To determine the units of the student's answer, let's analyze the given equation step-by-step:
[tex]\[
\frac{(0.63 \text{ mol}) \left(\frac{1 \text{ mL}}{10^{-3} \text{ L}}\right)}{\left(4.0 \frac{\text{ mol}}{\text{ L}}\right)} = ?
\][/tex]
First, let's clarify the units involved:
1. [tex]\(0.63 \text{ mol}\)[/tex] represents the amount of substance in moles.
2. [tex]\(\left(\frac{1 \text{ mL}}{10^{-3} \text{ L}}\right)\)[/tex] is a conversion factor; converting milliliters (mL) to liters (L). Since [tex]\(1 \text{ mL} = 10^{-3} \text{ L}\)[/tex], this factor effectively multiplies the number by [tex]\(10^3\)[/tex] and is dimensionless in this context.
3. [tex]\(4.0 \frac{\text{ mol}}{\text{ L}}\)[/tex] is the concentration in moles per liter (mol/L).
Now, plug these values into the equation and focus on the units:
[tex]\[
\frac{(0.63 \text{ mol}) \times (10^3)}{4.0 \frac{\text{ mol}}{\text{ L}}}
\][/tex]
Next, handle the units step-by-step:
1. Multiply [tex]\(0.63 \text{ mol}\)[/tex] by [tex]\(10^3\)[/tex], giving:
[tex]\[0.63 \text{ mol} \times 10^3 = 630 \text{ mol} \cdot \text{ mL} / \text{ L}\][/tex]
2. Then divide by the concentration [tex]\(4.0 \frac{\text{ mol}}{\text{ L}}\)[/tex]:
[tex]\[\frac{630 \text{ mol}}{4.0 \frac{\text{ mol}}{\text{ L}}} = 157.5 \text{ L}\][/tex]
Notice that the moles ([tex]\(\text{ mol}\)[/tex]) in the numerator and denominator cancel out, leaving us with the unit of liters (L):
[tex]\[
\frac{\text{ mol}}{\text{ mol} / \text{ L}} = \text{ L}
\][/tex]
So, the final result is in units of liters (L). Therefore, the student's answer should have the units:
[tex]\[
\boxed{L}
\][/tex]
