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Gas Laws

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Gas Pressure Just means that gas is pushing on something.

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Gas Pressure Tire Whats going on inside? Air: Nitrogen 78% Oxygen 21% Argon ~1% Carbon Dioxide <1% Each of these particles are constantly flying around. Like a lotto ball! They slam against the container and keep the tire full. The particles press against the walls.

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Measuring Gas Pressure Air: Nitrogen 78% Oxygen 21% Argon ~1% Carbon Dioxide <1% Think of a giant ball pit miles and miles up. At the bottom of the ball pit, is like us walking around. Thats the atmospheric pressure.

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Measuring Gas Pressure U-Tube Cant use it to measure atmospheric pressure, because atmospheric pressure presses on everything equally. Vacuum So how do we measure it? Vacuum It pushes down on this side, and it moves up on the other side.

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Measuring Gas Pressure Vacuum We can measure that! Take a ruler and measure low to high in milimeters! The fluid that is contained in this U tube, is mercury. If we measure this at sea level, we get. 760mmHg between the bottom and the top. 760 mmHg

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Measuring Gas Pressure What if we go up a mountain or down into a mine? Think about that ball pit again. If youre at the bottom of the ball pit will it weigh more or less than at the top? Sea Level More Pressure 760mmHgLess Pressure

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Measuring Gas Pressure of Containers 800 mmHg 40 mmHg What if I snap off the vacuum bulb? Because atmospheric pressure is pushing down! 760 mmHg

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Measuring Gas Pressure BarometerManometer

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Gas Pressure Conversions How do we measure things? Lots of ways! Same goes with gas pressure. Gas Pressure Units mmHgatmospherekilopascal Torr atmkPa Conversions 760 mmHg = 1 atm = 101.3kpa

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Gas Pressure Conversions The pressure inside a car tire is 225 kPa. Express this value in both atm and mmHg. 760 mmHg = 1 atm = 101.3 kPa 225 kPa x 1 atm 101.3 kPa =2.22 atm 225 kPa x 760 mmHg 101.3 kPa =1688 mmHg

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Boyles Law If we keep the temperature the same, we can predict what pressure and volume will do.

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Boyles Law Pressure and Volume Gas particles have a bunch of room. Gas particles are squeezed into smaller space. What about volume? V=High V=Low As pressure goes up, volume goes down. That means inverse relationship. P= Low P=High

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Boyles Teeter Totter When volume is high, pressure is low When the volume is low, pressure is high An Inverse relationship. Pressure Volume

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Boyles Law Boyles law is explained by the equation P 1 V 1 =P 2 V 2 Lets get right to it! At 1.70 atm, a sample of gas takes up 4.35 L. If the pressure on the gas is increased to 2.40 atm, what will the new volume be? P 1 V 1 = P 2 V 2 (before) (after) What do you know? P 1 (before pressure) = V 1 (before volume)= P 2 (after pressure) = V 2 = ?? (1.70 atm)(4.35L)=(2.40 atm)V 2 7.40atm/L = (2.40atm)V 2 V 2 =3.01L 1.70 atm 4.35 L 2.4 atm

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Boyles Law Does that answer make sense? At 1.70 atm, a sample of gas takes up 4.35 L. If the pressure on the gas is increased to 2.40 atm, what will the new volume be? We increased the pressure, so we pushed down that piston. We squeezed the molecules into a smaller space. So the volume should go down!

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Boyles Law If I have 5.6 liters of gas in a piston at a pressure of 1.5 atm and compress the gas until its volume is 4.8 L, what will the new pressure inside the piston be? P 1 V 1 = P 2 V 2 (before) (after) P 1 (before pressure) = V 1 (before volume)= P 2 (after pressure) = V 2 = (1.5atm)(5.6L) = (P 2 )(4.8L) 8.4 atm/L = (4.8L)P 2 1.8 atm = P 2 1.5 atm 5.6 L ? 4.8L

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Charles Law Charles law relates volume and temperature, while keeping pressure the same V 1 = V 2 T 1 T 2

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Charles Law How could we test the theory that temperature and volume are related? Think about kinetic theory and molecules.

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Charles Law HOT COLD T= HighT = Low V= High V = Low Charles law says that as the temp increases, so does volume. A direct relationship. Whats going on with the temp?

