If 5.0 g of NaOH are dissolved in water to give 250.0 g total mass of solution, what is the % concentration (w/w)?

Your goal here is to figure out the number of grams of sodium hydroxide present for every #"100.0 g"# of this solution by using the fact that #"250.0 g"# of this solution contain #"5.0 g"# of sodium hydroxide.

In other words, you must figure out the solution's percent concentration by mass, #"m/m %"#.

Now, you know that you can use the known composition of the solution as a conversion factor to help you find the mass of sodium hydroxide present in #"100.0 g"# of the solution.

So, let's assume that you have a sample of this solution that has a mass of exactly #"100.0 g"#. Since you want to know the mass of solute present in this sample, set up your conversion factor like this

#(5.0 quad color(blue)("g NaOH"))/(250.0 quad color(darkorange)("g solution"))" " color(white)((color(black)(larr color(blue)(" what you need") quad "goes on top"color(white)(aaaaaa)))/(color(black)( larr color(darkorange)(" what you have") quad "goes on the bottom")#

You will have

#100.0 color(red)(cancel(color(black)("g soluton"))) * "5.0 g NaOH"/(250.0color(red)(cancel(color(black)("g soluton")))) = "2.0 g NaOH"#

Since this represents the number of grams of sodium hydroxide present in #"100.0 g"# of this solution, you can say that the solution's percent concentration by mass is equal to

#color(darkgreen)(ul(color(black)("% m/m = 2.0% NaOH")))#

The answer is rounded to two sig figs, the number of sig figs you have for the mass of sodium hydroxide present in the original solution.

Alternatively, you can find the solution's percent concentration by mass by simply dividing the number of grams of sodium hydroxide by the total mass of the solution and multiplying the result by #100%#.

#"% m/m" = "mass of solute"/"mass of solution" * 100%#

In your case, you have

#"% m/m" = (5.0 color(red)(cancel(color(black)("g"))))/(250.0color(red)(cancel(color(black)("g")))) * 100% = 2.0%#