To determine the molarity of the resulting solution when 100 mL of 1 M NaOH is titrated against 50 mL of HCl, we need to follow a step-by-step approach. Here's the detailed explanation:
1. Identify the given values:
- Volume of NaOH solution: 100 mL
- Molarity of NaOH solution: 1 M
- Volume of HCl solution: 50 mL
2. Calculate the moles of NaOH:
- Moles of NaOH can be found using the formula:
[tex]\[
\text{moles of NaOH} = \text{molarity of NaOH} \times \text{volume of NaOH in liters}
\][/tex]
Converting 100 mL to liters (since 1 L = 1000 mL):
[tex]\[
100 \, \text{mL} = 0.100 \, \text{L}
\][/tex]
Thus,
[tex]\[
\text{moles of NaOH} = 1 \, \text{M} \times 0.100 \, \text{L} = 0.1 \, \text{moles}
\][/tex]
3. Total volume of the resulting solution:
- The total volume is the sum of the volumes of the NaOH and HCl solutions:
[tex]\[
\text{total volume} = 100 \, \text{mL} + 50 \, \text{mL} = 150 \, \text{mL}
\][/tex]
Converting 150 mL to liters:
[tex]\[
150 \, \text{mL} = 0.150 \, \text{L}
\][/tex]
4. Calculate the molarity of the resulting solution:
- Molarity (M) is defined as the number of moles of solute per liter of solution. The solute here is NaOH and its moles are 0.1 as calculated above. The total volume of the solution is 0.150 L. Thus, the molarity (M) can be calculated as:
[tex]\[
\text{Molarity} = \frac{\text{moles of solute}}{\text{liters of solution}} = \frac{0.1 \, \text{moles}}{0.150 \, \text{L}} = 0.6667 \, \text{M}
\][/tex]
So the resulting solution has a total volume of 150 mL, contains 0.1 moles of NaOH, and has a molarity of approximately 0.6667 M.
