Problem session 8 problems F090

# Problem session 8 problems F090 - we have encountered so...

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CHEM 3321 Problem Set #8 Fall, 2009 1. Interstellar space has an average temperature of about 10 K and an average density of hydrogen atoms of about one hydrogen atom per cubic meter. Compute the mean free path of hydrogen atoms in interstellar space. Assume the diameter of a hydrogen atom to be 100 pm. 2. On the average what is the time between collisions of a xenon atom at 300 K and (a) one torr and (b) one bar. 3. Calculate the pressure at which the mean free path of a hydrogen molecule well be 100 μ m, 1.0 mm, and 1.00 m at 20 C. 4. We can calculate the probability that the x-component of the velocity of a molecule lies within some range. For example, the probability that 0 x x xo v v v - is given by ( 29 0 2 1 0 0 2 1 0 0 2 2 x 0 2 / 2 1 2 / 2 1 0 0 2 w where 2 } { Pr 2 / v letting Now 2 2 2 } { Pr 0 2 0 2 0 0 2 x w w x x x v x kT mv v v x kT mv x x x v kT m dw e v v v ob w kT m dv e kT m dv e kT m v v v ob x x x x x = = - = = = - - - - - π π π It so happen the above integral cannot be evaluated in terms of any function that
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Unformatted text preview: we have encountered so far. It is customary to express the integral in terms of a new function call the error function, which is defined by ∫-= z x dx e z erf 2 1 2 2 ) ( Values of the error function are listed in some texts and on the internet. (a)Show that ) ( } { Pr w erf v v v ob x x x = ≤ ≤-(b) Calculate the probability that ( 29 ( 29 2 1 2 1 2 2 m kT v m kT x ≤ ≤-5. The distribution of speed for a gas in two dimensions is given by dv ve kt m dv v F kT mv 2 / 2 ) (-= Using this expression derive formulas for <v> and ,<v 2 > for a two dimensional gas. 6. What is the most probably kinetic energy for a molecule in the gas phase?...
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