Stoichiometry Calculation: How To Determine Moles Of Substances After Reaction

In the fascinating realm of chemistry, stoichiometry reigns supreme as the art and science of quantifying chemical reactions. Stoichiometry allows us to predict the precise amounts of reactants needed and products formed in a chemical reaction. In this comprehensive exploration, we'll embark on a journey to unravel a quintessential stoichiometric problem: determining the maximum yield of carbon dioxide ($CO_2$) from the combustion of butane ($C_4H_{10}$) in the presence of oxygen ($O_2$).

The Chemical Equation: A Stoichiometric Roadmap

Our voyage begins with the balanced chemical equation, the cornerstone of stoichiometric calculations. This equation serves as a meticulous blueprint, delineating the precise molar ratios between reactants and products. For the combustion of butane, the balanced equation stands as follows:

$2 C_4 H_{10} + 13 O_2 \rightarrow 8 CO_2 + 10 H_2 O$

This equation, in its elegant simplicity, reveals that two moles of butane react with thirteen moles of oxygen to produce eight moles of carbon dioxide and ten moles of water. These coefficients, the numerical sentinels before each chemical formula, are the linchpins of our stoichiometric calculations, dictating the proportions in which reactants combine and products emerge.

Moles of Each Substance: The Initial Inventory

Our scientist embarks on this chemical endeavor with a carefully measured inventory: 1.69 moles of butane ($C_4H_{10}$) and 13.9 moles of oxygen ($O_2$). These quantities represent the starting materials, the fuel and oxidizer that will drive the reaction. To predict the maximum yield of carbon dioxide, we must first identify the limiting reactant, the reactant that will be completely consumed, thereby dictating the extent of the reaction.

Identifying the Limiting Reactant: The Stoichiometric Bottleneck

The limiting reactant is the unsung hero of stoichiometry, the reactant that holds the key to the reaction's maximum potential. To pinpoint this crucial reactant, we embark on a simple yet powerful calculation: we compare the mole ratio of the reactants to their stoichiometric coefficients.

For butane, we divide the initial moles (1.69 mol) by its coefficient in the balanced equation (2):

$1. 69 \text{ mol } C_4H_{10} / 2 = 0.845$

For oxygen, we perform the same calculation, dividing the initial moles (13.9 mol) by its coefficient (13):

$2. 9 \text{ mol } O_2 / 13 = 1.069$

The smaller value, 0.845, corresponds to butane. This signifies that butane is the limiting reactant, the reactant that will be exhausted first, thereby halting the reaction's progress. Oxygen, with its higher value, is the excess reactant, present in a surplus beyond what is needed to react with all the butane.

Calculating the Maximum $CO_2$ Yield: Stoichiometry in Action

With the limiting reactant identified, we can now calculate the maximum yield of carbon dioxide, the theoretical upper limit of product formation. We employ the stoichiometric ratio between butane and carbon dioxide, gleaned from the balanced equation:

$3. \text{ mol } C_4H_{10} \text{ produces } 8 \text{ mol } CO_2$

This ratio serves as our conversion factor, allowing us to translate moles of butane consumed into moles of carbon dioxide produced. Multiplying the moles of butane (1.69 mol) by this ratio, we obtain:

$4. 69 \text{ mol } C_4H_{10} \times (8 \text{ mol } CO_2 / 2 \text{ mol } C_4H_{10}) = 6.76 \text{ mol } CO_2$

Therefore, the maximum amount of carbon dioxide that can be produced from this reaction is 6.76 moles. This is the theoretical yield, the ideal outcome assuming perfect reaction conditions and no losses.

Determining Remaining Reactants: The Post-Reaction Landscape

Having calculated the maximum carbon dioxide yield, we can now paint a complete picture of the reaction's aftermath. We can determine the amount of excess reactant, oxygen, remaining after the reaction has reached completion.

First, we calculate the moles of oxygen consumed in the reaction. Using the stoichiometric ratio between butane and oxygen:

$5. 69 \text{ mol } C_4H_{10} \times (13 \text{ mol } O_2 / 2 \text{ mol } C_4H_{10}) = 10.985 \text{ mol } O_2$

This tells us that 10.985 moles of oxygen were consumed in the reaction. To find the amount of oxygen remaining, we subtract this value from the initial amount of oxygen (13.9 mol):

$6. 9 \text{ mol } O_2 - 10.985 \text{ mol } O_2 = 2.915 \text{ mol } O_2$

Thus, 2.915 moles of oxygen remain unreacted after the combustion of butane.

Accounting for Water Production: A Complete Stoichiometric Inventory

Finally, let's complete our inventory by calculating the amount of water ($H_2O$) produced in the reaction. Using the stoichiometric ratio between butane and water:

$7. 69 \text{ mol } C_4H_{10} \times (10 \text{ mol } H_2O / 2 \text{ mol } C_4H_{10}) = 8.45 \text{ mol } H_2O$

Therefore, 8.45 moles of water are produced in the combustion of 1.69 moles of butane.

Summary of Substance Amounts: A Chemical Census

In summary, after the reaction has reached completion:

• Butane ($C_4H_{10}$): 0 moles (completely consumed)
• Oxygen ($O_2$): 2.915 moles
• Carbon dioxide ($CO_2$): 6.76 moles
• Water ($H_2O$): 8.45 moles

This stoichiometric analysis provides a comprehensive understanding of the reaction's outcome, quantifying the amounts of reactants consumed and products formed. It highlights the power of stoichiometry in predicting chemical transformations and optimizing reaction yields.

Beyond the Ideal: Real-World Considerations

While our calculations provide a solid theoretical foundation, it's crucial to acknowledge that real-world reactions rarely achieve 100% theoretical yield. Factors such as incomplete reactions, side reactions, and product losses during separation and purification can all contribute to lower actual yields. The actual yield is the amount of product obtained in a laboratory setting, while the percent yield is the ratio of the actual yield to the theoretical yield, expressed as a percentage:

$8. ercent Yield = (Actual Yield / Theoretical Yield) \times 100$

Understanding these nuances is essential for chemists and chemical engineers striving to optimize chemical processes and maximize product output. In the realm of industrial chemistry, even small improvements in percent yield can translate into significant economic gains.

The Stoichiometric Symphony: A Harmony of Moles

Stoichiometry, at its core, is a symphony of moles, a delicate dance of chemical quantities. By mastering the principles of stoichiometry, we gain the power to predict and control chemical reactions, paving the way for advancements in fields ranging from medicine to materials science. The combustion of butane, a seemingly simple reaction, unveils the profound insights that stoichiometry offers, underscoring its central role in the chemical sciences.

What are the amounts in moles of each substance present after the reaction between 1.69 mol of butane ($C_4H_{10}$) and 13.9 mol of oxygen ($O_2$) given the reaction $2 C_4 H_{10}+13 O_2 \rightarrow 8 CO_2+10 H_2 O$?

Stoichiometry Calculation How to Determine Moles of Substances After Reaction