Question

A solution contains 0.600 g of `Mg^(2+)` in enough water to make a 1930 mL solution. What is the concentration in milliequivalents per liter (mEq/L)?

Answer 1

`"25.6 mEq/L"`

Explanation:

Your strategy here will be use determine how many moles of magnesium your solution will contain by using magnesium's molar mass.

Once you know the number of moles of magnesium cations, you can determine how many equivalents you have.

So, magnesium has a molar mass of `"24.3050 g/mol"`. This means that one mole of magnesium cations will have a mass of `24.3050` grams.

In your case, the solution will contain

`0.600 color(red)(cancel(color(black)("g Mg"^(2+)))) * "1 mole Mg"^(2+)/(24.3050color(red)(cancel(color(black)("g Mg"^(2+))))) = "0.02469 moles Mg"^(2+)`

For an ion in aqueous solution, the number of equivalents will be equal to the number of moles of that ion multiplied by its valence.

`color(blue)("Eq" = "moles" xx "valence")`

As you know, magnesium has a valence of `2`, which is why it forms `(2+)` cations in solution. This means that you have

`"0.02469 moles Mg"^(2+) xx 2 = "0.04938 Eq Mg"^(2+)`

To express this value in milliequivalents, `"mEq"`, use the conversion factor

`"1 Eq" = 10^3"mEq"`

This will get you

`0.04938 color(red)(cancel(color(black)("Eq"))) * (10^3"mEq")/(1color(red)(cancel(color(black)("Eq")))) = "49.38 mEq"`

Finally, to get the magnesium cations' concentration in milliequivalents per liter, divide the number of mEq by the volume of the solution - do not forget to convert it to liters!

`["Mg"^(2+)] = "49.38 mEq"/(1930 * 10^(-3)"L") = color(green)("25.6 mEq/L")`