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Chapter 1: Problem 51

Vinegar contains \(5.00 \%\) acetic acid by mass and has a density of \(1.01 \mathrm{~g} / \mathrm{mL}\). What mass (in grams) of acetic acid is present in \(5.00 \mathrm{~L}\) of vinegar?

Short Answer

Expert verified
Answer: The mass of acetic acid in 5 liters of vinegar is 252.5 grams.

Step by step solution

01

Convert volume to milliliters

To convert the volume of vinegar from liters to milliliters, we need to know that 1 liter is equal to 1000 milliliters. So, we simply multiply the volume in liters by this conversion factor: \(5.00 \mathrm{L} \times \frac{1000 \mathrm{mL}}{1 \mathrm{L}} = 5000 \mathrm{mL}\)
02

Calculate the mass of vinegar

To find the mass of vinegar, we use the density formula, which is: \(\text{Density} = \frac{\text{Mass}}{\text{Volume}}\) We want to find the mass, so we can rearrange the formula as: \(\text{Mass} = \text{Density} \times \text{Volume}\) Now, we can plug in the density of vinegar and the volume in milliliters that we found in step 1: \(\text{Mass} = (1.01 \mathrm{g/mL}) \times (5000 \mathrm{mL}) = 5050 \mathrm{g}\)
03

Find the mass of acetic acid

We know that the vinegar contains \(5.00 \%\) acetic acid by mass. This means that out of every 100 grams of vinegar, there are 5 grams of acetic acid. To find the mass of acetic acid in 5050 grams of vinegar, we simply multiply the total mass by the mass percentage: \(\text{Mass of acetic acid} = 5050\,\mathrm{g} \times 0.0500 = 252.5\,\mathrm{g}\) So, there are 252.5 grams of acetic acid in 5 liters of vinegar.

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