You must add 75 mL water to 195 mL 90 % alcohol to make 270 mL of 65 % alcohol.
<em>Step 1.</em> Calculate the volume of 90 % alcohol needed
You can use the dilution formula
<em>V</em>1×<em>C</em>1 = <em>V</em>2×<em>C</em>2
where
<em>V</em>1 and<em> V</em>2 are the volumes of the two solutions
<em>C</em>1 and <em>C</em>2 are the concentrations
You can solve the above formula to get
<em>V</em>2 = <em>V</em>1 × <em>C</em>1/<em>C</em>2
<em>V</em>1 = 270 mL; <em>C</em>1 = 65 %
V2 = ?; _____<em>C</em>2 = 90 %
∴<em>V</em>2 = 270 mL × (65 %/90 %) = 195 mL
You need 195 mL of 90 % alcohol to make 270 mL of 65 % RA
<em>Step 2</em>. Calculate the amount of water to add.
Volume of water = 270 mL – 195 mL = 75 mL
