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Gases Pressure and Volume (Boyles Law) Temperature and Volume (Charles Law) Temperature and Pressure (Gay-Lussacs Law)

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Pressure and Volume ExperimentPressureVolume P x V (atm) (L) (atm x L) 18.0 2.0 16 24.04.0_____ 32.08.0_____ 41.016_____ Boyle's Law P x V = k (constant) when T remains constant P1V1= 8.0 atm x 2.0 L = 16 atm L P2V2= 4.0 atm x 4.0 L = 16 atm L P1V1 = P2V2 = k Use this equation to calculate how a volume changes when pressure changes, or how pressure changes when volume changes. new vol. old vol. x Pfactor new P old P x Vfactor V2 = V1 x P1 P2 = P1 x V1 P2 V2

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P and V Changes P1P1 P2P2 V1V1 V2V2

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Boyle's Law The pressure of a gas is inversely related to the volume when T does not change Then the PV product remains constant P 1 V 1 = P 2 V 2 P 1 V 1 = 8.0 atm x 2.0 L = 16 atm L P 2 V 2 = 4.0 atm x 4.0 L = 16 atm L

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PV Problem Freon-12, CCl 2 F 2, is used in refrigeration systems. What is the new volume (L) of a 1.6 L sample of Freon gas initially at 50 mm Hg after its pressure is changed to 200 mm Hg at constant T?

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PV Calculation Prepare a data table DATA TABLE Initial conditionsFinal conditions P 1 = 50 mm HgP 2 = 200 mm Hg V 1 = 1.6 LV 2 = ? ?

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Find New Volume (V 2 ) Solve for V 2 : P 1 V 2 = P 2 V 2 V 2 = V 1 x P 1 /P 2 V 2 = 1.6 L x 50 mm Hg = 0.4 L 200 mm Hg

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Learning Check GL1 A sample of nitrogen gas is 6.4 L at a pressure of 0.70 atm. What will the new volume be if the pressure is changed to 1.40 atm? (T constant) Explain. 1) 3.2 L 2) 6.4 L 3) 12.8 L

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Solution GL1 A sample of nitrogen gas is 6.4 L at a pressure of 0.70 atm. What will the new volume be if the pressure is changed to 1.40 atm? (T constant) 6.4 L x 0.70 atm = 3.2 L (1) 1.40 atm Volume must decrease to cause an increase in the pressure

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Learning Check GL2 A sample of helium gas has a volume of 12.0 L at 600. mm Hg. What new pressure is needed to change the volume to 36.0 L? (T constant) Explain. 1) 200. mmHg 2) 400. mmHg 3) 1200 mmHg

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Solution GL2 A sample of helium gas has a volume of 12.0 L at 600. mm Hg. What new pressure is needed to change the volume to 36.0 L? (T constant) Explain. 600. mm Hg x 12.0 L = 200. mmHg (1) 36.0 L Pressure decrease when volume increases.

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Charles Law V = 125 mL V = 250 mL T = 273 K T = 546 K Observe the V and T of the balloons. How does volume change with temperature?

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Charles Law: V and T At constant pressure, the volume of a gas is directly related to its absolute (K) temperature V 1 = V 2 T 1 T 2

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Learning Check GL3 Use Charles Law to complete the statements below: 1. If final T is higher than initial T, final V is (greater, or less) than the initial V. 2. If final V is less than initial V, final T is (higher, or lower) than the initial T.

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Solution GL3 V 1 = V 2 T 1 T 2 1. If final T is higher than initial T, final V is (greater) than the initial V. 2. If final V is less than initial V, final T is (lower) than the initial T.

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V and T Problem A balloon has a volume of 785 mL on a Fall day when the temperature is 21°C. In the winter, the gas cools to 0°C. What is the new volume of the balloon?

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VT Calculation Complete the following setup: Initial conditionsFinal conditions V 1 = 785 mLV 2 = ? T 1 = 21°C = 294 KT 2 = 0°C = 273 K V 2 = _______ mL x __ K = _______ mL V 1 K Check your answer: If temperature decreases, V should decrease.

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Learning Check GL4 A sample of oxygen gas has a volume of 420 mL at a temperature of 18°C. What temperature (in °C) is needed to change the volume to 640 mL? 1) 443°C2) 170°C 3) - 82°C

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Solution GL4 A sample of oxygen gas has a volume of 420 mL at a temperature of 18°C. What temperature (in °C) is needed to change the volume to 640 mL? 2) 170°C T 2 = 291 K x 640 mL = 443 K 420 mL = 443 K - 273 K = 170°C

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Gay-Lussacs Law: P and T The pressure exerted by a confined gas is directly related to the temperature (Kelvin) at constant volume. P (mm Hg)T (°C) 936100 761 25 691 0

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Learning Check GL5 Use Gay-Lussacs law to complete the statements below: 1. When temperature decreases, the pressure of a gas (decreases or increases). 2. When temperature increases, the pressure of a gas (decreases or increases).

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Solution GL5 1. When temperature decreases, the pressure of a gas (decreases). 2. When temperature increases, the pressure of a gas (increases).

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PT Problem A gas has a pressure at 2.0 atm at 18°C. What will be the new pressure if the temperature rises to 62°C? (V constant) T = 18°C T = 62°C

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PT Calculation P 1 = 2.0 atmT 1 = 18°C + 273 = 291 K P 2 = ?T 2 = 62°C + 273 = 335 K What happens to P when T increases? P increases (directly related to T) P 2 = P 1 x T 2 T1T1 P 2 = 2.0 atm x K = atm K ?

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Learning Check GL6 Complete with 1) Increases 2) Decreases 3) Does not change A. Pressure _____, when V decreases B. When T decreases, V _____. C. Pressure _____ when V changes from 12.0 L to 24.0 L (constant n and T) D. Volume _____when T changes from 15.0 °C to 45.0°C (constant P and n)

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Solution GL6 A. Pressure 1) Increases, when V decreases B. When T decreases, V 2) Decreases C. Pressure 2) Decreases when V changes from 12.0 L to 24.0 L (constant n and T) D. Volume 1) Increases when T changes from 15.0 °C to 45.0°C (constant P and n)

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