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The Gas Laws

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Pressure Force per unit area. Gas molecules fill container. Molecules move around and hit sides. Collisions are the force. Container has the area. Measured with a barometer.

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

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Units of pressure 1 atmosphere = 760 mm Hg 1 mm Hg = 1 torr 1 atm = 101,235 Pascals = kPa Can make conversion factors from these.

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What is 724 mm Hg in torr? torr torr torr 4.73,359 torr

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What is 724 mm Hg in kPa? kPa kPa kPa 4.73,359 kPa

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What is 724 mm Hg in atm? atm atm atm 4.73,359 atm

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The Gas Laws Boyles Law Pressure and volume are inversely related at constant temperature. PV= k As one goes up, the other goes down. P 1 V 1 = P 2 V 2 Graphically

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V P (at constant T)

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

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Examples 20.5 L of nitrogen at 25ºC and 742 torr are compressed to 9.8 atm at constant T. What is the new volume? L L L

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30.6 mL of carbon dioxide at 740 torr is expanded at constant temperature to 750 mL. What is the final pressure in kPa? kPa kPa kPa kPa

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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) V 1 = V 2 T 1 = T 2 Graphically

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V (L) T (ºC) He H2OH2O CH 4 H2H ºC

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Examples What would the final volume be if 247 mL of gas at 22ºC is heated to 98ºC, if the pressure is held constant? mL mL mL

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At what temperature would 40.5 L of gas at 23.4ºC have a volume of 81.0 L at constant pressure? K C K

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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) V 1 = V 2 n 1 = n 2

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Gay- Lussac Law At constant volume, pressure and absolute temperature are directly related. P = k T P 1 = P 2 T 1 = T 2

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Combined Gas Law If the moles of gas remains constant, use this formula and cancel out the other things that dont change. P 1 V 1 = P 2 V 2. T 1 T 2

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Ideal Gas Law PV = nRT V = L at 1 atm, 0ºC, n = 1 mole, what is R? R is the ideal gas constant. R = L atm/ mol K Tells you about a gas is NOW. The other laws tell you about a gas when it changes.

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Ideal Gas Law A hypothetical substance - the ideal gas 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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Example A 47.3 L container containing 1.62 mol of He is heated until the pressure reaches 1.85 atm. What is the temperature? K K K

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Gas Density and Molar Mass D = mass/Volume Let MMstand for molar mass MM = mass/n n= PV/RT PV = mass RT MM

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Example What is the density of ammonia at 23ºC and 735 torr? g/L g/L g/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 L. If not at STP, use the ideal gas law to calculate moles of reactant or volume of product.

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