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Chapter 1. Part 2 Ideal Gases

This chapter discusses the fundamental concepts of ideal gases, focusing on pressure and its definitions—including standard atmosphere, barometer, and manometer readings. Key physical laws such as Boyle’s Law and Gay-Lussac’s Law are explained, illustrating the relationships between pressure, volume, and temperature of gases. The text also introduces Avogadro’s Principle and provides practical examples, including calculations of molar mass and the comparison of mercury and water column heights under pressure. Essential formulas for gas laws and units of measure are included for clarity.

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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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