Question

What volume of ethyl alcohol and water must be mixed together to prepare $250ml$of $60\%$ by volume solution of alcohol in water?

Answer 1

For answering this question we should know about the concept of expressing concentration. Concentration can be expressed in various types such molarity which is number of moles per litre solution, mole fraction (number of moles of solute by total number of moles of substance), mass percentage (ratio of mass of solute to the mass of solution times $100$ ), volume percentage (ratio of volume of solute to the volume of solution times $100$ ) and some other types.

Complete answer:
We are given concentration in terms of volume percentage we will calculate the ratio of Volume of solute to the solution. we will use the following formula
$\dfrac{{{V_{solute}}}}{{{V_{solution}}}} \times 100 = X$
here ${V_{solute}}$is the volume of the solute, ${V_{solution}}$ is the volume of the solution and X is the volume percentage of solute in the solution. Let’s write the given values
Volume percentage of Ethyl alcohol, ${X_{alc.}} = 60$
Volume of the solution, ${V_{solution}} = 250ml$
Substituting the value in the above mentioned formula for calculating the volume percentage, we get
$\dfrac{{{V_{alc.}}}}{{250}} \times 100 = 60$
we get the result
${V_{alc.}} = 150ml$
Volume of ethyl alcohol is $150ml$
Now for calculating the volume of water we will subtract the volume of ethyl alcohol from the volume of the solution.
${V_{solution}} - {V_{alc.}} = {V_{water}}$
${V_{water}} = 250 - 150$
we get the Volume of water
${V_{water}} = 100ml$
So, for preparing $250ml$of $60\%$ by volume solution of alcohol in water, $150ml$ of ethyl alcohol is required and $100ml$ of water is required.

Note:
Careful when doing the calculation, you should mention volume of solute and volume of solution separately. Also be sure to check the unit of volume if the volume of solution is given in litres, then you have to convert the volume of solute and solvent to litres.