Stoichiometry of Limiting Reactants: Predicting Product Yield

📚 Stoichiometry of Limiting Reactants: Predicting Product Yield

Stoichiometry, derived from the Greek words stoicheion (element) and metron (measure), is the branch of chemistry that deals with the quantitative relationships between reactants and products in chemical reactions. When reactants are not present in perfect stoichiometric ratios, one reactant will be completely consumed before the others. This reactant is termed the limiting reactant because it limits the amount of product that can be formed. Identifying the limiting reactant is crucial for accurately predicting the yield of a reaction.

📜 A Brief History

The foundations of stoichiometry were laid in the late 18th century with the work of Antoine Lavoisier, who established the law of conservation of mass. Joseph Proust's law of definite proportions further contributed to the development of stoichiometry. However, it was John Dalton's atomic theory in the early 19th century that provided the theoretical basis for understanding and calculating the relationships between elements and compounds in chemical reactions.

🔑 Key Principles

• ⚖️Balanced Chemical Equations: The cornerstone of stoichiometry is a balanced chemical equation, which provides the molar ratios between reactants and products. Ensure each equation is balanced before proceeding. For example, consider the reaction: $2H_2 + O_2 \rightarrow 2H_2O$.
• 🧪Mole Ratios: Use the coefficients in the balanced equation to determine the mole ratios of reactants and products. In the previous example, 2 moles of $H_2$ react with 1 mole of $O_2$ to produce 2 moles of $H_2O$.
• 🔢Converting Mass to Moles: Convert the given masses of reactants to moles using their respective molar masses. Moles = Mass / Molar Mass.
• 🔎Identifying the Limiting Reactant: Divide the number of moles of each reactant by its stoichiometric coefficient in the balanced equation. The reactant with the smallest value is the limiting reactant.
• 📈Calculating Theoretical Yield: Once the limiting reactant is identified, use its moles and the appropriate mole ratio from the balanced equation to calculate the theoretical yield (maximum possible amount) of the product.
• 📉Calculating Percent Yield: The percent yield is the actual yield (experimentally obtained) divided by the theoretical yield, multiplied by 100. % Yield = (Actual Yield / Theoretical Yield) * 100.

🌍 Real-World Examples

• 🌾 Fertilizer Production: The Haber-Bosch process, $N_2(g) + 3H_2(g) \rightarrow 2NH_3(g)$, is used to synthesize ammonia, a key component of fertilizers. Stoichiometry and limiting reactants play a crucial role in maximizing ammonia production.
• 🚗 Combustion in Engines: The combustion of gasoline in car engines involves the reaction of hydrocarbons with oxygen. The air-fuel mixture must be optimized to ensure complete combustion and minimize pollutant formation. Stoichiometric calculations help determine the ideal air-fuel ratio.
• 💊 Pharmaceutical Synthesis: In drug manufacturing, precise stoichiometric control is essential to ensure the desired product yield and purity. Limiting reactants are carefully chosen to minimize the formation of unwanted byproducts.

📝 Worked Example

Consider the reaction between iron(III) oxide and carbon monoxide to produce iron and carbon dioxide:

$Fe_2O_3(s) + 3CO(g) \rightarrow 2Fe(s) + 3CO_2(g)$

If 160 g of $Fe_2O_3$ reacts with 84 g of $CO$, determine the limiting reactant and the theoretical yield of iron.

1. Calculate the moles of each reactant:
   • Molar mass of $Fe_2O_3$ = 159.69 g/mol. Moles of $Fe_2O_3$ = 160 g / 159.69 g/mol ≈ 1.002 mol.
   • Molar mass of $CO$ = 28.01 g/mol. Moles of $CO$ = 84 g / 28.01 g/mol ≈ 3.00 mol.
2. Determine the limiting reactant:
   • $Fe_2O_3$: 1.002 mol / 1 = 1.002
   • $CO$: 3.00 mol / 3 = 1.00
   • $CO$ is the limiting reactant.
3. Calculate the theoretical yield of iron:
   • From the balanced equation, 3 moles of $CO$ produce 2 moles of $Fe$.
   • Moles of $Fe$ = (3.00 mol $CO$) * (2 mol $Fe$ / 3 mol $CO$) = 2.00 mol $Fe$.
   • Molar mass of $Fe$ = 55.845 g/mol.
   • Theoretical yield of $Fe$ = 2.00 mol * 55.845 g/mol = 111.69 g.

✍️ Practice Quiz

Solve the following problems to test your understanding:

1. If 10.0 g of aluminum react with 35.0 g of copper(II) sulfate, what is the limiting reactant? $2Al(s) + 3CuSO_4(aq) \rightarrow Al_2(SO_4)_3(aq) + 3Cu(s)$
2. What mass of zinc is required to react with 6.00 g of hydrochloric acid? $Zn(s) + 2HCl(aq) \rightarrow ZnCl_2(aq) + H_2(g)$
3. If 4.0 g of hydrogen react with 4.0 g of oxygen, what mass of water will be produced? $2H_2(g) + O_2(g) \rightarrow 2H_2O(g)$
4. What is the limiting reactant when 5.0 g of silver nitrate reacts with 3.0 g of sodium chloride? $AgNO_3(aq) + NaCl(aq) \rightarrow AgCl(s) + NaNO_3(aq)$
5. How many grams of $CO_2$ are formed when 20.0 g of $C_6H_{12}O_6$ reacts with 20.0 g of $O_2$? $C_6H_{12}O_6(s) + 6O_2(g) \rightarrow 6CO_2(g) + 6H_2O(l)$

🎯 Conclusion

Understanding stoichiometry and limiting reactants is essential for accurate predictions in chemical reactions. By mastering these concepts, you can optimize reaction conditions and predict product yields in various chemical processes. Remember to always balance your equations and carefully convert between mass and moles for precise calculations.