Question

Question #de361

Answer 1

Here's how you can do that.

Explanation:

In order to convert the given concentration of sodium cations, `"Na"^(+)`, from milligrams per liter, `"mg L"^(-1)`, to millimoles per liter, `"mmol L"^(-1)`, you need to use the molar mass of elemental sodium.

Since you already know the concentration of the cations per liter, you can focus on converting milligrams to millimoles.

A sodium cation has the same molar mass as elemental sodium, `"Na"`

`M_M = "22.989770 g mol"^(-1)`

As you know, you can go from grams to milligrams by using the conversion factor

`color(purple)(|bar(ul(color(white)(a/a)color(black)("1 g" = 10^3"mg")color(white)(a/a)|)))`

You can use the same conversion factor to go from moles to millimoles

`color(purple)(|bar(ul(color(white)(a/a)color(black)("1 mol" = 10^3"mmol")color(white)(a/a)|)))`

This means that grams per mole,`"g mol"^(-1)`, will be equivalent to milligrams per millimole, `"mg mmol"^(-1)`, since

`[color(red)(cancel(color(black)("g")))/color(blue)(cancel(color(black)("mol"))) * (10^3"mg")/(1color(red)(cancel(color(black)("g")))) * (1color(blue)(cancel(color(black)("mol"))))/(10^3"mmol") = color(purple)(cancel(color(black)(10^3)))/color(purple)(cancel(color(black)(10^3)))"mg"/"mmol" = "1 mg mmol"^(-1)]`

This means that the molar mass of the sodium cations can be expressed as

`"22.989770 g mol"^(-1) = "22.989770 mg mmol"^(-1)`

You can use this value as a conversion factor to go from milligrams per liter to mmoles per liter

`8.034846159color(red)(cancel(color(black)("mg")))/"L" * "1 mmol Na"^(+)/(22.989770color(red)(cancel(color(black)("mg")))) = color(green)(|bar(ul(color(white)(a/a)"0.3494965870 mmol L"^(-1)color(white)(a/a)|)))`

I'll leave the answer rounded to ten sig figs, since that's how many sig figs you have for the concentration of the sodium cations.