Question

If given 0.090 moles of sodium sulfate in 12 mL of solution, what is the concentration?

Answer 1

`"7.5 M"`

Explanation:

In order to find a solution's molar concentration, or molarity, you need to determine how many moles of solute, which in your case is sodium sulfate, `"Na"_2"SO"_4`, you get in one liter of solution.

That is how molarity was defined -- the number of moles of solute in one liter of solution.

So, you know that you have `0.090` moles of solute in `"12 mL"` of solution. Your goal here will be to scale up this solution by using this information as a conversion factor to help you determine the number of moles of solute present in

`"1 L" = 10^3"mL"`

of solution. Convert the volume from milliliters to liters first

`12 color(red)(cancel(color(black)("mL"))) * "1 L"/(10^3color(red)(cancel(color(black)("mL")))) = "0.012 L"`

If `"0.012 L"` of solution contain `0.090` moles of solute, it follows that `"1 L"` will contain

`1 color(red)(cancel(color(black)("L solution"))) * ("0.09 moles Na"_2"SO"_4)/(0.012color(red)(cancel(color(black)("L solution")))) = "7.5 moles Na"_2"SO"_4`

So, if `"1 L"` of solution contains `7.5` moles of solute, it follows that the solution's molarity is

`"molarity" = color(green)(|bar(ul(color(white)(a/a)color(black)("7.5 mol L"^(-1) = "7.5 molar" = "7.5 M")color(white)(a/a)|)))`

The answer is rounded to two sig figs.