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GATE 2022 CH – Question 17

Mass Transfer · Fick's laws, molecular diffusion and mass transfer coefficients · 1 mark · Multiple choice

Consider two stationary spherical pure water droplets of diameters $d_1$ and $2d_1$. CO$_2$ diffuses into the droplets from the surroundings. If the rate of diffusion of CO$_2$ into the smaller droplet is $W_1$ mol s$^{-1}$, the rate of diffusion of CO$_2$ into the larger droplet is

  1. $2W_1$
  2. $4W_1$
  3. $W_1$
  4. $0.5W_1$

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Correct answer: (A) $2W_1$

Explanation

For steady diffusion from an infinite medium to a stationary sphere, the molar rate is $W = 2\pi dD\,\Delta C$, which is proportional to the diameter. Doubling the diameter doubles the rate: $2W_1$.