2

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**Rules for solving gas law problems:**

1st write down what is given and what is unknown, 2nd identify the gas law you want to use, and 3rd rearrange the formula to solve for the unknown and 4th solve the problem. (If temperature is involved, it MUST be converted to Kelvin! K = C)

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**A. Boyle’s Law - Pressure and Volume (when temperature remains constant)**

V1 = initial or old volume V1P1 = V2P2 V2 = final or new volume P1 = initial or old pressure P2 = final or new pressure

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Inverse Relationship (As pressure increases, volume decreases and as pressure decreases, volume increases.) P1 x V1 = P2 x V2 T T2

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**#2 from Boyles Law Problem Sheet**

A sample of carbon dioxide occupies a volume of 3.50 liters at 125 kPa pressure. What pressure would the gas exert if the volume was decreased to 2.00 liters? * P1 x V1 = P2 x V2 P1 = 125 kPa P2 = X V1 = 3.50 L V2 = 2.00 L 125 kPa x 3.50 L = P2 X 2.00L 2.00L L 219 kPa = P2

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**B. Charles’ Law -Volume and Temperature (when pressure is constant)**

V1 = V2 T1 = initial or old temperature T T2 T2 = final or new temperature Direct Relationship (As temperature increases, volume increases and as temperature decreases, volume decreases.)

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**#2 From Charles Law Problem Sheet**

Oxygen gas is at a temperature of 40O C when it occupies a volume of 2.3 liters. To what temperature should it be raised to occupy a volume of 6.5 liters? P1 = P2 = V1 = .3 L V2 = 6.5 L T1 = 40oC = 3l3 K T2 = X V1 = V2 T T2 2.3L = 6.5L 3l3 K T2 12.3 L x T2 = 6.5L X 313K 2.3L L T2 = 880K

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Boyle’s Law Review P1V1 = P2V2

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Boyle’s Law BOYLE's Law in Action

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**How does Pressure and Volume of gases relate graphically?**

PV = k Temperature, # of particles remain constant Pressure

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**Or to the volume if we changed the pressure?**

Boyle’s Mathematical Law: If we have a given amount of a gas at a starting pressure and volume, what would happen to the pressure if we changed the volume? Or to the volume if we changed the pressure? since PV equals a constant P1V1 = P2V2 Ex: A gas has a volume of 3.0 L at 2 atm. What will its volume be at 4 atm?

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**P1V1 = P2V2 Boyle’s Mathematical Law: P1V1 = V2 P2 (2 atm) (3.0 L) =**

List the variables or clues given: P1 = 2 atm V1 = 3.0 L P2 = 4 atm V2 = ? determine which law is being represented: P1V1 = P2V2 P1V1 = V2 P2 3) Plug in the variables & calculate: (2 atm) (3.0 L) = (4 atm) (V2) 1.5 L

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Charles’s Law Review Any relation to Bernet??

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Charles’ Law CHARLES' Law in Action

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**How does Temperature and Volume of gases relate graphically?**

V/T = k Pressure, # of particles remain constant Temp

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**V1 V2 = T1 T2 Charles’s Mathematical Law: since V/T = k**

If we have a given amount of a gas at a starting volume and temperature, what would happen to the volume if we changed the temperature? Or to the temperature if we changed the volume? since V/T = k = V1 V2 T T2 Ex: A gas has a volume of 3.0 L at 400K. What is its volume at 500K?

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**Charles’s Mathematical Law:**

List the variables or clues given: T1 = 400K V1 = 3.0 L T2 = 500K V2 = ? determine which law is being represented: V1 T1 V2 T2 = 3.0L X L = 3) Plug in the variables & calculate: 400K 500K 3.8 L

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**C. Gay-Lussac’s Law - Pressure and Temperature (when volume is constant)**

P1 = P2 T T2 Direct Relationship (As temperature increases, pressure increases and as temperature decreases, pressure decreases.) P1 x T2 = P2 x T1

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**#2 From Gay-Lussac’s Problem Sheet**

A gas has a pressure of atm at 50.0 °C. What is the pressure at standard temperature? (STP =Remember O oC or 273 K) (Change 50.0 °C to Kelvin) P1 = P2 T T2 P1 = atm P2 = atm V1 = V2 = T1 = 40 oC = 323 K T2 = O oC = 273 K 0.370 atm = P2 323 K K P2 = atm

