A bottle of 6.000 M NaOH is on the lab bench. You are instructed to use 75.00 mL of 0.5000 M NaOH. How much 6.000 M NaOH do you have to dilute to 75.00 mL to meet the requirement?

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To find the volume of 6.000 M NaOH needed to prepare 75.00 mL of 0.5000 M NaOH, use the dilution formula $M_1V_1 = M_2V_2$, where $M_1$ and $V_1$ are the molarity and volume of the concentrated solution, and $M_2$ and $V_2$ are the molarity and volume of the diluted solution. Plugging in the values: $6.000 \, \text{M} \times V_1 = 0.5000 \, \text{M} \times 75.00 \, \text{mL}$. Solving for $V_1$ gives $V_1 = \frac{0.5000 \times 75.00}{6.000} = 6.250 \, \text{mL}$.

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