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## Chapter 5

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**Chapter 5**Gases**Early Experiments**• Torricelli performed experiments that showed that air in the atmosphere exert pressure. • Torricelli designed the first barometer.**Unit of Pressure**1 standard atmosphere =1 atm =760 mm Hg =760 torr =101325 Pa**A gas that obeys Boyle’s law is called an ideal gas**Boyle’s Law : PV=k**Charles’s Law: V=bT**• The volume of a gas at constant pressure increases linearly with the temperature of the gas.**Avogadro’s Law : V=an**• A gas at constant temperature and pressure the volume is directly proportional to the number of moles of gas.**Ideal Gas Law**Equation of state for a gas • PV=nRT • P: atm • V: Liter • n: moles • R: 0.082 L atm K-1 • T: K**Laws for Gas experiments**• Boyle’s Law : PV=k • Charles’s Law : V=bT • Avogadro’s Law : V=an • The ideal Gas Law : PV=nRT (so called equation of state for idea gas)**Ideal Gas**• The volume of the individual particles can be assumed to be negligible. • The particles are assumed to exert no force on each other. • It expresses behavior that real gases approach at low pressure and high temperature.**Gas Stoichiometry**Standard Temperature and Pressure (STP) • T=0oC • P=1 atm • V=22.4 L Natural Temperature and Pressure (NTP) • T=25oC • P=1 atm • V=24.5L**The Model of Ideal Gas in Kinetic-Molecular Theory**• The volume of the individual particles can be assumed to be negligible. • The particles are assumed to exert no force on each other. • The particles are in constant motion. • The average kinetic energy of a collection of gas particles is assumed to be directly proportional to the Kelvin temperature of the gas.**An ideal gas particle in a cube wholse sides are of length L**(in meters).**The velocity u can be broken down into three perpendicular**components, ux, uy, and u2.**Pressure of an Ideal Gas**Let the container be a rectangular box with sides of length Lx, Ly and Lz. Let v be the velocity of a given molecule.**In the xy plane,vx2 + vy2 = vyx2 by the Pythagorean theorem.****A molecule collide with wall W where W is parallel to the xz**plane. Let i have the velocity components vx, vy, vz**The integration can be extended over the whole time interval**t1 to t2. 速度平方之平均值**The translational energy Etr= 1/2mv2**single particle**Temperature dependence with translation kinetic energy**one mole of particles single particle**Distribution of Molecular Speeds in an Ideal Gas**Root mean square speed is assumed that all molecules move at the same speed. The motions of gas molecules should have distribution of molecular speeds in equilibrium.**Collisions with a Wall**vydt ly dNw:粒子撞擊牆壁的數目**H2 at 25oC and 1atm**分子量單位:Kg**Definition of Pressure**• The pressure of a gas results from collisions between the gas particles and the walls of the container. • Each time a gas particle hits the wall, it exerts a force on the wall. • An increase in the number of gas particles in the container increases the frequency of collisions with the walls and therefore the pressure of the gas.**Suppose there is a tiny hole of area A in the wall**and that outside the container is a vacuum. Escape of a gas through a tiny hole is called effusion. collisions × area**Diffusion**Relative diffusion rates of NH3 and HCl molecules**Molecules Collisions and Mean Free Path**• Intermolecular collisions are important in reaction kinetics. • Assume a molecule as a hard sphere. • No intermolecular forces exist except at the moment of collision. zAA: the number of collisions per unit time that one particular A molecule makes with other A molecule [collisions s-1]**Calculate zAA and zAB**(rA+rB=d)**A**B