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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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Vacuum Barometer 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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**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? 724 torr 96.5 torr 0.953 torr 73,359 torr

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What is 724 mm Hg in kPa? 724 kPa 96.5 kPa 0.953 kPa 73,359 kPa

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What is 724 mm Hg in atm? 724 atm 96.5 atm 0.953 atm 73,359 atm

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**The Gas Laws Boyle’s Law**

Pressure and volume are inversely related at constant temperature. PV= k As one goes up, the other goes down. P1V1 = P2 V2 Graphically

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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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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? 2.04 L .264 L .467 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? 30.2 kPa .0397 kPa 4.025 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) V1 = V T1 = T2 Graphically

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He CH4 H2O V (L) H2 ºC T (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? 1100 mL 196 mL 311 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?**

592.8 K C 319.8 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) V1 = V n1 = n2

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Gay- Lussac Law At constant volume, pressure and absolute temperature are directly related. P = k T P1 = P T1 = T2

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

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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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? 316 K 658 K 27.1 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? 0.676 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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