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QUESTION

# What is the molar mass of magnesium nitride, "Mg"_3"N"_2, if the mass of one mole of magnesium is 24.31 g and of one mole of nitrogen is 14.01 g?

"100.95 g mol"^(-1)

The idea here is that you need to use the chemical formula for magnesium nitride, "Mg"_3"N"_2, to calculate the mass of one mole of the compound, i.e. its molar mass.

So, magnesium nitride is an ionic compound made up of magnesium cations, "Mg"^(2+), and nitride anions, "N"^(3-). The subscripts used in the compound's chemical formula tell you how many ions you get in one formula unit of magnesium nitride.

In this case, you have

"Mg"_ color(red)(3) "N"_ color(blue)(2) -> color(red)(3)"Mg"^color(blue)(2+) + color(blue)(2)"N"^color(red)(3-)

So, one formula unit of magnesium nitride contains color(red)(3) magnesium cations and color(blue)(2) nitride anions.

This means that one mole of magnesium nitride will contain color(red)(3) moles of magnesium cations and color(blue)(2) moles of nitride anions.

Now, you know that one mole of magnesium has a mass of "24.31 g". Since you get three moles of magnesium cations per mole of the compound, magnesium's contribution to the molar mass will be

color(red)(3) color(red)(cancel(color(black)("moles Mg"^(2+)))) * "24.31 g"/(1color(red)(cancel(color(black)("mole Mg"^(2+))))) = "72.93 g"

Likewise, you know that one mole of nitrogen has a mass of "14.01 g". Since you get two moles of nitride anions per mole of the compound, nitrogen's contribution will be

color(blue)(2) color(red)(cancel(color(black)("moles N"^(3-)))) * "14.01 g"/(1color(red)(cancel(color(black)("mole N"^(3-))))) = "28.02 g"

Therefore, the total mass of one mole of magnesium nitride will be

"72.93 g" + "28.02 g" = "100.95 g"

Since this is how many grams you get per mole, you can say that the molar mass will be

"molar mass" = color(green)(|bar(ul(color(white)(a/a)color(black)("100.95 g mol"^(-1))color(white)(a/a)|)))

I'll leave the answer rounded to five , despite the fact that you only have four sig figs for the molar masses of the two .