The molecular weight of NaCl is 58.44 grams/mole. If you had a 1.0 molar solution (1.0 M), you would have to put 58.44 g of salt in 1.0 liter of solution. How many moles of NaCl would you have in 100 mL of this solution?
1 Answer
Explanation:
The thing to remember about any solution is that the particles of solute and the particles of solvent are evenly mixed.
My own work
This essentially means that if you start with a solution of known molarity and take out a sample of this solution, the molarity of the sample will be the same as the molarity of the initial solution.
In your case, you dissolve
If you take
100 color(red)(cancel(color(black)("mL"))) * "1 L"/(10^3color(red)(cancel(color(black)("mL")))) = "0.1 L"
of this solution, this sample must have the same concentration as the initial solution, i.e.
Notice that the volume of the sample is
(1color(red)(cancel(color(black)("L"))))/(0.1color(red)(cancel(color(black)("L")))) = color(blue)(10)
times smaller than the volume of the initial solution, so it follows that it must contain
Sodium chloride was said to have a molar mass of
Since the initial solution was made by dissolving the equivalent of
"58.44 g " = " 1 mole NaCl"
in
"1 mole NaCl"/color(blue)(10) = color(green)(|bar(ul(color(white)(a/a)color(black)("0.1 moles NaCl")color(white)(a/a)|)))
This is equivalent to saying that the
"58.44 g NaCl"/color(blue)(10) = "5.844 g NaCl"
ALTERNATIVELY
You can get the same result by using the formula for molarity, which is
color(blue)(|bar(ul(color(white)(a/a)c = n_"solute"/V_"solution"color(white)(a/a)|)))
Rearrange this equation to solve for
c = n_"solute"/V_"solution" implies n_"solute" = c * V_"solution"
n_"NaCl" = "1.0 mol" color(red)(cancel(color(black)("L"^(-1)))) * overbrace(100 * 10^(-3)color(red)(cancel(color(black)("L"))))^(color(blue)("volume in liters")) = color(green)(|bar(ul(color(white)(a/a)color(black)("0.1 moles NaCl")color(white)(a/a)|)))
Keep in mind that the volume must always be expressed in liters when working with molarity.