Answer :
To solve this problem, let's break down the task into manageable steps.
1. Identify the initial conditions and the amount of water added:
- Initial volume of the NaCl solution: [tex]\( V_{\text{initial}} = 125.0 \, \text{mL} \)[/tex]
- Initial concentration of the NaCl solution: [tex]\( M_{\text{initial}} = 0.150 \, \text{M} \)[/tex]
- Volume of water added: [tex]\( V_{\text{water added}} = 25.0 \, \text{mL} \)[/tex]
2. Calculate the final volume of the solution after adding water:
- The final volume [tex]\( V_{\text{final}} \)[/tex] is simply the sum of the initial volume and the volume of water added:
[tex]\[ V_{\text{final}} = V_{\text{initial}} + V_{\text{water added}} = 125.0 \, \text{mL} + 25.0 \, \text{mL} = 150.0 \, \text{mL} \][/tex]
3. Use the dilution formula to calculate the final concentration:
[tex]\[ M_{\text{final}} = \frac{M_{\text{initial}} \times V_{\text{initial}}}{V_{\text{final}}} \][/tex]
- Here, [tex]\( M_{\text{initial}} \)[/tex] is the initial molarity (concentration), [tex]\( V_{\text{initial}} \)[/tex] is the initial volume, and [tex]\( V_{\text{final}} \)[/tex] is the final volume after dilution.
4. Substitute the known values into the dilution formula:
[tex]\[ M_{\text{final}} = \frac{0.150 \, \text{M} \times 125.0 \, \text{mL}}{150.0 \, \text{mL}} \][/tex]
5. Perform the calculation:
[tex]\[ M_{\text{final}} = \frac{18.75 \, \text{M} \cdot \text{mL}}{150.0 \, \text{mL}} = 0.125 \, \text{M} \][/tex]
So, the new concentration of the NaCl solution after adding [tex]\( 25.0 \, \text{mL} \)[/tex] of water is [tex]\( 0.125 \, \text{M} \)[/tex].
- Final volume: [tex]\( 150.0 \, \text{mL} \)[/tex]
- Final concentration: [tex]\( 0.125 \, \text{M} \)[/tex]
1. Identify the initial conditions and the amount of water added:
- Initial volume of the NaCl solution: [tex]\( V_{\text{initial}} = 125.0 \, \text{mL} \)[/tex]
- Initial concentration of the NaCl solution: [tex]\( M_{\text{initial}} = 0.150 \, \text{M} \)[/tex]
- Volume of water added: [tex]\( V_{\text{water added}} = 25.0 \, \text{mL} \)[/tex]
2. Calculate the final volume of the solution after adding water:
- The final volume [tex]\( V_{\text{final}} \)[/tex] is simply the sum of the initial volume and the volume of water added:
[tex]\[ V_{\text{final}} = V_{\text{initial}} + V_{\text{water added}} = 125.0 \, \text{mL} + 25.0 \, \text{mL} = 150.0 \, \text{mL} \][/tex]
3. Use the dilution formula to calculate the final concentration:
[tex]\[ M_{\text{final}} = \frac{M_{\text{initial}} \times V_{\text{initial}}}{V_{\text{final}}} \][/tex]
- Here, [tex]\( M_{\text{initial}} \)[/tex] is the initial molarity (concentration), [tex]\( V_{\text{initial}} \)[/tex] is the initial volume, and [tex]\( V_{\text{final}} \)[/tex] is the final volume after dilution.
4. Substitute the known values into the dilution formula:
[tex]\[ M_{\text{final}} = \frac{0.150 \, \text{M} \times 125.0 \, \text{mL}}{150.0 \, \text{mL}} \][/tex]
5. Perform the calculation:
[tex]\[ M_{\text{final}} = \frac{18.75 \, \text{M} \cdot \text{mL}}{150.0 \, \text{mL}} = 0.125 \, \text{M} \][/tex]
So, the new concentration of the NaCl solution after adding [tex]\( 25.0 \, \text{mL} \)[/tex] of water is [tex]\( 0.125 \, \text{M} \)[/tex].
- Final volume: [tex]\( 150.0 \, \text{mL} \)[/tex]
- Final concentration: [tex]\( 0.125 \, \text{M} \)[/tex]
