# Question 971d5

Oct 11, 2015

$1.66 \cdot {10}^{23} \text{atoms of H}$

#### Explanation:

The first thing to do here is write the chemical formula of ammonium sulfate, this will help you visualize how many atoms of hydrogen you get per formula unit.

SInce the ammonium cation, ${\text{NH}}_{4}^{+}$, has a 1+ charge, and the sulfate anion, ${\text{SO}}_{4}^{2 -}$, has a 2- charge, it follows that the chemical formula of ammonium sulfate will look like this

("NH"_4)_2"SO"_4

So, how many atoms of hydrogen would you get per formula unit of ammonium sulfate?

Since you need two ammonium cations to balance the negative charge of the sulfate anion, and each ammonium cation contains 4 hydrogen atoms, you get

$\text{no. of H atoms} = 2 \times 4 = 8$

To get how many atoms of hydrogen you get in $\text{4.56 g}$ of ammonium sulfate, you need to find how many moles of ammonium sulfate you get in that much mass of the compound.

To do that, use ammonium sulfate's molar mass

4.56color(red)(cancel(color(black)("g"))) * ("1 mole" ("NH"_4)_2"SO"_4)/(132.14color(red)(cancel(color(black)("g")))) = "0.03451 moles" ("NH"_4)_2"SO"_4

How many formula units would this many moles contain? Well, if one mole contain of ammonium sulfate contains $6.022 \cdot {10}^{23}$ formula units, you get that

0.03451color(red)(cancel(color(black)("moles"))) * (6.022 * 10^(23)"form. units")/(1color(red)(cancel(color(black)("mole")))) = 2.08 * 10^(22)"form. units"

Finally, if one formula unit contains 8 atoms of hydrogen, you will get

2.08 * 10^(22)color(red)(cancel(color(black)("form. units"))) * "8 atoms of H"/(1color(red)(cancel(color(black)("form. units")))) = color(green)(1.66 * 10^(23)"atoms of H")#