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**How do gases behave under different conditions?**

Unit 9 – The Gas Laws How do gases behave under different conditions?

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Essential Question What are the properties and behavior of gases under different conditions such as pressure, volume and temperature?

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States of Matter Gas Particles Liquid Particles Solid Particles

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**Properties of Gases An important property of gases is Compressibility**

Measure of how much the volume of matter decreases under pressure Why are gases so compressible? Large spaces between particles

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**Kinetic Molecular Theory**

Explains why ideal gases behave the way they do Assumptions that simplify the theory, but don’t work in real gases: The particles are so small we can ignore their volume The particles are in constant motion and their collisions cause pressure.

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**Kinetic Molecular Theory**

The particles do not affect each other, neither attracting or repelling. The average kinetic energy is proportional to the Kelvin temperature. The molecules move in a straight path All collisions are elastic We need the formula KE = 1/2 mv2

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**Pressure Force per unit area Factors Affecting Pressure Amount of gas**

More particles – more pressure Volume More volume – less pressure Temperature Higher temperature – more pressure

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**What causes pressure? Gas molecules fill container**

Molecules move around and hit sides Collisions are the force Container is the area

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**Barometer Vacuum 760 mm Hg 1 atm Pressure Measures air pressure**

The pressure of the atmosphere at sea level will hold a column of mercury 760 mm Hg. 1 atm = 760 mm Hg 760 mm Hg 1 atm Pressure

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**Manometer h Gas Column of mercury to measure pressure of a gas**

One end has gas, the other is open h is how much lower the pressure of the gas is than atmosphere h Gas

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Manometer h is how much higher the gas pressure is than the atmosphere. h Gas

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Reading a Manometer

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**Units of pressure 1 atmosphere = 760 mm Hg 1 mm Hg = 1 torr**

1 atm = 101,325 Pascals = kPa Occasionally, we must convert between these Examples: What is 724 mmHg in torr? in atm? in kPa? 724 torr 0.953 atm 96.5 kPa

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**Summary of Units of Pressure**

Abbreviation Unit Equivalent to 1 atm Atmosphere Atm 1 atm Millimeters of Hg mm Hg 760 mm Hg Torr 760 torr Pascal Pa 101,325 Pa Kilopascal kPa 101.3 kPa

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The Gas Laws There are several laws we use to quantify the behavior of gases The laws describe some combination of changes in pressure (P), volume (V), moles/amount of gas (n),or temperature (T) Standard Temperature and Pressure (STP) 0ºC and 1 atm 1 mole of gas occupies 22.4 L BE CAREFUL!! Units are vital to solving these problems Temperature must ALWAYS be in KELVIN

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Boyle’s Law Pressure and volume are inversely related at constant temperature PV= k, where k is a constant As one goes up, the other goes down P1V1 = P2 V2

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Boyle’s Law

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V P (at constant T)

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Slope = k V 1/P (at constant T)

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22.41 L atm O2 PV CO2 P (at constant T)

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Boyle’s Law Examples Given the volume of gas as 200.mL at 1.05atm pressure, calculate the volume of the same gas at 1.01atm. 208mL 30.6 mL of carbon dioxide at 740 torr is expanded at constant temperature to 750 mL. What is the final pressure in kPa? 4.0kPa 20.5 L of nitrogen at 25ºC and 742 torr are compressed to 9.8 atm at constant T. What is the new volume? 2.0L

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Charles’ Law Volume of a gas varies directly with the absolute temperature at constant pressure. V = kT (if T is in Kelvin) One goes up, the other goes up V1 = V2 T T2

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He CH4 H2O V (L) H2 ºC T (ºC)

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Charles’ Law Examples What would the final volume be if 247 mL of gas at 22ºC is heated to 98ºC , if the pressure is held constant? 311mL At what temperature would 40.5 L of gas at 23.4ºC have a volume of L at constant pressure? 593K or 320ºC

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Gay-Lussac’s Law At constant volume, pressure and absolute temperature are directly related. P = k T One goes up, the other goes up P1 = P2 T T2

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Gay-Lussac’s Law

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Gay-Lussac’s Law

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**Gay–Lussac’s Law Examples**

A steel tank contains a gas at 27.0°C and a pressure of 12.0atm. Determine the gas pressure when the tank is heated to 100.°C. 14.9 atm At 120°C, the pressure of a sample of nitrogen is 1.07atm. What will the pressure be at 205°C, assuming constant volume? 1.30 atm

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Avogadro's Law At constant temperature and pressure, the volume of gas is directly related to the number of moles. V = k n (n is the number of moles) V1 = V2 n n2

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**Combined Gas Law P1 V1 = P2 V2 . T1 T2**

Combines Boyles’, Charles’ and Gay-Lussac’s laws Describes the relationship between pressure, temperature, and volume If the moles of gas remains constant, use this formula and cancel out the other things that don’t change P1 V1 = P2 V T T2

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Examples A sample of gas has a volume of 4.18 L at 29ºC and 732 torr. What would its volume be at 24.8ºC and 756 torr? 3.99L 5.00L of air at a temperature of -50ºC has a pressure of 107kPa. What is its pressure if the temperature is raised to 102ºC and its volume to 7.00L 129kPa The volume of a gas-filled balloon is 30.0 L at 313 K and 153 kPa pressure.What would the volume be at standard temperature and pressure (STP)? 39.5 L