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Charles Law So now we can relate volume and temperature. V 1 = V 2 T 1 T 2 MUST ALWAYS USE KELVIN TEMPERATURE in gas laws A balloon takes up 625 L at 0°C. If it is heated to 80°C, what will its new volume be? Must convert to Kelvin. 0 °C + 273 = 273K 80 °C + 273 = 353K 625 L 0 °C ?? V 1 = T 1 = T 2 = V 2 = 80 °C

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Charles Law V 1 = V 2 T 1 T 2 A balloon takes up 625 L at 0°C. If it is heated to 80°C, what will its new volume be? V 1 = 625 L T 1 = 273K T 2 = 353K V 2 = ??L 625L = V 2 273K 353K 2.29L/K= V 2 353K 808L = V 2

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Charles Law At 27.00 °C a gas has a volume of 6.00 L. What will the volume be at 150.0 °C? Whats the equation? V 1 = V 2 T 1 T 2 V1=V1= T1=T1= V2=V2= T2=T2= 6.00 L 27 °C ?? 150.0 °C Must convert to Kelvin. 27 °C + 273 = 300K 150°C + 273 = 423K

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Charles Law At 27.00 °C a gas has a volume of 6.00 L. What will the volume be at 150.0 °C? V 1 = V 2 T 1 T 2 V1=V1= T1=T1= V2=V2= T2=T2= 6.00 L ?? 300K 423K 6.00L = V 2 300K 423K 0.02L/K = V 2 423K 8.46L = V 2

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Avogadros Law Relationship between: Amount of gas (n) and the Volume. What happens to one, when I change the other? I start with the first balloon, and then blow more air into it…will the volume increase? Yes, a direct relationship

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Avogadros Law As the amount (in moles) goes up, so does the volume. If we double the amount, it doubles the volume.

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Avogadros Law We only changed TWO things. The volume and the amount of particles. We didnt mess with the pressure or the temperature, they were held constant. V 1 = V 2 n 1 n 2

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Avogadros Law V 1 = V 2 n 1 n 2 Lets try! In a sample of gas, 50.0 g of oxygen gas (O 2 ) take up 48L of volume. Keeping the pressure constant, the amount of gas is changed until the volume is 79 L. How many mols of gas are now in the container? n 1 =n 2 = V 1 = V 2 = When doing Avogadro's law, n MUST be in moles! 50g 40L mol? 79L

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Avogadros Law V 1 = V 2 n 1 n 2 BeforeAfter n 1 =50gn 2 = g? V 1 = 48LV 2 = 79L When doing Avogadro's law, n MUST be in moles! 50g O 2 x 1 mol O 2 32g O 2 = 1.6 mol O 2 1.6mol 1.6 mol O 2 48L = n 2 79L 0.03 = n 2 79L 2.6 mol = n 2

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Gay-Lussacs Law The pressure and Kelvin temperature of a gas are directly proportional, when the volume remains constant.

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Gay Lussacs Law This law only applies to gases held at a constant volume. Only the pressure and temperature will change.volumepressuretemperature P 1 = P 2 T 1 T 2 P i =initial pressure P f = final pressure T i = initial temperature (kelvin) T f = final temperature (kelvin) The pressure in a sealed can of gas is 235 kPa when it sits at room temperature (20C). If the can is warmed to 48C, what will the new pressure inside the can be?

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Gay Lussacs Law The pressure in a sealed can of gas is 235 kPa when it sits at room temperature (20°C). If the can is warmed to 48°C, what will the new pressure inside the can be? P 1 = P 2 T 1 T 2 Must convert to Kelvin 20°C + 273 = 293K 48°C + 273 = 321K P 1 = P 2 = T 1 = T 2 = 235 kPa ? 20°C 48°C

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235 293 = P f 321 0.80 = P f 321 257.5 kPa = P f P 1 = P 2 = T 1 = T 2 = 235 kPa ? The pressure in a sealed can of gas is 235 kPa when it sits at room temperature (20°C). If the can is warmed to 48°C, what will the new pressure inside the can be? P 1 = P 2 T 1 T 2 293K 321K

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How to use these formulas Charles Law V 1 = V 2 T 1 T 2 Avogadros Law V 1 = V 2 n 1 n 2 Gay Lussacs Law P 1 = P 2 T 1 T 2 They are all pretty much the same equation, just different variables!

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Combined Gas Law Charles Law V 1 = V 2 T 1 T 2 Boyles Law (P 1 )(V 1 ) = (P 2 )(V 2 ) Gay Lussacs Law P 1 = P 2 T 1 T 2 What if I had a balloon. I wanted to increase the pressure and cool it down. What is the volume? Do we have an equation for that? P, T, V. We can combine the laws! Combined Gas Law (P 1 )(V 1 ) = (P 2 )(V 2 ) T 1 T 2

