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I have a question on an assignment that I don't quite understand. It says:

What volume of $\pu{0.0100 mol/L}$ $\ce{NaOH(aq)}$ would have the same number of moles of hydroxide ions as $\pu{100.00 mL}$ of drano max gel?

The pH of drano max gel is $14.7$.

My first step was to switch from pH $14.7$ into mol/L. That turned out to be $\pu{5 mol/L}$ of $\pu{OH}$ concentration. Then I multiplied the $5$ by $\pu{100 mL}$ ($\pu{0.1 L}$) and got $\pu{0.5 mol}$. Now I don't understand how to get the volume needed. Would you use the formula for dilution ($C_1V_1 = C_2V_2$)?

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Yes.

If you have for drano $C_1 = \pu{5 mol/L}$ and $V_1 = \pu{0.1 L}$ that is $\pu{0.5 mol}$, and for $\ce{NaOH}$ $C_2 = \pu{0.01 mol/L}$ and $C_2 = x$. Using formula for dilution:

$$C_1V_1 = C_2V_2 \quad \implies \quad V_2 = \frac{C_1V_1}{C_2}$$

General tip: With encountering questions like these, always think about what units you have (mol/L, L etc.) and what units you want to go to. Most of the time, it gets clear when you just look at the units.

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