Find series to describe dilution of solution

Question

1 mole of a substance is dissolved in 400ml of water. 100ml of this solution are removed and replaced with 100ml of water. This process is repeated $n$ times.

I want to find a series to describe the amount of substance after $n$ repetitions of this process and finally calculate the limit of that sequence as $n\to\infty$.

I came up with $a_n=(\frac14)^n\cdot 1\text { mole}$ which has the limit $0$ such as I would expect it. Is this somewhat correct?

Answer 1

Assume that dissolving 1 mole does not change the volume so you have 400ml of solution containing 1 mole initially, that is $a_0=1$. At each stage you remove $1/4$ of the solution and replace it with water, that is you retain $3/4$ of the substance from the previous step.

So $a_{n+1}=(3/4)a_n$, and we have: $a_0=1$, $a_1=(3/4)\times a_0=3/4$, $a_2=(3/4)\times a_1=(3/4)^2$, $\dots a_n=(3/4)^n,\ \dots$

Answer 2

No that is wrong.

You start out with 400, take out 100 ml of solution and replace that with 100 ml pure water. So you have $a_i=(\frac{300}{400})^i\cdot 1\text { mole}$ where i = 0,1,2,3...n.