Sure, let's fill in the missing part of the equation step by step.
Given the equation:
[tex]\[
\frac{\left(1.27 (1) \left(\frac{1 \text{ mL}}{10^{-3} \text{ L}}\right)\right)}{\left(2.8 \frac{\text{ mol }}{\text{ L }}\right)} = 4.5 \times 10^2 \text{ mL}
\][/tex]
1. First identify the parts of the equation:
- Numerator part: [tex]\(1.27 (1) \left(\frac{1 \text{ mL}}{10^{-3} \text{ L}}\right)\)[/tex]
- Denominator part: [tex]\(2.8 \frac{\text{ mol }}{\text{ L }}\)[/tex]
- Final value: [tex]\(4.5 \times 10^2 \text{ mL}\)[/tex]
2. Now, let's focus on calculating the numerator:
- The conversion factor [tex]\(\left(\frac{1 \text{ mL}}{10^{-3} \text{ L}}\right) \)[/tex] means converting [tex]\( \text{L} \)[/tex] to [tex]\( \text{mL} \)[/tex]:
[tex]\[
\frac{1 \text{ mL}}{10^{-3} \text{ L}} = 1000 \text{ mL}/\text{L}
\][/tex]
- Now multiplying this factor by [tex]\(1.27 \times 1\)[/tex]:
[tex]\[
1.27 \times 1 \times 1000 = 1270.0
\][/tex]
3. Now replace the numerator in the equation:
[tex]\[
\frac{1270.0}{2.8 \frac{\text{ mol}}{\text{ L}}} = 4.5 \times 10^2 \text{ mL}
\][/tex]
Finally, the completed equation is:
[tex]\[
\frac{1270.0}{2.8 \frac{\text{ mol}}{\text{ L}}} = 450.0 \text{ mL}
\][/tex]
However, in scientific notation, the right side of the equation is represented as [tex]\(4.5 \times 10^2 \text{ mL}\)[/tex], and [tex]\(450.0 \text{ mL}\)[/tex] are numerically the same. The missing part [tex]\(1270.0\)[/tex] has been carefully calculated and inserted back into the student's equation.
