Question

Define the following terms: mass-average velocity, diffusion velocity, stationary medium, and moving medium.

Short answer

Define Mass-average velocity, Diffusion velocity, stationary medium, and moving medium. Mass-average velocity is the weighted average velocity of all particles in a mixture, obtained by dividing the sum of the product of the mass and velocity of each particle by the total mass of the system. It represents the overall motion of a system. Diffusion velocity is the relative velocity of a species in a mixture due to concentration gradients. It is the rate at which a species moves from an area of higher concentration to an area of lower concentration based on random molecular motion. A stationary medium is a physical environment in which there is no macroscopic motion or net flow of the system as a whole. The medium remains fixed, allowing only the mass within it to move or change position. A moving medium is a physical environment that exhibits macroscopic motion or flow as a whole. In this case, the medium itself moves, along with the mass within it. Examples include fluid flow through a pipe or a river moving downstream.

Step-by-step solution

Mass-average velocity

Mass-average velocity is the average velocity of all the particles in a mixture, weighted by their respective masses. It is a measure of the overall motion of a system and can be obtained by dividing the sum of the product of the mass and velocity of each particle by the total mass of the system. Mathematically, it can be expressed as: $$ V_{mass-average} = \frac{\sum_{i=1}^{n}m_i v_i}{\sum_ {i=1}^{n} m_i} $$ where \(n\) is the number of particles in the system, \(m_i\) is the mass of the \(i\)-th particle, and \(v_i\) is the velocity of the \(i\)-th particle.

Diffusion velocity

Diffusion velocity is the relative velocity of a species (particle, molecule or ion) in a mixture due to concentration gradients. It is the velocity at which a species moves as a result of random molecular motion that occurs from an area of higher concentration to an area of lower concentration. The rate of diffusion is proportional to the concentration gradient, which can be mathematically represented by Fick's first law: $$ J_i = -D_{i}\frac{dc_i}{dx} $$ where \(J_i\) is the diffusion flux, \(D_{i}\) is the diffusion coefficient, \(c_{i}\) is the concentration, and \(x\) is the distance.

Stationary medium

A stationary medium is a physical system or environment in which no macroscopic motion of the medium takes place and there is no net flow or movement of the system as a whole. In this context, the medium remains fixed and only the mass within the medium can move or change its position.

Moving medium

A moving medium is a physical system or environment that exhibits macroscopic motion or flow as a whole. The medium itself moves along with the mass within it. An example of a moving medium is the flow of a fluid (liquid or gas) through a pipe or a river moving downstream.