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Question: How many milliliters of water must be added to \( 300ml \) of \( 70% \) alcoholic solution to make a...

How many milliliters of water must be added to 300ml300ml of 7070% alcoholic solution to make a 4040% alcoholic solution?

Explanation

Solution

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 c1V1=c2V2{{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 100100 parts of the solution. For example: alcohol solution means 10ml10ml of alcohol is present in 100ml100ml of solution.
Here, This is a dilution problem, so we can use the dilution formula;
c1V1=c2V2{{c}_{1}}{{V}_{1}}={{c}_{2}}{{V}_{2}}
Here we have, c1=71{{c}_{1}}=71%;{{V}_{1}}=300mL and c1=40{{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 mL225\text{ }mL of water to 300 mL300\text{ }mL of 70 70\text{ }% alcohol, and you would get 525 mL525\text{ }mL of 40 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.