8.3

Limiting Reagent and Percent Yield in Chemical Reactions

Overview of Limiting Reagent

• Definition: The limiting reagent is the reactant that runs out first in a chemical reaction, thereby determining the maximum amount of product that can be formed.

• Reagent in Excess: This is a reactant that is present in a quantity greater than necessary to completely react with the limiting reagent. Typically, it is chosen because it is cheaper or easier to procure.

Key Concepts

Theoretical Yield

• Definition: The theoretical yield is the amount of product that could be formed in a reaction based on the stoichiometry of the balanced equation, assuming complete conversion of the limiting reagent.

• Dependence: The amount of product formed is directly related to the number of moles of the limiting reagent that is available.

Percent Yield

• Definition: The percent yield is a measure of the efficiency of a reaction, calculated as:
  $Percent ext{ }Yield = rac{Mass ext{ }Isolated ext{ }of ext{ }Desired ext{ }Product}{Theoretical ext{ }Yield} imes 100$

• Interpretation: A higher percent yield indicates a more efficient reaction.

Challenges in Reaching 100% Conversion

• Reaching 100% conversion in a chemical reaction is statistically difficult. As reactants are converted to products, the likelihood of collisions between reactant molecules decreases because fewer reactant molecules remain.

• To maximize conversion, an excess of one reactant is often employed, allowing for a greater chance of successful reactions to occur.

Example Scenario: Combustion of Propane

• Setup: In a propane grill, propane (C$3$H$8$) combusts with oxygen (from the atmosphere).

• Excess Reagent: Oxygen is plentiful and considered the reagent in excess.

• Limiting Reagent: Propane runs out first, stopping the reaction.

• Outcome: The production of carbon dioxide (CO$2$) and water (H$2$O) is based on the amount of propane reacted.

Example Calculation: Freon 12 Production

• Chemicals Involved: Carbon tetrachloride (CCl$4$), antimony trifluoride (SbF$3$).

• Chemical Reaction: CCl$4$ + SbF$3$ → Freon 12 + SbCl$_3$

• Balanced Chemical Equation: Runs through balancing for carbon, fluorine, and chlorine.

  • Example Balanced Reaction:
    $3 ext{ }CCl<em>4 + 2 ext{ }SbF</em>3 <br>ightarrow 3 ext{ }C<em>2F</em>2 + 2 ext{ }SbCl_3$

Steps for Calculation

1. Calculate Moles from Mass:

   • Carbon Tetrachloride (CCl$_4$) Molar Mass = 154 g/mol

   • Antimony Trifluoride (SbF$_3$) Molar Mass = 179 g/mol

2. Determine Limiting Reagent:

   • From 150 grams of CCl$_4$, convert to moles:

     • $ext{Moles of CCl}_4 = rac{150 ext{ g}}{154 ext{ g/mol}}$.

   • From 130 grams of SbF$_3$, convert to moles:

     • $ext{Moles of SbF}_3 = rac{130 ext{ g}}{179 ext{ g/mol}}$.

3. Calculate Theoretical Yield from the limiting reagent:

   • Identify that CCl$4$ is the limiting reagent as it produces less Freon 12 (118 g compared to 132 g from SbF$3$).

Percent Yield Calculation

• After isolating 80.2 grams of Freon 12, compute percent yield:

  • Percent ext{ }Yield = rac{80.2 ext{ g}}{118 ext{ g}} imes 100 = 68 ext{ c }

Reagent in Excess Calculation

• Calculate how much of the excess reagent (SbF$_3$) remains after the reaction.

  • Initial amount of SbF$_3$: 130 grams

  • Amount needed for complete reaction with limiting reagent (based on balanced equation process): 116 grams.

  • Remaining amount of excess:

  • Excess = Initial - Needed = 130 g - 116 g = 14 g.

Conclusion

• The concepts of limiting reagent, reagent in excess, theoretical yield, and percent yield are vital in chemical reaction assessments. Understanding these principles aids in maximizing reaction efficiencies and yields.