Chapter 5.8, Problem 8P

To determine

To find how much water must evaporated from a 300L tank of a 2% salt solution to obtain a 5% solution.

Answer to Problem 8P

The water must evaporated from a 300L tank of a 2% salt solution to obtain a 5% solution will be $180L$ .

Explanation of Solution

Given that 300L tank of a 2% salt solution to obtain a 5% solution.

Formula:

  $(\%solution)\times (Waterinliters)=\text{}Solution(Liters)$

First we need to determine the $2\%$ amount of salt solution from 300L tank

  $300\times \frac{2}{100}=6L\mathrm{...............}(i)$

Suppose the water $x\text{}L$ evaporating has no salt so, the salt solution in liter be $0\%$

Now, the $5\%$ the total amount of the solution be in remaining water tank will be $(300-x)$

  $\frac{5}{100}(300-x)=0.05(300-x)\mathrm{.............}(ii)$

Compare equation ( i ) and equation ( ii )

  $\begin{array}{c}6=0.05(300-x)\\ 6=15-\mathrm{0.05.}x\\ 0.05x=15-6\\ x=\frac{9}{0.05}=180\end{array}$

Hence, 180 L water must evaporated from a 300L tank of a 2% salt solution to obtain a 5% solution.