# Question 24972

Apr 27, 2015

The molarity of the 1X Running Buffer will be 0.0035 M.

Start by looking at the 10X solution. You know that this buffer must have a 1% w/v percent concentration 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 percent concentration by mass unchanged, a larger volume will require more SDS present.

$\text{%w/v" = "grams of SDS"/"100 mL} \cdot 100$

"%w/v" = x/("1000 mL") * 100 => x = ("%w/v" * "1000 mL")/(100)

$x = \frac{1 \cdot 1000}{100} = \text{10 g SDS}$

To determine the molarity 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

$C = \frac{n}{V} = \text{0.03463 moles"/"1 L" = "0.03463 M}$

Because the concentration of a 10X solution is 10 times higher than the concentration of the 1X solution, the molarity of the 1X solution will be

${C}_{\text{1X" = C_"10X"/10 = "0.03463 M"/10 = "0.003463 M}}$

In other words, the 1X solution is obtained by diluting the 10X solution ten-fold.

I will leave the answer rounded to two sig figs, although your data indicates that it should be rounded to one sig fig

C_"1X" = color(green)("0.0035 M")#