Answer to Question #113391 in General Chemistry for chloe

Question

You decide to focus on pickling cucumbers. The cucumbers that you have are all approximately 12 cm in length and 3 cm in diameter. If the diffusion coefficient for H+ ions in cucumbers is the same as in water, 7 x 10-5 cm2/sec, how long will it take for the protons to reach the center of the cucumbers? Enter your answer in minutes without including the units.

Answer 1

Cross section area: A

A = 3.14 * 9/4 = 7.065 cm² approx 7!

The diffusion coefficient is (physical meaning) a rate of increasing of a surface area. So it takes 1 s for substance transfer through the area of 7 x 10-5 cm2.

We also take into consideration the gradient of concentration change per 1 lenght unit (1 cm ):

So in units of min:

(7 x 10-5 / 7) * 6 * 60 = 0.0036 min