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

2 Answers
Apr 26, 2016

Answer:

#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

Jun 17, 2016

Answer:

#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.