# How many milliliters of a 25% (m/v) NaOH solution would contain 75 g of NaOH?

Apr 26, 2016

$3.0 \cdot {10}^{2} \text{mL}$

#### Explanation:

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A solution's mass by volume percent concentration, $\text{% m/v}$, essentially tells you how many grams of solute you get per $\text{100 mL}$ of solution.

$\textcolor{b l u e}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \text{% m/v" = "mass of solute"/"100 mL solution} \times 100 \textcolor{w h i t e}{\frac{a}{a}} |}}}$

In your case, a sodium hydroxide solution is said to have a $\text{25% m/v}$ concentration, which means that every $\text{100 mL}$ of this solution will contain $\text{25 g}$ of sodium hydroxide, $\text{NaOH}$.

Therefore, the volume of solution that will contain $\text{75 g}$ of sodium hydroxide will be

$75 \textcolor{red}{\cancel{\textcolor{b l a c k}{\text{g NaOH"))) * overbrace("100 mL solution"/(25color(red)(cancel(color(black)("g NaOH")))))^(color(purple)("= 25% m/v")) = color(green)(|bar(ul(color(white)(a/a)3.0 * 10^2"mL} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

The answer is rounded to two sig figs.

Or

Jun 17, 2016

$3.0 \cdot {10}^{2} \text{mL}$

#### Explanation:

A solution's mass by volume percent concentration, $\text{% m/v}$, tells you how many grams of solute you get per $\text{100 mL}$ of solution.

In your case, a $\text{25% m/v}$ solution of sodium hydroxide, $\text{NaOH}$, will contain $\text{25 g}$ of sodium hydroxide for every $\text{100 mL}$ of solution.

This means that you can use the solution's percent concentration as a conversion factor to help you determine how many milliliters would contain that many grams of sodium hydroxide.

75 color(red)(cancel(color(black)("g NaOH"))) * overbrace("100 mL solution"/(25color(red)(cancel(color(black)("g NaOH")))))^(color(blue)("= 25% m/v")) = color(green)(|bar(ul(color(white)(a/a)color(black)(3.0 * 10^2"mL")color(white)(a/a)|)))

The answer is rounded to two sig figs.