A substance is allowed to diffuse along a 10-cm length of tubing filled with water.The cross section of the tube is 5.3 cm².If the diffusion coefficient is 5.0 × 10¯¹⁰ m²/s,and 6.5 × 10¯¹⁴ kg is transported along the tube in 16 s,what is the difference in the concentration levels of the substance at the two ends of the tube? A)3.9E-1 kg/m³ B)4.3E-2 kg/m³ C)1.5E-3 kg/m³ D)8.1E-4 kg/m³

Question

Quizplus · Accepted Answer

First, we need to find the cross-sectional area of the tubing: 
Area = π(r^2) = π(5.3cm/2)^2 = 22.1 cm^2 = 0.00221 m^2 
Next, we can use the formula for the amount of substance transported by diffusion: 
Amount = (diffusion coefficient)(area)(concentration gradient)(time) 
We can rearrange this formula to solve for the concentration gradient: 
Concentration gradient = (Amount)/(diffusion coefficient)(area)(time) 
Plugging in the given values: 
Concentration gradient = (6.5 × 10¯^14 kg)/(5.0 × 10¯^11 m^2/s)(0.00221 m^2)(16 s) 
Concentration gradient = 0.0015 kg/m 
However, the question asks for the difference in concentration levels at the two ends of the tube, so we need to divide this by the length of the tube: 
Difference in concentration levels = (0.0015 kg/m)/(0.1 m) = 0.015 kg/m = 1.5E-3 kg/m

Therefore, the best choice is C.

A Substance Is Allowed to Diffuse Along a 10-Cm Length