Question

How many kilograms of water must be evaporated from 40kg of a 10% salt solution to produce a 25% solution?

Answer 1

Hint: In the above question, it is asked how much kilograms of water needs to be evaporated from 40kg so that the salt concentration changes from 10% to 25%. Here, since, the water has evaporated, the concentration of salt is constant. So, first we have to find the concentration of salt from the 40kg then we have to find the concentration of solution when 25% salt is present. Then, by subtracting the mass of salt from the solution, we can get the amount of water that needs to be evaporated.

Formula Used
Weight of salt = percentage of weight of solution.

Complete step by step solution
In the above question, initially 40kg of solution is present and we have to find out c
concentration of salt.
Weight of salt = 10% of weight of the solution= $\dfrac{{{{10}}}}{{{{100}}}}{{ \times 40 = 4}}$ kg.
Now, we know the weight of salt and its percentage in a solution. So, the weight of the solution which contains 25% salt can be obtained by:
Weight of salt = $\dfrac{{{{25}}}}{{{{100}}}}{{ \times }}$ Weight of solution, which implies that:
Weight of solution = $\dfrac{{{{100}}}}{{{{25}}}}{{ \times }}$Weight of salt = $\dfrac{{{{100}}}}{{{{25}}}}{{ \times 4 = 16}}$ kg
Mass of water evaporated = ${{40 - 16 = 24}}$ kg
Therefore, the weight of water that is evaporated is equal to 24kg.

Note
In these types of questions, where concentration of salt is changing without changing the amount of salt in that solution, then, we can use simple mathematics to calculate the amount of water in the latter case. And hence, mass of water evaporated can be found.