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The first question involves calculating the diffusion rates and velocities between two connected bulbs with nitrogen (N₂) and hydrogen (H₂) gases. Here's a breakdown of how to solve it:

**Given dataThe first question involves calculating the diffusion rates and velocities between two connected bulbs with nitrogen (N₂) and hydrogen (H₂) gases. Here's a breakdown of how to solve it:

**Given **

- Internal diameter of the tube \( d = 1 \, \text{mm} = 1 \times 10^{-3} \, \text{m} \)
- Length of the tube \( L = 0.15 \, \text{m} \)
- Temperature \( T = 25^\circ \, \text{C} \) (or 298 K)
- Pressure \( P = 1 \, \text{atm} \)
- Diffusivity \( D_{AB} = 7.84 \times 10^{-5} \, \text{m}^2/\text{s} \)
- Nitrogen content at the ends:
  - End 1: 80 mol%
  - End 2: 25 mol%

We will use Fick's law of diffusion to calculate the mass transfer rate.

### Part a) Rate and direction of mass transfer (mol/s)

Fick's first law of diffusion states:

\[
J_A = -D_{AB} \frac{C}{L} (y_A^{(1)} - y_A^{(2)})
\]

Where:
- \( J_A \) is the molar flux of species A (N₂) in mol/m²·s
- \( D_{AB} \) is the diffusivity of A in B
- \( C \) is the total molar concentration
- \( L \) is the length of the tube
- \( y_A^{(1)} \) and \( y_A^{(2)} \) are the mole fractions of nitrogen at ends 1 and 2, respectively.

We need to calculate the total concentration, \( C \), using the ideal gas law:

\[
C = \frac{P}{RT}
\]

Where:
- \( P = 1 \, \text{atm} = 101325 \, \text{Pa} \)
- \( R = 8.314 \, \text{J/mol·K} \)
- \( T = 298 \, \text{K} \)

Once we calculate \( J_A \), we can find the rate of mass transfer by multiplying by the cross-sectional area of the tube:

\[
\text{Rate of transfer} = J_A \times A
\]

The cross-sectional area \( A \) is:

\[
A = \pi \left( \frac{d}{2} \right)^2
\]

### Part b) Convective (bulk) velocity

The bulk velocity \( u \) is determined from the diffusion flux and total flux through the tube. This can be done by applying the total mass balance.

### Part c) Species velocities relative to stationary coordinates

The species velocities are calculated using:

\[
v_A = J_A / C_A
\]
\[
v_B = J_B / C_B
\]

Where \( C_A \) and \( C_B \) are the concentrations of nitrogen and hydrogen, respectively.

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I'll now proceed with the detailed calculations. Would you like to see those steps, or should I continue solving directly?

Learn how to calculate the rate and direction of mass transfer for nitrogen and hydrogen in a two-bulb system connected by a tube. Using Fick's Law of Diffusion, the Ideal Gas Law, and specific data points such as diffusivity and mole fractions, solve this chemical engineering problem step-by-step.

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