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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 x 10-9 m2/s respectively. Sherwood number is given as Sh = 2.0 + 0.6 0.33 Re0.5 Sc0.33 . The initial rate of dissolution (in kmol/s) of benzoic acid approximately is
- a)3.54 x 10−11
- b)3.54 x 10−12
- c)3.54 x 10−13
- d)3.54 x 10−14
Correct answer is option 'B'. Can you explain this answer?
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To find the initial rate of dissolution of benzoic acid, we need to use the Sherwood number equation:
Sh = 2.0 * Re^0.5 * Sc^0.33
First, we need to find the Reynolds number (Re). The Reynolds number is given by:
Re = (ρ * v * D) / μ
Where:
ρ = density of water = 1000 kg/m^3
v = velocity of benzoic acid = 0 (since it is submerged in still water)
D = diameter of the ball = 1.5 cm = 0.015 m
μ = dynamic viscosity of water = 0.001 kg/(m·s)
Plugging in these values, we get:
Re = (1000 * 0 * 0.015) / 0.001
Re = 0
Next, we need to find the Schmidt number (Sc). The Schmidt number is given by:
Sc = μ / (ρ * D)
Plugging in the values, we get:
Sc = 0.001 / (1000 * 0.015)
Sc = 0.0667
Now, we can plug in the values of Re and Sc into the Sherwood number equation:
Sh = 2.0 * 0^0.5 * 0.0667^0.33
Sh = 2.0 * 0 * 0.341
Sh = 0
The Sherwood number is 0, which means there is no mass transfer occurring. Therefore, the initial rate of dissolution of benzoic acid is approximately 0 kmol/s.
Sh = 2.0 * Re^0.5 * Sc^0.33
First, we need to find the Reynolds number (Re). The Reynolds number is given by:
Re = (ρ * v * D) / μ
Where:
ρ = density of water = 1000 kg/m^3
v = velocity of benzoic acid = 0 (since it is submerged in still water)
D = diameter of the ball = 1.5 cm = 0.015 m
μ = dynamic viscosity of water = 0.001 kg/(m·s)
Plugging in these values, we get:
Re = (1000 * 0 * 0.015) / 0.001
Re = 0
Next, we need to find the Schmidt number (Sc). The Schmidt number is given by:
Sc = μ / (ρ * D)
Plugging in the values, we get:
Sc = 0.001 / (1000 * 0.015)
Sc = 0.0667
Now, we can plug in the values of Re and Sc into the Sherwood number equation:
Sh = 2.0 * 0^0.5 * 0.0667^0.33
Sh = 2.0 * 0 * 0.341
Sh = 0
The Sherwood number is 0, which means there is no mass transfer occurring. Therefore, the initial rate of dissolution of benzoic acid is approximately 0 kmol/s.
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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 x 10-9 m2/s respectively. Sherwood number is given as Sh = 2.0 + 0.6 0.33 Re0.5 Sc0.33 . The initial rate of dissolution (in kmol/s) of benzoic acid approximately isa)3.54 x 10−11b)3.54 x 10−12c)3.54 x 10−13d)3.54 x 10−14Correct answer is option 'B'. Can you explain this answer?
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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 x 10-9 m2/s respectively. Sherwood number is given as Sh = 2.0 + 0.6 0.33 Re0.5 Sc0.33 . The initial rate of dissolution (in kmol/s) of benzoic acid approximately isa)3.54 x 10−11b)3.54 x 10−12c)3.54 x 10−13d)3.54 x 10−14Correct answer is option 'B'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about 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 x 10-9 m2/s respectively. Sherwood number is given as Sh = 2.0 + 0.6 0.33 Re0.5 Sc0.33 . The initial rate of dissolution (in kmol/s) of benzoic acid approximately isa)3.54 x 10−11b)3.54 x 10−12c)3.54 x 10−13d)3.54 x 10−14Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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 x 10-9 m2/s respectively. Sherwood number is given as Sh = 2.0 + 0.6 0.33 Re0.5 Sc0.33 . The initial rate of dissolution (in kmol/s) of benzoic acid approximately isa)3.54 x 10−11b)3.54 x 10−12c)3.54 x 10−13d)3.54 x 10−14Correct answer is option 'B'. Can you explain this answer?.
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