QuestionAdd how much water to $10 \mathrm{~mL}$ of $9 \%$ alcohol to make it $5 \%$ ? Answer in $\mathrm{mL}$ .

Studdy Solution

STEP 1

Assumptions1. The initial volume of the alcohol solution is10 mL. The initial concentration of the alcohol solution is9%
3. We want to reduce the concentration to5%
4. We are adding only water to the solution, which does not contain any alcohol

STEP 2

First, we need to find the initial amount of alcohol in the solution. We can do this by multiplying the initial volume of the solution by the initial concentration.
$Initial\, alcohol = Initial\, volume \\times Initial\, concentration$

STEP 3

Now, plug in the given values for the initial volume and initial concentration to calculate the initial amount of alcohol.
$Initial\, alcohol =10\, mL \\times9\%$

STEP 4

Convert the percentage to a decimal value.
$9\% =0.09$ $Initial\, alcohol =10\, mL \\times0.09$

STEP 5

Calculate the initial amount of alcohol.
$Initial\, alcohol =10\, mL \\times0.09 =0.9\, mL$

STEP 6

Now that we have the initial amount of alcohol, we can find the final volume of the solution. This can be done by dividing the initial amount of alcohol by the final concentration.
$Final\, volume = Initial\, alcohol / Final\, concentration$

STEP 7

Plug in the values for the initial amount of alcohol and the final concentration to calculate the final volume.
$Final\, volume =0.9\, mL /5\%$

STEP 8

Convert the percentage to a decimal value.
$5\% =0.05$ $Final\, volume =0.\, mL /0.05$

STEP 9

Calculate the final volume.
$Final\, volume =.9\, mL /.05 =18\, mL$

STEP 10

Now that we have the final volume, we can find the amount of water that needs to be added. This can be done by subtracting the initial volume from the final volume.
$Water\, added = Final\, volume - Initial\, volume$

STEP 11

Plug in the values for the final volume and the initial volume to calculate the amount of water that needs to be added.
$Water\, added =18\, mL -10\, mL$

STEP 12

Calculate the amount of water that needs to be added.
$Water\, added =18\, mL -10\, mL =8\, mL$ We need to add8 mL of water.

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