Question

The average time it takes for a molecule to diffuse a distance of x cm is given by t=x^2/2D where t is the time in seconds and D is the diffusion coefficient. Given that the diffusion coefficient of glucose is 5.7 x 10^-7 cm2/s, calculate the time it would take for a glucose molecule to diffuse 10 pm, which is roughly the size of a cell.

Answer 1

Using the diffusion equation with the provided diffusion coefficient, it is calculated that a glucose molecule would take approximately 8.77 x 10^-16 seconds to diffuse across a distance of 10 picometers.

Step-by-step explanation:

The question asks us to calculate the average time it would take for a glucose molecule to diffuse a certain distance, specifically 10 picometers (pm), with the provided diffusion coefficient of glucose. To find the time t, we need to use the equation t = x2 / (2*D), where x is the distance to diffuse and D is the diffusion coefficient. First, it is necessary to convert the distance from picometers to centimeters since the diffusion coefficient is given in cm2/s. There are 1012 picometers in a centimeter, so 10 pm equals 10 x 10-12 cm. Plugging these values into the equation, we get:

t = (10 x 10-12)2 / (2*(5.7 x 10-7)) cm2/s

t = (10-22) / (1.14 x 10-6)

t = 8.77 x 10-16 seconds

Therefore, it would take approximately 8.77 x 10-16 seconds for a glucose molecule to diffuse 10 pm.

Answer 2

Step-by-step explanation:

time to diffuse x cm is given by the relation

t = X² /2D

D = 5.7 x 10⁻⁷

t = X² / 2 x 5.7 x 10⁻⁷ = X² x 10⁷ / 11.4 s

X = 10 pm = 10 x 10⁻¹² m = 10 x 10⁻¹⁰ cm = 10⁻⁹ cm

t =( 10 ⁻⁹)² x 10⁷ / 11.4 = 10⁻¹¹ / 11.4 = 8.77 x 10⁻¹³ s