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**D. Combined Gas Law - Pressure, Temperature, and Volume (None of the variables are constant)**

Combined GAS Law (Initial) (Final) Peas x Vegetables P1 x V1 = P2 x V2 Table T T2 P1 x V1 x T2 = P2 x V2 x T1

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**Ex: Find the final volume of 25. 0 ml of a Gas at STP**

Ex: Find the final volume of 25.0 ml of a Gas at STP. If the conditions change to 14 oC and 740 mmHg P1 x V1 = P2 x V2 T T2 P1 = 760 mmHg P2 = 740 mmHg V1 = 25.0mL V2 = ? T1 = 0 oC = 273 K T2 = 14 oC = 287 K (760 mmHg) (25.0 ml) = (740 mmHg) (V2) 273 K K (287K) (69.6 mmHg . ml) = (740 mmHg) (V2) (287K) K K STP Temperature = 273K Pressure =760 mmHg 19974 mmHg.mL = (740 mmHg) (V2) 740 mmHg mmHg 27ml = V2

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Gay-Lussac’s Law P P2 T T2 =

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Gay-Lussac’s Law

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**How does Pressure and Temperature of gases relate graphically?**

P/T = k Volume, # of particles remain constant Temp

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**Or to the temp. if we changed the pressure?**

Gay-Lussac’s Mathematical Law: If we have a given amount of a gas at a starting temperature and pressure, what would happen to the pressure if we changed the temperature? Or to the temp. if we changed the pressure? since P/T = k P P2 T T2 = Ex: A gas has a pressure of 3.0atm at 400K. What is its pressure at 500K?

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**Gay-Lussac’s Mathematical Law:**

List the variables or clues given: T1 = 400K P1 = 3.0 atm T2 = 500K P2 = ? determine which law is being represented: P1 T1 P2 T2 = 3) Plug in the variables & calculate: 3.0atm X L = 400K 500K 3.8 atm

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**Summary of the Named Gas-Laws:**

RELAT-IONSHIP CON-STANTS Boyle’s P V P1V1 = P2V2 T, n Charles’ V T V1/T1 = V2/T2 P, n Gay-Lussac’s P T P1/T1 = P2/T2 V, n

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III. Ideal VS Real Gases Ideal gases always obey the kinetic theory. (Closest to ideal would be the noble gases.) Real gases vary from the kinetic theory at various temperatures and pressures.

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**E. Ideal Gas Law (PV = nRT) – to use this law, all units must be as follows:**

P = pressure in atm V = volume in liters n = number of moles T = temperature in Kelvin R = (0.0821L) (1atm) (1mol) (1K) R is the ideal gas constant (page 342 in book describes where this constant came from.)

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**1f. How many moles of CH4 gas are there in 85.0L at STP?**

2f. What volume will be occupies by 1.50grams of nitrogen monoxide gas at 348K and pressure of 300.mmHg? 3f. A volume of 11.2L of a gas at STP has how many moles?

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**F Daltons Law of Partial Pressures**

The pressure of each gas in a mixture is called the partial pressure of that gas. Daltons Law of Partial Pressure states that the total pressure of a mixture of gases is equal to the sum of the partial pressures of the component gases.

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**PT = P1 + P2 + P3 + ……. PT = total pressure**

P# = the partial pressures of the individual gases

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1e. A mixture of gases has the following partial pressure for the component gases at 20.0C in a volume of 2.00L: oxygen 180.torr, nitrogen 320.torr, and hydrogen 246torr. Calculate the pressure of the mixture. 2e. What is the final pressure of a 1.50L mixture of gases produced from 1.50L of neon at atm, 800.mL of nitrogen at 150.mmHg and 1.2oL of oxygen at 25.3kPa? Assume constant temperature. (Hint use Boyle’s law.)

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**Daltons Law applied to Gases Collected by Water Displacement – Figure 10-15 page 324**

Patm or PT= Pgas + PH2O Patm or PT= barometric pressure or total pressure Pgas = pressure of the gas collected PH2O = vapor pressure of water at specific temperature (Found on page 899 of you textbook.)

