Sure, let's break down the equation and determine the units of the student's answer step-by-step.
The student has the following equation:
[tex]\[
\left(5.7 \frac{ \text{mol} }{ \text{L} }\right)\left(0.34 \text{L}\right)\left(112.30 \frac{ \text{g} }{ \text{mol} }\right)=\text{ ? } \square
\][/tex]
1. Identify the units of each term in the equation:
- [tex]\(5.7 \frac{ \text{mol} }{ \text{L} }\)[/tex] has units of [tex]\(\frac{ \text{mol} }{ \text{L} }\)[/tex]
- [tex]\(0.34 \text{L}\)[/tex] has units of [tex]\(\text{L}\)[/tex]
- [tex]\(112.30 \frac{ \text{g} }{ \text{mol} }\)[/tex] has units of [tex]\(\frac{ \text{g} }{ \text{mol} }\)[/tex]
2. Combine the units by multiplying term-by-term:
- First, combine [tex]\(5.7 \frac{ \text{mol} }{ \text{L} }\)[/tex] and [tex]\(0.34 \text{L}\)[/tex]:
[tex]\[
\left(5.7 \frac{ \text{mol} }{ \text{L} }\right) \times \left(0.34 \text{L}\right) = 5.7 \times 0.34 \left( \frac{ \text{mol} }{ \text{L} } \times \text{L} \right) = 5.7 \times 0.34 \text{mol}
\][/tex]
Notice that the liters (L) cancel out, leaving us with moles (mol).
- Next, take the result in moles and multiply by [tex]\(112.30 \frac{ \text{g} }{ \text{mol} }\)[/tex]:
[tex]\[
(5.7 \times 0.34 \text{mol}) \times \left(112.30 \frac{ \text{g} }{ \text{mol} }\right) = 5.7 \times 0.34 \times 112.30 \left( \text{mol} \times \frac{ \text{g} }{ \text{mol} } \right) = 5.7 \times 0.34 \times 112.30 \text{g}
\][/tex]
Here, the moles (mol) cancel out, leaving us with grams (g).
3. Conclusion:
- The remaining unit after canceling out in the multiplication process is grams (g).
So, the units of the student's answer are:
[tex]\[
\boxed{g}
\][/tex]
