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GASES

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General Properties of Gases There is a lot of “free” space in a gas. Gases can be expanded infinitely. Gases fill containers uniformly and completely. Gases diffuse and mix rapidly.

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Properties of Gases Gas properties can be modeled using math. Model depends on— V = volume of the gas (L, mL) T = temperature (K) ALL temperatures in the entire chapter MUST be in Kelvin!!! No Exceptions! n = amount (moles) P = pressure (atmospheres, mmHg, torr, kPa)

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Pressure Column height measures Pressure of atmosphere 1 standard atmosphere (atm) * = 760 mm Hg (or torr) * = 101.3 kPa (SI unit is PASCAL)

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Pressure conversions A.) What is 475 mm Hg expressed in atm? 475 mmHg 1 atm = 0.625 atm 760 mm Hg B.) The pressure of a tire is measured as 29.4 psi. What is this pressure in mm Hg? 29.4 psi 760 mmHg = 1.52 x 10 3 mmHg 14.7 psi

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Your Turn: Learning Check for Pressure Conversions A.) What is 2 atm expressed in torr? B.) The pressure of a tire is measured as 32.0 psi. What is this pressure in kPa?

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Boyle’s Law This means Pressure and Volume are INVERSELY PROPORTIONAL if moles and temperature are constant (do not change). For example, P goes up as V goes down. P1V1 = P2 V2 V1 is the original volume V2 is the new volume P1 is original pressure P2 is the new pressure Sample Problem Suppose you have a gas with 45.0 ml of volume and has a pressure of 760.mmHg. If the pressure is increased to 800mmHg and the temperature remains constant then according to Boyle's Law the new volume is 42.8 ml. (760mmHg)(45.0ml) = (800mmHg)(V2) V2 = 42.8ml Robert Boyle

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Charles’s Law V and T are directly proportional. If one temperature goes up, the volume goes up! V1 V2 T1 = T2 V1 is the initial volume T1 is the initial temperature V2 is the final volume T2 is the final temperature Sample Problem You have a gas that has a volume of 2.5 liters and a temperature of 250 K. What would be the final temperature if the gas has a volume of 4.5 liters? V1 / T1 = V2 / T2 V1 = 2.5 liters T1 = 250 K V2 = 4.5 liters T2 = ? Solving for T2, the final temperature equals 450 K. Important: Charles's Law only works when the pressure is constant. Note: Charles's Law is fairly accurate but gases tend to deviate from it at very high and low pressures. Jacques Charles

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Gay-Lussac’s Law If n and V are constant, then P α T P and T are directly proportional. P1 P2 T1 T2 If one temperature goes up, the pressure goes up! Sample problem The pressure inside a container is 770 mmHg at a temperature of 57 C. What would the pressure be at 75 C? P1= 770 mmHg T1 = 57°C T2= 75°C P2 = ? =

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Combined Gas Law Since they are all related to each other, we can combine them into a single equation. BE SURE YOU KNOW THIS EQUATION! P1 V1 P2 V2 T1 T2 =

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Combined Gas Law Problem A sample of helium gas has a volume of 0.180 L, a pressure of 0.800 atm and a temperature of 29°C. What is the new temperature(°C) of the gas at a volume of 90.0 mL and a pressure of 3.20 atm? Set up Data Table P1 = 0.800 atm V1 = 180 mL T1 = 302 K P2 = 3.20 atm V2= 90 mL T2 = ??

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Calculations P1 = 0.800 atm V1 = 180 mL T1 = 302 K P2 = 3.20 atm V2= 90 mL T2 = ?? P1 V1 P2 V2 T1 = T2P1 V1 T2 = P2 V2 T1 T2 = P2 V2 T1 P1 V1 T2 = 3.20 atm x 90.0 mL x 302 K 0.800 atm x 180.0 mL T2 = 604 K - 273 = 331 °C

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