0 votes
35 views
in Physical Chemistry by (370 points)
A beaker containing 1L of water is divided into two equal compartments by a semi-permeable membrane. One side of the membrane has 1M NaCl solution and the other side is pure water. Determine the time taken for the concentration of NaCl on both sides of the membrane to become equal through diffusion. Given: Molecular weight of NaCl is 58.44 g/mol, and diffusion coefficient of NaCl in water is 1.6 x 10^-9 m^2/s.

1 Answer

0 votes
by (230 points)
To determine the time taken for the concentration of NaCl on both sides of the membrane to become equal through diffusion, we can use Fick's second law of diffusion. Fick's second law states that the rate of change of concentration with time is proportional to the second derivative of concentration with respect to distance.C/t = D *  d^2C/dx^2 Where C is the change in concentration, t is the change in time, D is the diffusion coefficient, and d^2C/dx^2 is the second derivative of concentration with respect to distance.In this case, we want to find the time it takes for the concentration of NaCl to become equal on both sides of the membrane. When the concentrations are equal, the change in concentration  C  will be zero. Therefore, we can set up the equation as follows:0 = D *  d^2C/dx^2 Since we are given the diffusion coefficient  D  of NaCl in water as 1.6 x 10^-9 m^2/s, we can plug this value into the equation:0 =  1.6 x 10^-9 m^2/s  *  d^2C/dx^2 To solve for the time  t , we need to integrate the equation with respect to time:t =  d^2C/dx^2  /  1.6 x 10^-9 m^2/s  dtUnfortunately, this equation cannot be solved analytically, as it requires knowledge of the concentration profile  C  as a function of distance  x  and time  t . However, we can estimate the time it takes for the concentrations to become equal using numerical methods or simulations.Alternatively, we can use the following equation to estimate the time it takes for the concentrations to become equal:t =  L^2  /  2 * D Where t is the time, L is the distance between the two compartments, and D is the diffusion coefficient.Assuming the distance between the two compartments is 0.1 m  since the beaker contains 1 L of water and is divided into two equal compartments , we can plug in the values:t =  0.1 m ^2 /  2 * 1.6 x 10^-9 m^2/s t  3.125 x 10^9 sThis is an approximate value, and the actual time it takes for the concentrations to become equal may be different due to factors such as the geometry of the beaker and the properties of the semi-permeable membrane. However, this estimation gives us an idea of the time scale involved in the diffusion process.

Related questions

Welcome to Sarvan Science Q&A, where you can ask questions and receive answers from other members of the community.
...