To determine the correct method for preparing the solution, we need to use the dilution equation:
[tex]\[ M_1 \times V_1 = M_2 \times V_2 \][/tex]
where:
- [tex]\( M_1 \)[/tex] is the molarity of the stock solution (1.75 M),
- [tex]\( V_1 \)[/tex] is the volume of the stock solution needed,
- [tex]\( M_2 \)[/tex] is the molarity of the final solution (0.100 M),
- [tex]\( V_2 \)[/tex] is the volume of the final solution (2.00 L).
We need to solve for [tex]\( V_1 \)[/tex] (the volume of the 1.75 M stock solution):
1. Substitute the known values into the equation:
[tex]\[ 1.75 \, \text{M} \times V_1 = 0.100 \, \text{M} \times 2.00 \, \text{L} \][/tex]
2. Solve for [tex]\( V_1 \)[/tex]:
[tex]\[ V_1 = \frac{0.100 \, \text{M} \times 2.00 \, \text{L}}{1.75 \, \text{M}} \][/tex]
[tex]\[ V_1 = \frac{0.200 \, \text{M} \cdot \text{L}}{1.75 \, \text{M}} \][/tex]
[tex]\[ V_1 = 0.1142857142857143 \, \text{L} \][/tex]
3. Convert liters to milliliters (since 1 L = 1000 mL):
[tex]\[ V_1_{\text{ml}} = 0.1142857142857143 \, \text{L} \times 1000 \, \text{mL/L} \][/tex]
[tex]\[ V_1_{\text{ml}} = 114.28571428571429 \, \text{mL} \][/tex]
Therefore, you need to measure 114 mL of the 1.75 M stock solution and dilute it to a total volume of 2.00 L to obtain a 0.100 M solution.
This corresponds to the option:
Measure 114 mL of the 1.75 M solution, and dilute it to 2.00 L.
