The problem requires us to calculate the mass percentage of acetic acid in vinegar, given that vinegar must contain at least 40 grams of acetic acid per liter. We also need to determine if a tested vinegar sample complies with this guideline.
To find the mass percentage of acetic acid in vinegar, we use the formula for mass percentage:
\[
\text{Mass percentage} = \left( \frac{\text{mass of solute}}{\text{mass of solution}} \right) \times 100\%
\]
Given:
- Mass of acetic acid (solute) = 40 grams
- Volume of vinegar (solution) = 1 liter = 1000 mL
- Density of vinegar = 1.00 g/mL
First, calculate the mass of the vinegar solution:
\[
\text{Mass of solution} = \text{density} \times \text{volume} = 1.00 \, \text{g/mL} \times 1000 \, \text{mL} = 1000 \, \text{g}
\]
Now, calculate the mass percentage:
\[
\text{Mass percentage} = \left( \frac{40 \, \text{g}}{1000 \, \text{g}} \right) \times 100\% = 4.0\%
\]
To determine if the tested vinegar complies with federal guidelines, we need to know the mass of acetic acid in the tested sample. However, the problem does not provide this information, so we cannot answer this part without additional data.
- The mass percentage of acetic acid in vinegar must be \(\boxed{4.0\%}\).
- Additional data is needed to determine if the tested vinegar complies with federal guidelines.