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Chapter 1. Part 2 Ideal Gases

Chapter 1. Part 2 Ideal Gases. Section 1.5, 1.6, 1.7, 1.8. Pressure. Standard Atmosphere the pressure exerted by a column of mercury 760 mm high at 0 º C SI Unit 1 atm = 101325 Pa = 760 Torr 1 Torr  1 mmHg 1 Pa = 1 Kg m -1 s -2 = 1 N m -2 1 Bar = 100 kPa =0.986923 atm.

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Chapter 1. Part 2 Ideal Gases

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  1. Chapter 1. Part 2 Ideal Gases Section 1.5, 1.6, 1.7, 1.8

  2. Pressure • Standard Atmosphere the pressure exerted by a column of mercury 760 mm high at 0 ºC • SI Unit 1 atm = 101325 Pa = 760 Torr 1 Torr  1 mmHg 1 Pa = 1 Kg m-1 s-2 = 1 N m-2 • 1 Bar = 100 kPa =0.986923 atm Barometer 氣壓計

  3. Manometer 壓力計 • P = r g h P pressure r density g gravity h height

  4. Example 1 例題 • Compare the length of a column of mercury to that of a column of water required to produce a pressure of 1.000 bar. The densities of mercury and water at 0.00 ºC are 13.596 g cm-3 and 0.99987 g cm-3, respectively. Answer Formula P = rHgg hHg = rwaterg hwater Unit Conversion 1 bar = 0.986923 atm; 1 atm = 760 mmHg 1 bar = 750.06 mm Hg 13.596 g /cm3 g  750.06 mm = 0.99987 g/cm3 g hw hw = 10199 mm

  5. Boyle’s Law • At constant temperature, the pressure of a fixed amount of gas is inversely proportitional to its volume 1/P V; P=constant / V PV = constant (n and T are fixed)

  6. Gay-Lussac’s Law • At constant pressure, the volume of a fixed amount of gas varies linearly with the temperature V T V = constant  T PV = constant (n and P are fixed) Kelvin Temperature (K)

  7. Avogadro’s Principle • At a given temperature and pressure, equal volumes of gas contain the same number of molucules V  n Mole (莫耳) 任何物質與0.012kg C-12 擁有相同的數量 1 mole = 6.022137  1023 Molar volume Vm = V / n The molar volume of a gas is almost the same for all gases at the same temperature and pressure

  8. Ideal Gases • Boyle’s Law : P  1/V • Charle’s Law : V = A + B q

  9. Equation of State for an Ideal Gas • Pressure of the sample= f(amount, volume, temperature) PV = nRT P : pressure of the sample V : volume of the sample occupies n :amount of substances in the sample T : temperature of the sample • Boyle’s Law : P  1/V • Charle’s Law : V = A + B q • Avogadro’s Principle : V  n http://www.phy.ntnu.edu.tw/demolab/java/idealGas/

  10. Gas Constant R R = 8.31451 J / K mol = 8.31451 kPaL/K mol = 1.98722 cal/ k mol = 8.20578×10-2 L atm /K mol = 62.364 L Torr/K mol

  11. 其他形式的理想氣體狀態方程式 • n amount of substance • M molar mass of the substance • r density of the gas (=m/M)

  12. Example 2 例題 Calculate the average molar mass of air at sea level and 0 °C if the density of air is 1.29 kg m-3. Amswer

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