Diffusion of Sucrose in Gelatin. A layer of gelatin in water 5 mm thick and con-taining 5.1 wt % gelatin at 293 K separates two solutions of sucrose. The concentra-tion of sucrose in the solution at one surface of the gelatin is constant at 2.0 g sucrose/100 mL solution, and 0.2 g/100 mL at the other surface. Calculate the flux of sucrose in kg sucrose/s

the flux of sucrose is 9.072 × 10⁻⁷  kg sucrose / m² sec

Explanation:

Given the data in the question;

water-gelatin solution separating two different concentration solutions of sucrose; 5.1 wt % gelatin at 293 K; at this conditions diffusivity of sucrose in water gelatin solution is;

=  0.252 × 10⁻⁹ m²/sec.

we know that; 1 L = 0.001 m³, 1mL = 0.001 L

= 2.0 g sucrose/100 mL = 2.0 × 10⁻³ kg sucrose / 100 × 10 ⁻³ L

 = 2.0kg sucrose / 100 L

= 2.0 kg sucrose / 100 × 10⁻³ m³

 =  20 kg sucrose / m³

=  0.2 g sucrose/100 mL = 0.2 × 10⁻³ kg sucrose / 100 × 10⁻³ × 10⁻³ L

= 2 kg sucrose / m³

Thickness ß = 5 mm = 5 × 10⁻³ m

Now, flux of sucrose in kg sucrose / m³sec will be;

using the formula, = /ß ( - )

we substitute

= (0.252 × 10⁻⁹ m²/sec /  5 × 10⁻³ m) ( 20 kg sucrose / m³ - 2 kg sucrose / m³ )

= (0.252 × 10⁻⁶ / 5) × 18 kg sucrose / m² sec

 = 4.536 ×  10⁻⁶  / 5 kg sucrose / m² sec

= 9.072 × 10⁻⁷  kg sucrose / m² sec

Therefore, the flux of sucrose is 9.072 × 10⁻⁷  kg sucrose / m² sec

the dissolution of polymer can be thermodynamically described in 2 steps.