Calculating Time for Bacteria to Reach the Top of a Beaker

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Homework Statement

In the bottom of a 200 ml glass beaker, 2 trillion molecules of a bacteria are released into 20 ml of H2O. The beaker is covered to prevent contamination and keep100% humidity. The bacteria has a molecular weight of 200,000 daltons.

Homework Equations

How much time will it take for the first molecules to rise to the top rim of the beaker (to reach your hand). The assumption is normal room temperature.

The Attempt at a Solution

 

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This problem is difficult to solve because the rate of diffusion of the bacteria is affected by numerous factors, including temperature, concentration gradients, and the viscosity of the medium. For simplicity, we can assume that the molecules diffuse at a rate of 0.01 cm2/s. Therefore, it will take 2 trillion molecules * 200,000 daltons / 0.01 cm2/s = 4 x 1017 seconds, or about 1.3 million years, for the first molecules to reach the top of the beaker.