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3e. Oxygen gas from the decomposition reaction of potassium chlorate was collected by water displacement at a pressure of 731torr and a temperature of 20.0C. What was the partial pressure of the oxygen gas collected? 4e. Solid magnesium and hydrochloric acid react producing hydrogen gas that was collected over water at a pressure of 759mmHg and measured 19.0mL. The temperature of the solution at which the gas was collected was 25.0C. What would be the pressure of the dry hydrogen gas? What would be the volume of the dry hydrogen gas at STP?

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**G. Solving for Density and /or Molar Mass of a gas using the Ideal Gas Law**

1. Density (units are g/L) Use the Ideal Gas Law to find moles (n), convert n to grams OR use the Ideal Gas Law to find the volume. Divide n (in grams) by the volume.

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1g. What is the density of a sample of ammonia gas, NH3, if the pressure is atm and the temperature is 63.0C? 2g. What is the density of argon gas at a pressure of 551 torr and a temperature of 25.0C?

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2. Molar Mass (units are g/mol) If density is given, use the density of the gas to determine the molar mass (use 1 L at the volume and solve for n). If a mass is given, use the Ideal Gas Law to solve for n and then find the molar mass.

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**3g. The density of a gas was found to be 2. 00g/L at 1. 50atm and 27**

3g. The density of a gas was found to be 2.00g/L at 1.50atm and 27.0C. What is the molar mass of the gas? 4g. What is the molar mass of a gas if 0.427g of the gas occupies a volume of 125mL at 20.0C and 0.980atm?

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H. Molar Volume of Gases Recall that 1 mole of a compound contains X 1023 molecules of that compound – it doesn’t matter what the compound is. One mole of any gas, at STP, will occupy the same volume as one mole of any other gas at the same temperature and pressure, despite any mass differences. The volume occupied by one mole of a gas at STP is known as the standard molar volume of a gas. It has been found to be 22.4liters. We can use this as a new conversion factor 1mol of gas/22.4L of same gas. (Avogadro’s Law states that equal volumes of gases at the same temperature and pressure contain equal numbers of molecules.

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**1h. What volume, in L, is occupied by 32.0 grams of oxygen gas at STP?**

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**I. Stoichiometry of Gases**

Just like mole ratios can be written from an equation so can a volume ratio-same concept! 2CO(g) + O2 (g) 2CO2 (g)

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1i. Using the above equation, what volume of oxygen gas is needed to react completely with 0.626L of carbon monoxide to form carbon dioxide? 2i. How many grams of solid calcium carbonate must be decomposed to produce 5.00L of carbon dioxide gas at STP? 3i. How many liters of hydrogen gas at 35.0C and 0.980atm are needed to produce 8.75L of gaseous water according to the following equation? WO3(s) + 3H2(g) W(s) + 3H2O(g)

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**J. Graham’s Law IV. Effusion and Diffusion**

Graham’s Law states that the rates of diffusion/effusion of gases at the same temperature and pressure are inversely proportional to the square roots of their molar masses. Effusion is the process whereby the molecules of a gas confined in a container randomly pass through a tiny opening in the container. (onions on page 352)

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**Rate of diffusion/effusion of A = √(MB/MA) Rate of diffusion/effusion of B**

MA or B = molar mass of that compound Gas A is the lighter, faster gas Rate of diffusion/effusion is the same as the velocity (or speed) of the gas. After the rates of diffusion/effusion for two gases are determined, the gas with the lower molar mass will be the one diffusing/effusing fastest.

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**1j. Compare the rates of effusion for hydrogen and oxygen at the same temperature and**

pressure. (Which one effuses faster and how much faster is it effusing?) 2j. A sample of hydrogen effuses through a porous container about 9 times faster than an unknown gas. Estimate the molar mass of the unknown gas.

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Graham’s Law and Time Graham’s Law and Time – the time it takes a gas to effuse is directly proportional to its molar mass. tA = MA t = time tB MB

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3j. A sample of an unknown gas flows through the wall of a pours cup in 39.9 minutes. An equal volume of helium (under same temperature and pressure) flows through in 9.75 minutes. What is the molar mass of the unknown gas?

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**Pressure and Volume (Boyle’s Law) Gas Demonstrations**

Bell Jar – Shaving Cream As pressure decreases the volume of the gas increases. Bell Jar – Balloon Bell Jar – Peeps Cartesian Diver

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