To solve this problem, follow these detailed steps:
1. Understand the Given Values:
- Volume: [tex]\( 0.42 \)[/tex] liters (L)
- Conversion Factor: [tex]\( \frac{1 \, \text{mL}}{10^{-3} \, \text{L}} \)[/tex]
- Density: [tex]\( 2.16 \, \frac{\text{g}}{\text{mL}} \)[/tex]
- Molar Mass: [tex]\( 37.39 \, \frac{\text{g}}{\text{mol}} \)[/tex]
2. Convert Volume from Liters to Milliliters:
- The conversion factor [tex]\( \frac{1 \, \text{mL}}{10^{-3} \, \text{L}} \)[/tex] means that [tex]\( 1 \, \text{L} = 1000 \, \text{mL} \)[/tex].
- Therefore, [tex]\( 0.42 \, \text{L} = 0.42 \times 1000 \, \text{mL} = 420 \, \text{mL} \)[/tex].
3. Calculate the Mass in Grams:
- Using the density [tex]\( 2.16 \, \frac{\text{g}}{\text{mL}} \)[/tex]:
[tex]\[
420 \, \text{mL} \times 2.16 \, \frac{\text{g}}{\text{mL}} = 907.2 \, \text{g}
\][/tex]
4. Calculate the Number of Moles:
- Using the molar mass [tex]\( 37.39 \, \frac{\text{g}}{\text{mol}} \)[/tex]:
[tex]\[
\frac{907.2 \, \text{g}}{37.39 \, \frac{\text{g}}{\text{mol}}} = 24.263171971115273 \, \text{mol}
\][/tex]
5. Determine the Units of the Student's Answer:
- The final step involves understanding the units:
- Volume converted to mass is in grams (g).
- Mass converted to moles is in moles (mol).
Thus, the unit of the student's answer is [tex]\( \boxed{\text{mol}} \)[/tex].
