To determine the volume of stock solution needed to prepare the desired diluted solution, we can apply 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,
- [tex]\( V_1 \)[/tex] is the volume of the stock solution required,
- [tex]\( M_2 \)[/tex] is the molarity of the final diluted solution,
- [tex]\( V_2 \)[/tex] is the final volume of the diluted solution.
### Given Values:
- [tex]\( M_1 = 1.75 \, M \)[/tex] (molarity of the stock solution),
- [tex]\( M_2 = 0.100 \, M \)[/tex] (molarity of the final diluted solution),
- [tex]\( V_2 = 2.00 \, L \)[/tex] (final volume of the diluted solution).
### Rearranging the Dilution Equation:
To find [tex]\( V_1 \)[/tex]:
[tex]\[ V_1 = \frac{M_2 \times V_2}{M_1} \][/tex]
### Substituting the Given Values:
[tex]\[ V_1 = \frac{0.100 \, M \times 2.00 \, L}{1.75 \, M} \][/tex]
### Calculating [tex]\( V_1 \)[/tex]:
[tex]\[ V_1 = \frac{0.200 \, M \cdot L}{1.75 \, M} \][/tex]
[tex]\[ V_1 = 0.1142857142857143\, L \][/tex]
### Convert [tex]\( V_1 \)[/tex] to milliliters (mL):
[tex]\[ V_1 = 0.1142857142857143 \, L \times 1000 \, \text{mL/L} \][/tex]
[tex]\[ V_1 \approx 114.29 \, \text{mL} \][/tex]
So, in order to prepare 2.00 L of a 0.100 M [tex]\( NH_4NO_3 \)[/tex] solution from a 1.75 M stock solution, you should measure out approximately 114 mL of the 1.75 M stock solution and dilute it to a total volume of 2.00 L with water.
### Correct Choice:
The correct answer is:
Measure 114 mL of the 1.75 M solution, and dilute it to 2.00 L.
