calculating number of ions

Question

A sample of ammonium nitride ((NH₄)₃N) has a mass of 3.22 g.

(a) How many NH₄⁺ ions are present? 

 ions 

(b) How many N^3- ions are present? 

 ions 

Answer 1

To know how many ions there are, we need to know how many moles there are. So calculate the molar mass of (NH₄)₃N:

From the periodic table, Nitrogen = 14.007 g/mol and there 3 plus 1 or 4 atoms of N so: 56.028 for N

From the periodic table, Hydrogen = 1.008 g/mol and there 12 atoms of H so: 12.096 for H

Total for (NH₄)₃N = 68.124 g/mol

Since there are 3.22 g then there are 3.22/68.124 = 0.0472667 moles of (NH₄)₃N

Since there are 3 NH₄⁺ ions for each molecule of (NH₄)₃N then there are (3)(0.0472667) = 0.1418 moles of NH₄ ions. Each mole has 6.022 x 10²³ ions in it so there are (0.1418)(6.022 x 10²³) = 8.54 x 10²² NH₄⁺ ions

Since there is one N^3- ion for each molecule of (NH₄)₃N then there are 0.0472667 moles of N^3- ions. Each mole has 6.022 x 10²³ ions in it so there are (0.0472667)(6.022 x 10²³) = 2.85 x 10²² N^3- ions