To determine the units of the student's answer for the given multiplication, let's carefully analyze the units involved in the calculation:
Given equation:
[tex]\[ \left(6.1 \frac{\text{mol}}{\text{L}}\right) (0.33 \text{ L}) \left(75.62 \frac{\text{g}}{\text{mol}}\right) = ? \][/tex]
1. Start with the units in the first term:
[tex]\[ 6.1 \frac{\text{mol}}{\text{L}} \][/tex]
This term has units of moles per liter (mol/L).
2. Look at the units in the second term:
[tex]\[ 0.33 \text{ L} \][/tex]
This term is in liters (L).
3. Finally, consider the units in the third term:
[tex]\[ 75.62 \frac{\text{g}}{\text{mol}} \][/tex]
This term has units of grams per mole (g/mol).
Now, multiply the units together:
[tex]\[ \left(\frac{\text{mol}}{\text{L}}\right) \cdot (\text{L}) \cdot \left(\frac{\text{g}}{\text{mol}}\right) \][/tex]
4. When multiplying these units together, observe that the liters (L) in the numerator and denominator will cancel each other out:
[tex]\[ \left(\frac{\text{mol}}{\text{L}} \cdot \text{L}\right) = \text{mol} \][/tex]
5. Now, you are left with:
[tex]\[ \text{mol} \cdot \left(\frac{\text{g}}{\text{mol}}\right) \][/tex]
6. Notice that the moles (mol) in the numerator and denominator will also cancel each other out:
[tex]\[ \text{mol} \cdot \left(\frac{\text{g}}{\text{mol}}\right) = \text{g} \text{ (grams)} \][/tex]
So the resulting units are grams (g). Therefore, the units of the student's answer are:
[tex]\[ g \][/tex]
Thus, the expected units for the student's answer are [tex]\( \boxed{g} \)[/tex].
