A molecule takes 3.0 seconds to diffuse across a membrane. If the thickness of the membrane is doubled, then how long does it take the molecule to diffuse across the thicker membrane?
Question
A molecule takes 3.0 seconds to diffuse across a membrane. If the thickness of the membrane is doubled, then how long does it take the molecule to diffuse across the thicker membrane?
Solution
The time it takes for a molecule to diffuse across a membrane is directly proportional to the square of the thickness of the membrane. This is known as Fick's second law of diffusion.
Given that the original time for diffusion is 3.0 seconds when the thickness is 'x', if the thickness is doubled (2x), the time for diffusion will be proportional to (2x)^2 = 4x^2.
Since the time is directly proportional to the square of the thickness, doubling the thickness will quadruple the time taken for diffusion.
So, if it originally took 3.0 seconds for the molecule to diffuse across the membrane, when the thickness of the membrane is doubled, it will take 3.0 seconds * 4 = 12.0 seconds for the molecule to diffuse across the thicker membrane.
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