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Gas Law Summary Kinetic Molecular Theory 1. Gas particles are in constant, random straight line motion 2. There are no attractive of repulsive forces between molecules 3. Gases are far apart compared with their size 4. Gas particles have elastic collisions with each other and the walls of their container 5. Absolute temperature is a measure of kinetic energy of a gas Conversions Pressure Conversion: 1 atm = 101.325 kPa = 760 mmHg Temperature Conversion: K = °C + 273 Volume Conversion: 1 mL = 1 x 10-­‐3 L At STP 1 mol = 22.4 L Pressure conversions: Temperature Conversions: 134.5 kPa = 1.327 atm 523K = 250 °C 134.5 kPa 1 atm 523K = °C + 273 101.325 kPa 523K – 273 = 250 °C 562 mmHg = 74.9 kPa 321 °C = 594 K 562 mmHg 101.325 kPa 760 mmHg K = 321 °C + 273 K = 594 4.23 atm = 3210 mmHg Volume Conversions: 4.23 atm 760 mmHg 1 atm 4326 mL = 4.326 L 4326 mL 1 x 10-­‐3 L 1 mL Mole Conversion: 3.45 mol = 77.3 L @ STP 23.8 L = 23800 mL 3.45 mol 22.4 L 23.8 L 1 mL 1 mol 1 x 10-­‐3 L Gas Law Summary Equations and Relationships Avogadro’s Law: as moles increase, volume increases . as moles decrease, volume decreases . Boyle’s Law: as pressure decreases , volume increases as pressure increases , volume decreases Charles’ Law as temperature increases, volume increases . as temperature decreases, volume decreases . Ideal Gas Law Equation: PV = nRT R value for kPa: 8.31 LkPa/molK R value for atm: 0.0821 Latm/molK Trick to remember equations: !! !!
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STP: standard temperature (0°C/273 K) and pressure (1 atm) Dalton’s Law Equation: Ptotal = PA + PB + PC….
Gas Law Problems A container consists of 25% oxygen, 25% hydrogen and 50% nitrogen. The total pressure of the container is 60.0 atm. What is the partial pressure of hydrogen in the container? (60.0 atm)(0.25) = 15 atm A clown in the park gave a child a balloon filled with 7.00 L of helium at 301 K. What will the volume of the balloon be when the child takes it into an air-­‐conditioned house at 22°C? 22°C + 273 = 295 K !!
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A balloon contains 1.47 moles and has a volume of 5.18 L. If the amount of gas decreases to 1.25 mol, what is the new volume? !!
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Gas Law Summary If the temperature remains constant, 800 mL of nitrogen at 2.0 atm must be compressed to what pressure to reach 500 mL? P1V1 = P2V2 (2.0 atm)(800 mL) = (x)(500 mL) divide both sides by 500, x = 3 atm A gas occupies 22.0 mL with conditions of 393 mm Hg at 7.00°C. What will be the volume of that gas if conditions change to 373 mm Hg at 15.0°C? 7.00°C + 273 = 280K 15.0°C + 273 = 288K !! !!
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cross multiply, in your calculator: 393*22.0*288/280/373 enter, x = 23.8 mL Determine the pressure of a gas (in atm) in a 1.0 liter container that consists of 5.0 moles at 27°C. 27°C + 273 = 300K PV = nRT (x)(1.0L) = (5.0 mol)(0.0821 Latm/molK)(300K) divide both sides by 1.0, x = 120 atm The volume of a gas at STP is 18.6 L. What is the quantity of gas in this sample? 1 mol = 22.4L @STP 18.6 L = 0.830 mol 1 mol 22.4 L