Question

How many milliliters of water must be added to $ 300ml $ of $ 70% $ alcoholic solution to make a $ 40% $ alcoholic solution?

Answer 1

Hint :In this question, the concept of percentages will be used. The relation between the percentage and the amount of substance in a mixture is given by $ {{c}_{1}}{{V}_{1}}={{c}_{2}}{{V}_{2}} $ when two solutions of the same compound but of different molarity and volumes are added to obtain a new solution.

Complete Step By Step Answer:
First have to understand the term ‘solution’ and its properties. So, a solution is a homogeneous mixture of two or more substances. Homogeneous mixture means a mixture in which the solute particle is evenly present in the solvent. Here, in this question alcohol is a solute particle and water is solvent. The age strength of a solution is defined as the amount of solute present in per $ 100 $ parts of the solution. For example: alcohol solution means $ 10ml $ of alcohol is present in $ 100ml $ of solution.
Here, This is a dilution problem, so we can use the dilution formula;
 $ {{c}_{1}}{{V}_{1}}={{c}_{2}}{{V}_{2}} $
Here we have, $ {{c}_{1}}=71%;{{V}_{1}}=300mL $ and $ {{c}_{1}}=40%;{{V}_{1}}=? $
Now we need to calculate the volume of water we need to add to the initial solution to make the final solution. We can calculate this water to be added by substituting the given values of solution from the final solution.
 $ {{V}_{2}}={{V}_{1}}\times \dfrac{{{c}_{1}}}{{{c}_{2}}}=300mL\times \dfrac{70%}{40%}=525mL $
Thus, you would add $ 225\text{ }mL $ of water to $ 300\text{ }mL $ of $ 70\text{ }% $ alcohol, and you would get $ 525\text{ }mL $ of $ 40\text{ }% $ alcohol.

Note :
Remember we need to calculate the volume of water to be added to make the solution three moles. While solving these kinds of problems, we need to clearly understand the given information. We have to form algebraic equations for calculating the required values.