Start by looking at the 10X solution. You know that this must have a 1% w/v of sodium dodecyl sulfate (SDS), and that you have 1-L of solution.
A 1% w/v solution will contain 1 g of SDS in 100 mL of solution, which means that, in order to keep the by mass unchanged, a larger volume will require more SDS present.
##”%w/v” = “grams of SDS”/”100 mL” * 100##
##”%w/v” = x/(“1000 mL”) * 100 => x = (“%w/v” * “1000 mL”)/(100)##
##x = (1 * 1000)/100 = “10 g SDS”##
To determine the of the 10X solution, use the molar mass given to calculate how many moles of SDS are present
##10cancel(“g SDS”) * “1 mole SDS”/(288.8cancel(“g SDS”)) = “0.03463 moles SDS”##
Since you have 1 L of solution, you’ll get
##C = n/V = “0.03463 moles”/”1 L” = “0.03463 M”##
Because the concentration of a 10X solution is 10 times higher than the concentration of the 1X solution, the of the 1X solution will be
##C_”1X” = C_”10X”/10 = “0.03463 M”/10 = “0.003463 M”##
In other words, the 1X solution is obtained by the 10X solution ten-fold.
I will leave the answer rounded to two , although your data indicates that it should be rounded to one sig fig
##C_”1X” = color(green)(“0.0035 M”)##
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