Project ForgeMass Transfer
Diffusion
GATE 2014
Hard
A spherical ball of benzoic acid (diameter=1.5 cm) is submerged in a pool of still water. The solubility and diffusivity of benzoic acid in water are 0.03 kmol/m³ and 1.25×10⁻⁹ m²/s respectively. Sherwood number is given as Sh=2.0+0.6Re^0.5·Sc^0.33. The initial rate of dissolution (in kmol/s) of benzoic acid approximately is
- A3.54×10⁻¹¹
- 3.54×10⁻¹²
- C3.54×10⁻¹³
- D3.54×10⁻¹⁴
Explanation
'Still water' means Re=0, so Sh=2.0 exactly (the stagnant-medium limit). kc=Sh·D/d=2.0×1.25×10⁻⁹/0.015=1.667×10⁻⁷ m/s. Surface area A=πd²=π(0.015)²=7.069×10⁻⁴ m². Rate=kc·A·Cs=1.667×10⁻⁷×7.069×10⁻⁴×0.03≈3.53×10⁻¹² kmol/s.
Source: GATE CH 2014 (2014)
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