The molar average velocity of a binary mixture of species A and B can be defined as the weighted average of the individual molar velocities of each species, where the weights are given by the respective mole fractions of each species in the mixture.

Let's break down the formula for the molar average velocity:

a) naVa + nbVb

Here, na and nb represent the number of moles of species A and B, respectively, and Va and Vb represent their respective molar velocities. This formula simply adds up the product of the number of moles and molar velocity for each species.

b) (naVa + nbVb)/n

In this formula, n represents the total number of moles in the mixture. By dividing the sum of the individual moles and molar velocities by the total number of moles, we obtain the molar average velocity. This formula takes into account the relative amounts of each species in the mixture.

c) (naVa + nbVb)/2

Option c) suggests dividing the sum of the individual moles and molar velocities by 2. This formula assumes equal mole fractions for both species, which may not be the case in a binary mixture. It does not accurately represent the molar average velocity.

d) naVa - 2nbVb/n

Option d) suggests subtracting 2 times the product of the number of moles of species B and its molar velocity from the product of the number of moles of species A and its molar velocity, divided by the total number of moles. This formula is incorrect and does not represent the molar average velocity.

The correct answer is option b) because it correctly accounts for the relative amounts of each species in the mixture and calculates the molar average velocity as the weighted average of the individual molar velocities.