Answer:
82.7 mL
Explanation:
We can use the dilution equation to solve this question. It represents that the initial molarity multiplied by its volume is equal to the final molarity multiplied by its volume. The reason this formula works is because molarity multiplied by volume gives moles, and moles stay constant during the dilution process.
[tex]\begin{document}\fbox{ \parbox{0.9\linewidth}{ \[ \textbf{Dilution Equation:}~ M_1V_1 = M_2V_2 \] - \( M_1 \): Initial molarity (2.00 M in the problem). \\ - \( V_1 \): Initial volume (248.1 mL in the problem). \\ - \( M_2 \):~Final molarity (1.50 M in the problem). \\ - \( V_2 \):~Final volume (calculated value in the problem). }}[/tex]
Solving:
We are solving for V2:
[tex]M_1V_1 = M_2V_2[/tex]
Divide M2 by both sides to get the equation in terms of V2:
[tex]V_2 = \frac{M_1 \times V_1}{M_2} ~~ \text{(Plug in given information)}\\\\V_2 = \frac{2.00 \, \text{M} \times 248.1 \, \text{mL}}{1.50 \, \text{M}} \\\\ V_2 = \frac{496.2 \, \text{mL}}{1.50} \\\\ \boxed{V_2 = 330.8 \, \text{mL} }[/tex]
Now that we have the final volume of water subtract it from the initial volume to find how much was added:
[tex]\text{Water added} = V_2 - V_1 \\\\\text{Water added} = 330.8 ~ \text{mL} - 248.1 ~\text{mL} \\\\ \text{Water added} = \boxed{82.7 ~ \text{mL} }[/tex]
Therefore, 82.7 mL of water was added.