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Question 1.18: What volume of isopropanol (rubbing alcohol) would you use i...

What volume of isopropanol (rubbing alcohol) would you use if you needed 25.0 g? The density of isopropanol is 0.7855 g /mL at 20 °C.
ANALYSIS The known information is the mass of isopropanol needed (25.0 g). The density (0.7855 g /mL) acts as a conversion factor between mass and the unknown volume of isopropanol.

BALLPARK ESTIMATE Because 1 mL of isopropanol contains only 0.7885 g of the alcohol, obtaining 1 g of alcohol requires almost 20% more than 1 mL, or about 1.2 mL. Therefore, a volume of about 25 \times   1.2 mL = 30 mL is needed to obtain 25 g of alcohol.

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STEP 1: Identify known information. Mass of rubbing alcohol = 25.0 g
Density of rubbing alcohol = 0.7855 g/mL
STEP 2: Identify answer and units. Volume of rubbing alcohol = ?? mL
STEP 3: Identify conversion factors. Starting with the mass of isopropanol (in g), the corresponding volume (in mL) can be calculated using density (g/mL) as the conversion factor . Density = g/mL   \rightarrow    1/density = mL/g
STEP 4: Solve. Starting with the known information, set up the equation with conversion factors so that unwanted units cancel. 25.0 \cancel {g  alcohol}  \times \frac {1 mL  alcohol}{ 0.7855  \cancel {g  alcohol}}= 31.8 mL   alcohol

BALLPARK CHECK Our estimate was 30 mL.

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