Explanation:

Molar flux is defined as the amount of substance per unit area per unit time. It is denoted by J and expressed in units of mol/m²s. Molar flux can be measured with respect to a stationary observer or with respect to an observer moving with molar average velocity.

Molar average velocity is defined as the average velocity of all the molecules in the solution. It is denoted by u and expressed in units of m/s. When we measure molar flux with respect to a stationary observer, we are measuring the flux of molecules passing through a stationary plane. When we measure molar flux with respect to an observer moving with molar average velocity, we are measuring the flux of molecules passing through a plane moving with the same velocity as the average velocity of the molecules in the solution.

The condition at which molar flux with respect to a stationary observer and with respect to an observer moving with molar average velocity is the same is when the solution is very dilute. This is because in a very dilute solution, the molecules are far apart and do not interact with each other. Therefore, the average velocity of the molecules is the same as the velocity of the solvent molecules, and the molar flux with respect to a stationary observer and with respect to an observer moving with molar average velocity is the same.

In a highly concentrated solution, the molecules are close together and interact with each other. This leads to a difference in the average velocity of the molecules and the velocity of the solvent molecules, resulting in a difference in molar flux with respect to a stationary observer and with respect to an observer moving with molar average velocity.

At moderate concentrations, the interaction between molecules is not as strong as in highly concentrated solutions, but it is not as weak as in very dilute solutions. Therefore, there may be a slight difference in molar flux with respect to a stationary observer and with respect to an observer moving with molar average velocity.

In conclusion, the condition at which molar flux with respect to a stationary observer and with respect to an observer moving with molar average velocity is the same is when the solution is very dilute.