# quiz10s11 - [Numbers without decimal points are considered...

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Unformatted text preview: [Numbers without decimal points are considered infinitely precise. Show reasonable significant figures and proper units. Answers should be in reasonable units for the quantity.] 1. (10 points) Calculate the average speed and the mean free path of an oxygen molecule at 1 bar and 298.15 K. [HINT: For the molecular diameter of oxygen, use the Lennard-Jones parameter.] The average speed is found in section 8 of the Handbook on page 8-1. Substitution gives: 1 1 1 1 17 . 444 031998 . 15 . 298 31451 . 8 8 8 s m mol kg K mol K J M RT v The mean free path is also found in section 8 on page 8-2. Using the Lennard-Jones diameter of Table 8.2 (page 8-3) in the Handbook and using the ideal-gas law to find the number density, the calculation of the mean free path gives nm mol Pa K mol K J m PL RT d 3 . 72 10 0221367 . 6 10 15 . 298 31451 . 8 10 358 . 2 1 2 1 1 23 5 1 1 2 9 2 2. (10 points) Normalize the 2-D speed distribution function by finding the value of A in this equation: v e A v F kT mv 2 / 2 ) ( . Show all work clearly to get full credit, with explanations of steps in the procedure. Normalization requires that the integral of the function over all possible values of the parameter be equal to unity. The possible values of the speed span from 0 to infinity. So, the equation to solve is this: 1 ) ( dv v F . Substitution in this equation gives: . 1 2 / 2 vdv e A kT mv Using the integral table, one can evaluate the integral: kT m A kT m A 1 2 2 1 . The normalized probability function is: v e kT m v F kT mv 2 / 2 ) ( CHEMISTRY 444.10/80 Spring, 2011 QUIZ 1 February 18, 2011 NAME: EMIL JANNINGS Score ______/20 [Numbers without decimals are infinitely precise. Show proper number of decimal places and units.] 1. (10 points) The diffusion coefficient of sucrose in water at 298 K is 0.522 10-9 m 2 s-1 . Remembering that diffusion in solution is in three dimensions, determine the time it, on average, takes a sucrose molecule to diffuse through the solution by a root-mean-square distance of exactly 1 mm. In three dimensions, the rms distance is found by summing the rms components: Dt Dt x z y x r 6 ) 2 ( 3 3 2 2 2 2 2 where it is assumed that diffusion is isotropic and the steps in each direction on average are the same. Therefore, the rms distance is: Dt r 6 . Inverting this equation to find the time gives: min 32 . 5 319 ) 10 522 . 6 /( ) 10 ( 6 / ) ( 1 2 9 2 3 2 s s m m D r t 2. (10 points) The molar mass of myoglobin is 16.8 kg mol-1 . The diffusion coefficient of myoglobin in water has been determined by Riveros-Moreno to be 1.05 10-10 m 2 s-1 at 20...
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quiz10s11 - [Numbers without decimal points are considered...

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