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AP Chapter 5

# The root mean square velocity is u2 u rms combine

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Unformatted text preview: gas (KE) =N ( 1 avg A 2 NA is Avogadro's number Combine these two equations u2 = 3RT = u rms NAm mu 2 ) 3 RT 2 1 3 N A ( mu 2 ) = RT 2 2 3RT u2 = NAm (KE)avg = 41 42 m is kg for one particle, so Nam is kg for a mole of particles. We will call it M u rms = 3RT M Where M is the molar mass in kg/mole, kg/mole, and R has the units 8.3145 J/Kmol. The velocity will be in m/s 7 Example Calculate the root mean square velocity of carbon dioxide at 25C. Calculate the root mean square velocity of hydrogen at 25C. Calculate the root mean square velocity of chlorine at 250C. Range of velocities The average distance a molecule travels before colliding with another is called the mean free path and is small (near 10-7) Temperature is an average. There are molecules of many speeds in the average. Shown on a graph called a velocity distribution 44 43 273 K number of particles number of particles 2 2 - 2RT f(v) = 4 ve 2RT 3 Mv 2 273 K 2 2 - 2RT f(v) = 4 ve 2RT 3 Mv 2 1273 K Molecular Velocity 45 46 Molecular Velocity Velocity Average increases as temperature increases. Spread increases as temperature increases. Mv 2 2 - 2RT f(v) = 4 ve 2RT 47 48 Effusion Passage of gas through a small hole, int...
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