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Boyle’s law Volume of a gas is inversely proportional to the pressure on a gas. Volume of a gas is inversely proportional to the pressure on a gas. V 1/P V 1/P Therefore VP = k (some constant for each gas) Therefore VP = k (some constant for each gas) V i P i = V f P f V i P i = V f P f i is initial f is final i is initial f is final

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Boyle’s Law If you have 145 mL of a gas at 67 kPa. What volume will it occupy at 127 kPa? If you have 145 mL of a gas at 67 kPa. What volume will it occupy at 127 kPa? VP = VP VP = VP 145 mL (67kPa) = V (127 kPa) 145 mL (67kPa) = V (127 kPa) V = 76 mL V = 76 mL

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You can see Boyle’s Law If you fill a cup with water under the water level, turn it upside down and pick it up. If you fill a cup with water under the water level, turn it upside down and pick it up. This will (attempt to) increase the volume inside the cup. This will (attempt to) increase the volume inside the cup. Which will decrease the pressure. Which will decrease the pressure. The outside pressure will push in allowing you to pick up the water against gravity. The outside pressure will push in allowing you to pick up the water against gravity. as long as you don’t raise the cup over the water line as long as you don’t raise the cup over the water line

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Water in a cup Water Cup (with a little bit of air in it) Gravity wants to pull the water in the cup down. However if it fell it would leave a big space of nothing (vacuum) Air pressure pushes to stop the vacuum from forming by pushing on the surface of the liquid. Not allowing the water level to rise. The water will fall once the air pressure equals the pressure (weight divided by area) of the water being lifted. Which would make the water level rise.

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Barometer Pressure can be measured with a barometer. Pressure can be measured with a barometer. Which works just like the cup but with mercury. Which works just like the cup but with mercury. Mercury Complete vacuum (no air or anything) And you simply measure how high the mercury can be held. This is inches of Hg or mm Hg (torr). This is how pressure is reported on the news There is not an infinite amount of mercury that can be suspended. Only until its pressure equals the outside air pressure. Once it falls a little you can measure it. mm of Hg are also called torr after the inventor of the barometer Evangelista Torricelli

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If it is so dangerous why use mercury? Mercury is very dense, so you don’t need that tall of a tube to make it so it will start to fall. Mercury is very dense, so you don’t need that tall of a tube to make it so it will start to fall. A little smaller than a meter will pretty much always fall a little under normal conditions. A little smaller than a meter will pretty much always fall a little under normal conditions. If you used water it would have to be over 10 m high to get it to fall a little. If you used water it would have to be over 10 m high to get it to fall a little. Standard pressure is 760 torr or 29.9 in Hg Standard pressure is 760 torr or 29.9 in Hg

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Modern Barometers Digital Barometers and barometers with a dial use a sensor on a sealed drum. Digital Barometers and barometers with a dial use a sensor on a sealed drum. The top of the drum is flexible. The top of the drum is flexible. Sealed inside the drum is air at a known (calibrated) pressure. Sealed inside the drum is air at a known (calibrated) pressure. Higher outside pressure caves the drum in. Higher outside pressure caves the drum in. Lower outside pressure bows the drum out. Lower outside pressure bows the drum out.

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High pressure low pressure drum

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High pressure low pressure drum

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High pressure low pressure drum

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Heating things make them expand… and cooling makes them contract. and cooling makes them contract. This is noticeably true with gases. This is noticeably true with gases. This is the Charles’ Law This is the Charles’ Law ~The volume of a gas is directly proportional to the temperature of that gas. ~The volume of a gas is directly proportional to the temperature of that gas. V T; V/T = k V T; V/T = k V i /T i = V f /T f V i /T i = V f /T f

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Charles’ Law If you have 6.7 L of a gas at 298 K, what volume will it occupy at 0 o C? If you have 6.7 L of a gas at 298 K, what volume will it occupy at 0 o C? V/T = V/T V/T = V/T 6.7 L / (298 K) = V / (273 K) 6.7 L / (298 K) = V / (273 K) *Temp must be in Kelvin because zero would make it undefined! *Temp must be in Kelvin because zero would make it undefined! V = 6.1 L V = 6.1 L

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Charles’ Law If you have.731 L of a gas at 318 K, what temperature will it be if it occupies 1.34 L? If you have.731 L of a gas at 318 K, what temperature will it be if it occupies 1.34 L? V/T = V/T V/T = V/T.731 L / (318 K) = 1.34 L / T.731 L / (318 K) = 1.34 L / T *Those who do the math without writing it down first commonly make mistakes. *Those who do the math without writing it down first commonly make mistakes. T = 583 K T = 583 K

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Gay-Lussac’s Law The pressure of a gas is directly proportional to its temperature. The pressure of a gas is directly proportional to its temperature. T/P = T/P T/P = T/P This is why an aerosol can or a tire feels cooler when air is released. This is why an aerosol can or a tire feels cooler when air is released. It is also how a diesel engine ignites the fuel. It compresses it until it ignites. It is also how a diesel engine ignites the fuel. It compresses it until it ignites.

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Refrigeration/Air Conditioning Refrigeration and air conditioning work using these principals. Refrigeration and air conditioning work using these principals. WE CANNOT MAKE COLD AIR!! WE CANNOT MAKE COLD AIR!! We can only separate cold air from hot air. We can only separate cold air from hot air. AC works by compressing air at one point (causing it to heat up) and decompressing at another, causing it to cool down. AC works by compressing air at one point (causing it to heat up) and decompressing at another, causing it to cool down.

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AC refrigerator

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Combined Gas Law This is made by combining Charles’ and Boyle’s Law. This is made by combining Charles’ and Boyle’s Law. V i P i / T i = V f P f / T f V i P i / T i = V f P f / T f Temperature has to be in Kelvin (so it can never be 0) Temperature has to be in Kelvin (so it can never be 0) volume and pressure can be in any unit as long as it is the same on both sides. volume and pressure can be in any unit as long as it is the same on both sides.

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A problem If a gas occupies 34 L at 1.2 atm and 290 K, what volume will it occupy at 1.1 atm and 280 K? If a gas occupies 34 L at 1.2 atm and 290 K, what volume will it occupy at 1.1 atm and 280 K? V i P i / T i = V f P f / T f V i P i / T i = V f P f / T f 34L (1.2atm) / 290 K = V (1.1atm)/280K 34L (1.2atm) / 290 K = V (1.1atm)/280K V = 36 L V = 36 L

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A problem If a gas occupies 24 mL at 115 kPa and 13 o C, what volume will it occupy at 101 kPa and 0 o C? If a gas occupies 24 mL at 115 kPa and 13 o C, what volume will it occupy at 101 kPa and 0 o C? 24 mL (115kPa)/286 K = V (101kPa)/273 K 24 mL (115kPa)/286 K = V (101kPa)/273 K V = 26 mL (don’t forget to convert temp to K) V = 26 mL (don’t forget to convert temp to K)

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