Question

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

Answer 1

`3.0 * 10^2"mL"`

Explanation:

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A solution's mass by volume percent concentration, `"% m/v"`, essentially tells you how many grams of solute you get per `"100 mL"` of solution.

`color(blue)(|bar(ul(color(white)(a/a)"% m/v" = "mass of solute"/"100 mL solution" xx 100color(white)(a/a)|)))`

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

Therefore, the volume of solution that will contain `"75 g"` of sodium hydroxide will be

`75 color(red)(cancel(color(black)("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"color(white)(a/a)|)))`

The answer is rounded to two sig figs.

Or

Answer 2

`3.0 * 10^2"mL"`

Explanation:

A solution's mass by volume percent concentration, `"% m/v"`, tells you how many grams of solute you get per `"100 mL"` of solution.

In your case, a `"25% m/v"` solution of sodium hydroxide, `"NaOH"`, will contain `"25 g"` of sodium hydroxide for every `"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.