# Question 62d7e

Jul 27, 2017

Here's why we do that.

#### Explanation:

You know that ammonium dichromate has the following chemical formula

("NH"_ 4)_ 2"Cr"_ 2"O"_ 7

The chemical formula of ammonium dichromate tells you the number of atoms each constituent element contributes to the formula unit of this compound.

Now, when we want to distribute a subscript to more than one atom, we use parentheses. If no parentheses are present, then the subscript is only distributed to the atom that comes directly before it.

In this case, we have

("NH"_ 4)_ color(blue)(2) "Cr"_ 2 "O"_ 7 = {(color(blue)(2) xx "1 N" = 2 xx "N"), (color(blue)(2) xx "4 H" = 8 xx "H"), (color(white)(2 xx "1 N" = )2 xx "Cr"), (color(white)(2 xx "1 N" = )7 xx "O") :}

This means that $1$ mole of ammonium dichromate will contain

• two moles of nitrogen atoms, $2 \times \text{N}$
• eight moles of hydrogen atoms, $8 \times \text{H}$
• two moles of chromate atoms, $2 \times \text{Cr}$
• seven moles of oxygen atoms, $7 \times \text{O}$

So in order to find the mass of $1$ mole of ammonium dichromate, i.e. its molar mass, you need to add the molar masses of each individual atom that makes up this compound.

You will end up with

 2 xx "14.0067 g mol"^(-1) + color(white)(aaaa) -> color(blue)("2 moles of N")
8 xx "1.00794 g mol"^(-1)color(white)(aaaaaaa) -> color(blue)("8 moles of H")
2 xx "51.9961 g mol"^(-1)color(white)(aaaaaaa) -> color(blue)("2 moles of Cr")
7 xx "15.9994 g mol"^(-1)color(white)(aaaaaaa) -> color(blue)("7 atoms of O")#
$\frac{\textcolor{w h i t e}{a a a a a a a a a a a a a a a a a a}}{\textcolor{w h i t e}{a}}$
$\textcolor{w h i t e}{a a} {\text{252.06492 g mol"^(-1)color(white)(aaa) -> color(blue)("the molar mass of"color(white)(a)("NH"_4)_2"Cr"_2"O}}_{7}$