Let's solve the given equation step-by-step to determine the units of the student's answer.
The equation given is:
[tex]\[
\frac{\left(1.10 \frac{ g }{ mL }\right)\left(\frac{1 mL}{10^{-3} L}\right)}{\left(65.99 \frac{ g }{ mol }\right)}=\text { ? }
\][/tex]
Step 1: Identify the components of the equation.
- [tex]\(1.10 \frac{g}{mL}\)[/tex] is the density.
- [tex]\(\frac{1 mL}{10^{-3} L}\)[/tex] is the conversion factor from milliliters to liters.
- [tex]\(65.99 \frac{g}{mol}\)[/tex] is the molar mass.
Step 2: Analyze the units.
- The numerator [tex]\(\left(1.10 \frac{g}{mL}\right) \left(\frac{1 mL}{10^{-3} L}\right)\)[/tex] has units [tex]\(\frac{g}{mL} \times \frac{mL}{L}\)[/tex].
Since [tex]\(\frac{mL}{mL}\)[/tex] cancels out, leaving [tex]\(g/L\)[/tex], we are left with:
[tex]\[
\frac{1.10 \, g \times 10^{3} \, L^{-1}}{65.99 \frac{g}{mol}}
\][/tex]
Step 3: Simplify the units obtained so far.
- [tex]\(g\)[/tex] cancels out since there is [tex]\(g\)[/tex] in both the numerator and denominator.
This leaves us with [tex]\( \frac{L^{-1}}{mol^{-1}} = \frac{mol}{L} \)[/tex].
So, the final units of the student's answer are [tex]\(mol/L\)[/tex].
Therefore, the student's answer would be:
[tex]\[
\boxed{mol/L}
\][/tex]