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**Ideal Gas Law PV = nRT An Equation of state An Empirical Equation**

Independent of how you end up where you are at Does not depend on the path An Empirical Equation Based on experimental evidence Tells you about current state of gas The other laws tell you about a gas when it changes Given 3 factors you can determine the fourth

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**Ideal Gas Law PV = nRT R is the ideal gas constant**

V = L at P = 1 atm, T = 0ºC, n = 1 mole What is R? R = (L·atm)/(mol·K) With different units: R = 8.31 (L·kPa)/(mol·K)

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**Ideal Gas Law Ideal gases are hypothetical substances**

Think of it as a limit Gases only approach ideal behavior at low pressure (< 1 atm) and high temperature Use the laws anyway, unless told to do otherwise They give good estimates

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Ideal Gas Law

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Examples A 47.3 L container containing 1.62 mol of He is heated until the pressure reaches 1.85 atm. What is the temperature? 658K Kr gas in a 18.5 L cylinder exerts a pressure of atm at 24.8ºC What is the mass of Kr? 546g Kr

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Real Gases Real gas particles have volume and there are attractions between the particles (especially polar molecules) A real gas behaves ideally at low pressure and high temperature. Under conditions of high pressures and low temperatures, deviations from the expected results of the ideal gas law will occur. Need to add correction factors to the ideal gas law to account for these.

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**Gas Density and Molar Mass**

D = m/V Let M stand for molar mass M = m/n n= PV/RT M = m PV/RT M = mRT = mRT = DRT PV VP P

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Gas Density Example What is the density of ammonia at 23ºC and 735 torr? M = DRT P D = MP / RT D = (17.04g/mol)(735torr/760 torr/atm) ( (L·atm)/(mol·K)(296K) D = 0.678g/L

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**Gases and Stoichiometry**

Reactions happen in moles At Standard Temperature and Pressure (STP), 0ºC and 1 atm 1 mole of gas occupies 22.4 L If not at STP, use the ideal gas law to calculate moles of reactant or volume of product.

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**4NH3(g) + 5O2(g) ® 4NO(g) +6H2O(g)**

Examples Consider the following reaction: 4NH3(g) + 5O2(g) ® 4NO(g) +6H2O(g) What volume of NO at STP will be produced from 23.7L of NH3? 23.7L What volume of O2 measured at STP will be consumed when 10.0L NH3 is reacted? 12.5L

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**Examples Mercury can be produced by the following reaction:**

2HgO ® 2Hg +O2 What volume of oxygen gas can be produced from 4.10 g of mercury (II) oxide at STP? 0.229L At 400.ºC and 740 torr? 0.580L

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**NaHCO3(s)+ HCl(aq)® NaCl(aq) +CO2(g)+H2O(l)**

Examples Using the following reaction: NaHCO3(s)+ HCl(aq)® NaCl(aq) +CO2(g)+H2O(l) Calculate the mass of sodium hydrogen carbonate necessary to produce 2.87 L of carbon dioxide at 25ºC and 2.00 atm 19.7g NaHCO3

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Dalton’s Law The total pressure in a container is the sum of the pressure each gas would exert if it were alone in the container. The total pressure is the sum of the partial pressures. PTotal = P1 + P2 + P3 + P4 + P5 ... For each P = nRT/V

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**Dalton's Law PTotal = n1RT + n2RT + n3RT +... V V V**

In the same container R, T and V are the same. PTotal = (n1+ n2 + n3+...)RT V PTotal = (nTotal)RT V

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**Dalton’s Law of Partial Pressure**

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Dalton’s Law Examples Air contains oxygen, nitrogen, carbon dioxide, and trace amounts of other gases. What is the partial pressure of oxygen at kPa of total pressure if the partial pressures of nitrogen, carbon dioxide,and other gases are kPa, kPa, and kPa, respectively? 21.22kPa

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**The mole fraction Ratio of moles of the substance to the total moles.**

Symbol is Greek letter chi c c1 = n1 = P nTotal PTotal

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Examples The partial pressure of nitrogen in air is 592 torr. Air pressure is 752 torr, what is the mole fraction of nitrogen? 0.787 What is the partial pressure of nitrogen if the container holding the air is compressed to atm? 4.13 atm

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**Examples 4.00 L CH4 1.50 L N2 3.50 L O2 0.752 atm 2.70 atm 4.58 atm**

When these valves are opened, what is each partial pressure and the total pressure?

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**Vapor Pressure Water evaporates!**

When that water evaporates, the vapor has a pressure. Gases are often collected over water so the vapor. pressure of water must be subtracted from the total pressure. It must be given.

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**Example N2O can be produced by the following reaction**

what volume of N2O collected over water at a total pressure of 94 kPa and 22ºC can be produced from 2.6 g of NH4NO3? ( the vapor pressure of water at 22ºC is 21 torr)

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**Effusion Passage of gas through a small hole, into a vacuum.**

The effusion rate measures how fast this happens. Graham’s Law the rate of effusion is inversely proportional to the square root of the mass of its particles.

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**Diffusion The spreading of a gas through a room.**

Slow considering molecules move at 100’s of meters per second. Collisions with other molecules slow down diffusions. Best estimate is Graham’s Law.

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