To calculate the time required for the eosin molecules to diffuse to a distance of 10 cm from the source of the solution, we can use Fick's second law of diffusion. Fick's second law states that the rate of change of concentration with respect to time is proportional to the second derivative of concentration with respect to position. Mathematically, it can be represented as:C/t = D * C/xwhere:C/t is the rate of change of concentration with respect to time,D is the diffusion coefficient,C/x is the second derivative of concentration with respect to position.However, to solve this problem, we can use a simplified version of Fick's second law, which is derived for one-dimensional diffusion in a semi-infinite medium:x = 2 * D * t where:x is the distance from the source of the solution,D is the diffusion coefficient,t is the time required for the molecules to diffuse to the distance x.We are given the distance x 10 cm and the diffusion coefficient D 2.5 x 10^-10 m^2/s . We need to find the time t.First, let's convert the distance x from cm to meters:x = 10 cm * 1 m / 100 cm = 0.1 mNow, we can rearrange the equation to solve for t:t = x / 2 * D Substitute the values of x and D:t = 0.1 m / 2 * 2.5 x 10^-10 m^2/s t = 0.01 m / 5 x 10^-10 m^2/s t = 0.01 m / 5 x 10^-10 m^2/s * 1 s / 1 x 10^-10 m^2 t = 0.01 / 5t = 0.002 sSo, the time required for the eosin molecules to diffuse to a distance of 10 cm from the source of the solution is 0.002 seconds.