Question

You need a 55% alcohol solution. On hand, you have a 550 mL of a 95% alcohol mixture. How much pure water will you need to add to obtain the desired solution?​

Answer 1

We need to add 400 ml of pure water to obtain the solution at 55%

Explanation:

Concentration

The concentration of a solution measures the amount of solute that has been dissolved in a given amount of solution. The question states the alcohol is the solute and water is the solvent to produce the mix or solution.

The concentration can be calculated with the formula:

`\displaystyle c=(solute)/(solute+solvent)*100\%`

Originally, the mixture was 95% concentrated.

Substituting in the formula:

`\displaystyle 95\%=(solute)/(solute+solvent)*100\%`

We know there were 550 ml of solution (solute+solvent), thus

`solution*0.95=solute=522.5\ ml`

Now we know there were 522.5 ml of alcohol.

We now need to add x ml of water to have a 55% concentrated solution. Recall that water is solvent, the solute keeps its original value, thus:

`\displaystyle 55\%=(solute)/(550+x)*100\%`

Operating:

`0.55(550+x)=522.5`

Dividing by 0.55

`550+x=950`

Thus
`x=950-550=400`

We need to add 400 ml of pure water to obtain the solution at 55%