Answer:
The present percentage of pure alcohol in the solution is 72.25% of pure alcohol
Step-by-step explanation:
The volume of pure alcohol poured from the 2 l bottle of pure alcohol = 300 ml of pure alcohol
The volume of water added into the bottle after pouring out the pure alcohol = 300 ml of water
The volume of diluted alcohol poured out of the bottle = 300 ml of diluted alcohol
The volume of water added into the bottle of diluted alcohol after pouring out the 300 ml of diluted alcohol = 300 ml of water
Step 1
After pouring the 300 ml of pure alcohol and adding 300 ml of water to the bottle, the percentage concentration, C%₁ is given as follows;
C%₁ = (Volume of pure alcohol)/(Total volume of the solution) × 100
The volume of pure alcohol in the bottle = 2 l - 300 ml = 1,700 ml
The total volume of the solution = The volume of pure alcohol in the bottle + The volume of water added = 1,700 ml + 300 ml = 2,000 ml = 2 l
∴ C%₁ = (1,700 ml)/(2,000 ml) × 100 = 85% percent alcohol
Step 2
After pouring out 300 ml diluted alcohol from the 2,000 ml, 85% alcohol and adding 300 ml of water, we have;
Volume of 85% alcohol = 2,000 ml - 300 ml = 1,700 ml
The volume of pure alcohol in the 1,700 ml, 85% diluted alcohol = 85/100 × 1,700 = 1,445 ml
The total volume of the diluted solution = The volume of the 85% alcohol in the solution + The volume of water added
∴ The total volume of the twice diluted solution = 1,700 ml + 300 ml = 2,000 ml
The present percentage of pure alcohol in the solution, C%₂ = (The volume of pure alcohol in the 1,700 ml, 85% diluted alcohol)/(The total volume of the diluted solution) × 100
∴ C%₂ = (1,445 ml)/(2,000 ml) × 100 = 72.25 %
The present percentage of pure alcohol in the solution, C%₂ = 72.25%
