Understanding Molar Fluxes in Ammonia Evaporation
This problem involves analyzing molar fluxes during the evaporation of ammonia (component 1) into stagnant air (component 2). We are given that the process is steady-state, indicated by constant liquid level and ammonia concentration at the gas interface.
Analyzing Molar Flux ($N_i$)
The molar flux relative to a fixed location ($N_i$) is defined for each component.
- Ammonia ($N_1$): Since ammonia is evaporating and its concentration is maintained constant at the interface and in the bulk gas (steady state), the molar flux of ammonia relative to a fixed coordinate system, $N_1$, must be constant.
- Air ($N_2$): The problem states that the air in the bottle is stagnant. This implies that there is no net movement of air molecules relative to a fixed point. Therefore, the molar flux of air relative to a fixed location is zero: $N_2 = 0$.
Analyzing Diffusive Molar Flux ($J_i$)
The diffusive molar flux relative to the molar average velocity ($J_i$) has a specific relationship:
- The diffusive flux $J_i$ is defined as $J_i = N_i - C_{avg} \bar{v}$, where $C_{avg}$ is the total molar concentration and $\bar{v}$ is the molar average velocity.
- It can be shown that for any two components in a mixture, the sum of their diffusive fluxes relative to the molar average velocity is always zero: $J_1 + J_2 = 0$. This is a fundamental property derived from the definition of $J_i$.
Conclusion
Based on the analysis:
- Ammonia flux relative to a fixed point is constant: $N_1 = \text{constant}$.
- Air flux relative to a fixed point is zero due to stagnation: $N_2 = 0$.
- The sum of diffusive fluxes relative to the molar average velocity is zero: $J_1 + J_2 = 0$.
These conditions match Option 1.
Important Questions from Molecular Diffusion
Consider a non-reactive binary mixture of two ideal gases A and B in an isothermal horizontal closed tube. Due to the concentration difference at the two ends of the tube, equimolal counterdiffusion occurs along the axial direction. No concentration gradients exist in the radial direction. The profile for partial pressure of component A ($p_A$) as a function of axial distance $z$ is shown in the figure. The partial pressure of component B ($p_B$) approaches zero at $z = 0.8 \text{ m}$. At a location $z = z_1$ the partial pressures of the components A and B are equal. The value of $z_1$ (in m) is _____ (rounded off to two decimal places).
- For a binary mixture of components A and B, $N_A$ and $N_B$ denote the total molar fluxes of components A and B, respectively. $J_A$ and $J_B$ are the corresponding molar diffusive fluxes. Which of the following is true for equimolar counter-diffusion in the binary mixture?
- Consider the following two cases for a binary mixture of ideal gases A and B under steady state conditions. In Case 1, the diffusion of A occurs through non-diffusing B. In Case 2, equimolal counter diffusion of A and B occurs. In both the cases, the total pressure is 100 kPa and the partial pressures of A at two points separated by a distance of 10 mm are 10 kPa and 5 kPa. Assume that the Fick's first law of diffusion is applicable. What is the ratio of molar flux of A in Case 1 to that in Case 2?
- In a binary gas-liquid system, $N_{A,EMD}$ is the molar flux of a gas $A$ for equimolar counter diffusion with a liquid $B$. $N_{A,UMD}$ is the molar flux of $A$ for steady one- component diffusion through stagnant $B$. Using the mole fraction of $A$ in the bulk of the gas phase as $0.2$ and that at the gas-liquid interface as $0.1$ for both the modes of diffusion, the ratio of $N_{A,UMD}$ to $N_{A,EMD}$ is equal to ________ (rounded off to two decimal places).
- 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
