To solve the problem given in solution stoichiometry, let's break down the steps to fill in the missing part of the equation. We are given an incomplete equation:
[tex]\[
\frac{(0.67 \text{ mol})\left(\frac{1 \text{ mL}}{10^{-3} \text{ L}}\right)}{(4.1 \square)} = 1.6 \times 10^2 \text{ mL}
\][/tex]
Step 1: Identify the components
- The numerator, which includes the moles and a conversion factor from liters to milliliters.
- The denominator, which appears to have a missing value.
Step 2: Understand the conversion
- [tex]\(0.67 \text{ mol}\)[/tex] is given.
- [tex]\( \frac{1 \text{ mL}}{10^{-3} \text{ L}} \)[/tex] represents the conversion from liters to milliliters.
Step 3: Calculate the product
First, let's multiply the moles by the conversion factor:
[tex]\[
0.67 \text{ mol} \times 10^3 \text{ mL} = 670 \text{ mL}
\][/tex]
Step 4: Plug in the known entities into the equation:
[tex]\[
\frac{670 \text{ mL}}{4.1 \square} = 1.6 \times 10^2 \text{ mL}
\][/tex]
Step 5: Solve for the unknown (the missing value in the denominator)
- Let [tex]\( \square \)[/tex] represent the missing value.
- Rearrange the equation to solve for [tex]\( \square \)[/tex]:
[tex]\[
4.1 \square = \frac{670 \text{ mL}}{1.6 \times 10^2 \text{ mL}}
\][/tex]
Step 6: Calculate the right-hand side:
[tex]\[
4.1 \square = \frac{670}{160} \text{ mL}
\][/tex]
[tex]\[
4.1 \square = 4.1875
\][/tex]
Step 7: Solve for [tex]\( \square \)[/tex]:
[tex]\[
\square = \frac{4.1875}{4.1}
\][/tex]
Simplifying:
[tex]\[
\square \approx 1.02
\][/tex]
Thus, the correct value that should fill the empty box is:
[tex]\[
4.1 \times 1.02 = 4.1875
\][/tex]
Step 8: Therefore, the final step of the equation:
[tex]\[
\frac{(0.67 \text{ mol})\left(\frac{1 \text{ mL}}{10^{-3} \text{ L}}\right)}{(4.1 \times 1.02)} = 1.6 \times 10^2 \text{ mL}
\][/tex]
The missing part of the student's equation should be [tex]\( \boxed{1.02} \)[/tex].
