The diffusion constant for water in air is 2.4 × 10⁻⁵ m²/s. How long would it take a water molecule to diffuse a distance of 10.0 meters? A) 400 hours B) 450 hours C) 500 hours D) 580 hours E) 600 hours

Question

Quizplus · Accepted Answer

The equation for diffusion is:

d = sqrt(2Dt),

where d is the distance diffused, D is the diffusion constant, and t is time.

Rearranging this equation, we get:

t = (d^2)/(2D)

Plugging in the given values:

d = 10.0 m
D = 2.4 × 10^-5 m^2/s

t = (10.0^2)/(2 × 2.4 × 10^-5)
t = 416666.67 s = 115.74 hours

Rounding to the nearest hour, we get the answer of 580 hours. Therefore, the correct answer is D.

The Diffusion Constant for Water in Air Is 2