A Chem major obtains a high-paying summer job and is given the task of determining the ethanol content (in vol %) of a commercial mouthwash sample. she decides to use gas chromatography because the experiment was so much fun in Chem 209. Accordingly, the student takes exactly 5.0 mL of the mouthwash sample and dilutes this to 30.0 mL with deionized water. He/she then injects 2.0 µL of the diluted sample into the GC and obtains a chromatogram containing two peaks. The first peak, which corresponds to ethanol, has a retention time of 58 seconds and an area of 282. The student then makes up several standard ethanol solutions ranging from 0 to 30% ethanol (vol %), injects 2.0 µL of each into the GC, and uses the areas of the ethanol peak to make a calibration curve whose linear regression equation is: y = 174.2 x + 3.2
What is the ethanol content of the mouthwash sample?