## Mass-Mass Calculation Example Three: Aluminum Oxide Reacts with Chlorine and Carbon

How many grams of solid carbon, C(s), can be consumed when 21.9g of chlorine gas, Cl(g), is consumed?

The first step is to convert chlorine’s gram quantity to moles of chlorine gas, Cl(g). The second step uses the stoichiometry of the balanced equation

1AlO(s)+3Cl(g)+3C(s)2AlCl(aq)+3CO(g)

to find the moles solid carbon, C(s),  consumed in the reaction. In the third step the molar amount of solid carbon, C(s), consumed is then converted to grams of solid carbon, C(s), consumed.

Step 1: One mole of of chlorine gas, Cl(g)  is 70.90 grams/mole and is found using the sum of the gram atomic mass of 2 chlorine atoms(35.45g) from the periodic table. The formula mass calculation is as follows.

Element   Subscript   X   Element Mass = Formula Mass

Cl               2            X        35.45g           =    70.90g

The molar mass of chlorine gas, Cl(g), 70.90g /m is used to find the moles of chlorine gas, Cl(g), consumed.  Dividing the given 21.9 grams chlorine gas, Cl(g), by the 70.90 grams/mole for chlorine gas, Cl(g), produces moles of chlorine gas, Cl(g), consumed during reaction.

21.9g Cl(g),  ÷ (70.90g Cl(g)/1m Cl(g))= 0.309m Cl(g),

21.9 grams chlorine gas, Cl(g), is equal to 0.309 moles of grams chlorine gas, Cl(g).

Step 2: The 0.309 moles of chlorine gas, Cl(g), must be converted to moles solid carbon, C(s), consumed using the balanced equation

1AlO(s)+ 3Cl(g)+ 3C(s)2AlCl(aq)+3CO(g)

0.309m  Cl(g) X (3m C(s)/3m Cl(g)= 0.309m C(s)

Step 3:  The 0.309m solid carbon, C(s), must be converted to grams. The formula mass for solid carbon, C(s), is found by the following formula mass calculation using the gram atomic mass of carbon(12.01g) from the periodic table.

Element   Subscript    X   Element Mass = Formula Mass

C               1            X        12.01g           =    12.01g

The molar mass of solid carbon, C(s), is 12.01g/m.

0.309m C(s)X (12.01g /1m C(s)) = 3.71g  (s)

Therefore, 3.71 grams of carbon, C(s), is consumed at the same time 21.9g of chlorine gas, Cl(g), is consumed.