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

10.2 Real-World Applications of Equation Stoichiometry 381
Example 10.3 - Limiting Reactant
Titanium carbide, TiC, is the hardest of the known metal carbides. It can be made by
heating titanium(IV) oxide, TiO 2 , with carbon black to 2200 °C. (Carbon black is a
powdery form of carbon that is produced when vaporized heavy oil is burned with
50% of the air required for complete combustion.)
TiO 2 + 3C → TiC + 2CO
a. What is the maximum mass of titanium carbide, TiC, that can be formed from
the reaction of 985 kg of titanium(IV) oxide, TiO 2 , with 500 kg of carbon, C?
b. Why do you think the reactant in excess was chosen to be in excess?
Objective 6
Objective 7
Solution
a. Because we are given amounts of two reactants and asked to calculate an
amount of product, we recognize this as a limiting reactant problem. Thus we
first calculate the amount of product that can form from each reactant. The
reactant that forms the least product is the limiting reactant and determines
the maximum amount of product that can form from the given amounts of
reactants.
? kg TiC = 985 kg TiO 2
1 × 59.878 kg TiC
1 × 79.866 kg TiO 2
= 738 kg TiC
1 × 59.878 kg TiC
? kg TiC = 500 kg C = 831 kg TiC
3 × 12.011 kg C
The limiting reactant is TiO 2 because it results in the least amount of product.
b. We are not surprised that the carbon is provided in excess. We expect it to
be less expensive than titanium dioxide, and the excess carbon can be easily
separated from the solid product by burning to form gaseous CO or CO 2 .
Exercise 10.2 - Limiting Reactant
The uranium(IV) oxide, UO 2 , used as fuel in nuclear power plants has a higher
percentage of the fissionable isotope uranium-235 than is present in the UO 2 found
in nature. To make fuel grade UO 2 , chemists first convert uranium oxides to uranium
hexafluoride, UF 6 , whose concentration of uranium-235 can be increased by a process
called gas diffusion. The enriched UF 6 is then converted back to UO 2 in a series of
reactions, beginning with
UF 6 + 2H 2 O → UO 2 F 2 + 4HF
a. How many megagrams of UO 2 F 2 can be formed from the reaction of 24.543
Mg UF 6 with 8.0 Mg of water?
b. Why do you think the reactant in excess was chosen to be in excess?
Objective 6
Objective 7