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Combined Gas Law A 40.0L balloon is filled with air at sea level (1.00 atm, 25.0 °C). It's tied to a rock and thrown in a a cold body of water, and it sinks to the point where the temperature is 4.0 ° C and the pressure is 11.00 atm. What will its new volume be? (P 1 )(V 1 ) = (P 2 )(V 2 ) T 1 T 2 Convert to Kelvin 25°C + 273 = 298K 4°C + 273 = 277K P 1 = 1 atm P 2 = 11 atm V 1 = 40 L V 2 = ?? T 1 = 298K T 2 = 277K (1)(40) = (11)(V 2 ) 298K277K 0.13 = (11)(V 2 ) 277K 36.01 = (11)(V 2 ) 3.27 L = V 2 P 1 = P 2 = V 1 = V 2 = T 1 = T 2 = 1 atm 11 atm 40 L ?? 25°C 4°C

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Ideal Gas Law How can we describe whats going on in this container? What variables can we think of? Temperature (T) 313K Pressure (P) 3.18 atm Volume (V)95.2 L Amount of Gas (n)7.5 mol Did you know that if we know 3 of the 4 variables, we can find the last one?

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Ideal Gas Law Ideal gas law: PV = nRT Temperature (T) 313K Pressure (P) Volume (V) 95.2 L Amount of Gas (n)7.5 mol How would we rearrange the problem to find P? ?? P = nRT V What if we needed the amount of gas (n)? 3.18 atm ?? PV = n RT

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Ideal Gas Law PV = nRT So what is R? R is a constant! For most cases, R = 0.0821 L atm/mol K Those units look familiar. V = L P = atm T = K n = mol The units on R MUST match the units in the problem!

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Ideal Gas Law R will come in many forms. R = 62.4 LmmHg /K mol R = 8.31 LkPa /K mol NOT A BIG DEAL! The R constant will always be given, just use the right constant.

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Ideal Gas Law 2.3 moles of Helium gas are at a pressure of 1.70 atm, and the temperature is 41°C. What is volume of the gas? PV = nRT P = V = n = R = T = 0.0821 Latm/K mol 1.70 atm ?? 2.3 mol 41°C Convert to Kelvin 41°C + 273 = 314K

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Ideal Gas Law PV = nRT P = V = n = R = T = 0.0821 Latm/K mol 1.70 atm ?? 2.3 mol 314K 2.3 moles of Helium gas are at a pressure of 1.70 atm, and the temperature is 41°C. What is volume of the gas? Rearrange the equation. V = nRT P V = (2.3 mol)(314K) x 0.0821 L atm 1.70 atm K mol V = 59.3 1.7 V = 34.9 L

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Ideal Gas Law At a certain temperature, 3.24 moles of CO2 gas at 2.15 atm takes up a volume of 35.28 L. What is this temperature (in Celsius)? P = V = T = n = R = 2.15 atm 35.28 L ?? 3.24 mol 0.0821 Latm/K mol Do the units given match the R?

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Ideal Gas Law V = T = n = R = 2.15 atm 35.28 L ?? 3.24 mol 0.0821 Latm/K mol At a certain temperature, 3.24 moles of CO2 gas at 2.15 atm takes up a volume of 35.28 L. What is this temperature (in Celsius)? P = PV = nRT Rearrange the equation. T = PV nR T = (2.15 atm)(35.28L) X K mol (3.24 mol) 0.0821 L atm

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Ideal Gas Law Charles Law V 1 = V 2 T 1 T 2 Avogadros Law V 1 = V 2 n 1 n 2 Gay Lussacs Law P 1 = P 2 T 1 T 2 Who wants to memorize all of these?!?! Ideal Gas Law PV = nRT Combined Law (P 1 )(V 1 ) = (P 2 )(V 2 ) T 1 T 2 You dont have to!

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Gas Law Just memorize one! Ideal Gas Law PV = nRT Can use it for any of the gas law problems! Warning: If this blows your mind and you get totally confused, just memorize the equations.

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Gas Law BeforeAfter P 1 = 3 atmP 2 = 7atm T 1 = ??T 2 = 150k Rearrange the ideal equation so that the variables given are on the same side PV =nRT V P = nRT T VT P= nR T V Youve found the equation you need to use. You dont need n, R, or V. P 1 = P 2 T 1 T 2

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Gas Law P 1 = 1,217 mmHg P 2 = 732 mmHg V 1 = ?? V 2 = 42L PV = nRT Rearrange the equation so the variables youre looking for are on the same side of the equation. Easy! PV is already on the same side. Now just double it. P 1 V 1 = P 2 V 2

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Gas Law V 1 = 7.5L V 2 = 1.2L n 1 = 32 mol n 2 = ? PV = nRT Rearrange the equation so V and n are on the same side. PV = nRT P P V = nRT P V = nRT n Pn V 1 = V 2 n 1 n 2

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Gas Law BeforeAfter V 1 = ?V 2 = 54L P 1 = 96 kPaP 2 = 112 kPa T 1 = 12KT 2 = 42K PV = nRT Rearrange so V, T, P are on same side. PV = nRT T T P 1 V 1 = P 2 V 2 T 1 T 2

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