chemistry

posted by .

The time dependent concentration of solute particles in a solution is given by

c(r, t) = [n/8(pi D t)^(3/2)] e^(-r^2 /4 D t)

where r^2 = x^2 + y^2 + z^2 with x, y, and z being the values of three components of the position in the Cartesian coordinate system.

a) Show that the above distribution satisfies the following three dimensional diffusion equation:

(partial/partial t)c(r,t) = D (partial^2 / partial x^2 + partial^2 / partial y^2 + partial^2 / partial z^2) c(r, t)

b) Find out the expression for average distance <r> as a function of time, where <...> means average over c(r, t)

c) Find out the experession for average mean-square distance <r^2>

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. chemistry help asap???

    Why is boiling-point elevation a colligative property?
  2. Chemistry

    When 4.73 g of a nonelectrolyte solute is dissolved in 965 mL of water at 28 °C, the resulting solution exerts an osmotic pressure of 945 torr. What is the molar concentration of the solution?
  3. chemistry

    a. Find the amount of solute based on this information Volume = 500 ml Concentration of solution= 15% (w/w) Solute (molar mass) = H2SO4 is 98.0g/mol b. Find the molar mass Amount of solute= 117.0g Volume of solution= 2.00L concentration …
  4. chemistry

    a. Find the amount of solute based on this information Volume = 500 ml Concentration of solution= 15% (w/w) Solute (molar mass) = H2SO4 is 98.0g/mol b. Find the molar mass Amount of solute= 117.0g Volume of solution= 2.00L concentration …
  5. Chemistry

    When 4.54 g of a nonelectrolyte solute is dissolved in 565 mL of water at 29 °C, the resulting solution exerts an osmotic pressure of 835 torr. What is the molar concentration of the solution?
  6. Chemistry

    When 3.10 g of a nonelectrolyte solute is dissolved in water to make 755 mL of solution at 26 °C, the solution exerts an osmotic pressure of 821 torr. What is the molar concentration of the solution?
  7. Chemistry

    When 3.15 g of a nonelectrolyte solute is dissolved in water to make 135 mL of solution at 21 °C, the solution exerts an osmotic pressure of 869 torr. What is the molar mass of the solute?
  8. chemistry

    Which step during the dissolving process releases energy?
  9. chemistry

    Which answer choice correctly explains the role of the kinetic theory of matter in the process of solutes being dissolved into solvents?
  10. Calculus II

    Suppose a cell of volume V cc is surrounded by a homogeneous chemical solution of concentration C g/cc. Let y denote the concentration of the solute inside the cell at any time t and suppose that, initially, the concentration is y0. …

More Similar Questions