Chapter 10 - An Introduction to Chemistry: Chemical Calculations ...

10.2 Real-World Applications of Equation Stoichiometry 379
Now let’s apply what we have learned from the bicycle example to a calculation that
deals with a chemical reaction. Electronic grade (EG) silicon used in the electronics
industry is a purified form of metallurgical grade silicon, which is made from the
reaction of silica, SiO 2 , with carbon in the form of coke at 2000 °C. (Silica is found in
nature as quartz or quartz sand.)
SiO 2 (s) + 2C(s)
2000 °C
Si(l ) + 2CO(g)
If 1000 moles of carbon are heated with 550 moles of silica, what is the maximum
number of moles of metallurgical grade silicon, Si, that can be formed? This example
is similar to the bicycle example. We need two times as many wheels as frames to build
bicycles, and to get a complete reaction of silicon dioxide and carbon, we need two
atoms (or moles of atoms) of carbon for every formula unit (or mole of formula units)
of silicon dioxide.
1 frame + 2 wheels → 1 bicycle
SiO 2 (s) + 2C(s)
→ Si(l ) + 2CO(g)
In the reaction between carbon and silicon dioxide, we can assume that one of the
reactants is in excess and the other is limiting, but we do not yet know which is which.
With the bicycle example, we discovered which component was limiting (and also the
maximum number of bicycles that can be made) by calculating the maximum number
of bicycles we could make from each component. The component that could make the
fewer bicycles was limiting and that number of bicycles was the maximum number of
bicycles that could be made.
For our reaction between carbon and silicon dioxide, we can determine which
reactant is the limiting reactant by first calculating the maximum amount of silicon
that can be formed from the given amount of each reactant. The reactant that forms
the least product will run out first and limit the amount of product that can form. The
coefficients in the balanced equation provide us with conversion factors to convert
from moles of reactants to moles of products.
? mol Si = 1000 mol C
? mol Si = 550 mol SiO 2
1 mol Si
2 mol C
1 mol Si
1 mol SiO 2
= 500 mol Si
= 550 mol Si
The carbon will be used up after 500 moles of silicon have been formed. The silicon
dioxide would not be used up until 550 moles of silicon were formed. Because the
carbon produces the least silicon, it runs out first and limits the amount of product that
can form. Therefore, the carbon is the limiting reactant, and the maximum amount of
product that can form is 500 moles Si.
Now let’s work a problem that is similar but deals with masses of reactants and
products rather than moles. If 16.491 g of carbon are heated with 32.654 g of silica,
what is the maximum mass of metallurgical grade silicon, Si, that can be formed?