Theoretical Yield Calculation Citric Acid And Baking Soda Reaction

Introduction

In this article, we will delve into the fascinating world of stoichiometry and explore how to calculate the theoretical yield of a chemical reaction. Specifically, we will focus on the reaction between citric acid ($H_3C_6H_5O_7$) and baking soda ($NaHCO_3$), a common household experiment that produces carbon dioxide ($CO_2$). The theoretical yield is a crucial concept in chemistry, representing the maximum amount of product that can be formed from a given amount of reactants, assuming perfect reaction conditions and no loss of product during the process. Understanding how to calculate this yield is essential for chemists and anyone interested in the quantitative aspects of chemical reactions.

Stoichiometry: The Language of Chemical Reactions

Before diving into the specific calculation, it's important to grasp the fundamental principles of stoichiometry. Stoichiometry is the branch of chemistry that deals with the quantitative relationships between reactants and products in chemical reactions. It's like the grammar and syntax of the chemical world, allowing us to predict how much of each substance is needed or produced in a reaction. The balanced chemical equation is the cornerstone of stoichiometry, providing the mole ratios between the different species involved. In our case, the balanced equation for the reaction between citric acid and baking soda is:

$H_3C_6H_5O_7 + 3NaHCO_3 \rightarrow 3CO_2 + 3H_2O + Na_3C_6H_5O_7$

This equation tells us that one mole of citric acid reacts with three moles of baking soda to produce three moles of carbon dioxide, three moles of water, and one mole of trisodium citrate. These mole ratios are the key to calculating theoretical yields. Using stoichiometry to predict theoretical yield is an important skill to master in chemistry.

Problem Statement: Determining the Theoretical Yield of Carbon Dioxide

Let's consider the problem at hand. We have a 13.00 g sample of citric acid ($H_3C_6H_5O_7$) reacting with an excess of baking soda ($NaHCO_3$). The balanced chemical equation for this reaction is:

$H_3C_6H_5O_7 + 3NaHCO_3 \rightarrow 3CO_2 + 3H_2O + Na_3C_6H_5O_7$

The question we aim to answer is: What is the theoretical yield of carbon dioxide ($CO_2$) in this reaction? To solve this, we need to follow a step-by-step approach, converting the mass of citric acid to moles, using the stoichiometric ratios to find the moles of carbon dioxide produced, and finally converting the moles of carbon dioxide back to mass. Understanding this step-by-step process is crucial for mastering stoichiometry problems and accurately predicting the outcome of chemical reactions.

Step-by-Step Calculation of Theoretical Yield

To determine the theoretical yield of carbon dioxide, we will follow these steps:

1. Convert the mass of citric acid to moles: To do this, we need the molar mass of citric acid ($H_3C_6H_5O_7$).
2. Use the stoichiometric ratio from the balanced equation to find the moles of carbon dioxide produced: The balanced equation provides the mole ratio between citric acid and carbon dioxide.
3. Convert the moles of carbon dioxide to grams: We will use the molar mass of carbon dioxide for this conversion.

Step 1: Converting Mass of Citric Acid to Moles

The first step in calculating the theoretical yield is to convert the given mass of citric acid (13.00 g) into moles. To do this, we need the molar mass of citric acid ($H_3C_6H_5O_7$). The molar mass is calculated by summing the atomic masses of all the atoms in the molecule. Looking at the periodic table, we find the following atomic masses:

• Hydrogen (H): 1.01 g/mol
• Carbon (C): 12.01 g/mol
• Oxygen (O): 16.00 g/mol

Therefore, the molar mass of citric acid is:

(3 × 1.01 g/mol) + (6 × 12.01 g/mol) + (5 × 1.01 g/mol) + (7 × 16.00 g/mol) = 192.12 g/mol

Now, we can convert the mass of citric acid to moles using the formula:

Moles = Mass / Molar mass

Moles of citric acid = 13.00 g / 192.12 g/mol = 0.0677 moles

Thus, we have 0.0677 moles of citric acid. This conversion is crucial because stoichiometry is based on mole ratios, not mass ratios. Converting to moles allows us to accurately relate the amount of reactants to the amount of products formed.

Step 2: Using the Stoichiometric Ratio to Find Moles of Carbon Dioxide

Next, we need to determine how many moles of carbon dioxide ($CO_2$) will be produced from the 0.0677 moles of citric acid. This is where the balanced chemical equation comes into play. The balanced equation:

$H_3C_6H_5O_7 + 3NaHCO_3 \rightarrow 3CO_2 + 3H_2O + Na_3C_6H_5O_7$

tells us that 1 mole of citric acid ($H_3C_6H_5O_7$) reacts to produce 3 moles of carbon dioxide ($CO_2$). This gives us the stoichiometric ratio we need: 3 moles $CO_2$ / 1 mole $H_3C_6H_5O_7$.

We can now use this ratio to calculate the moles of carbon dioxide produced:

Moles of $CO_2$ = Moles of citric acid × (Moles of $CO_2$ / Moles of citric acid)

Moles of $CO_2$ = 0.0677 moles $H_3C_6H_5O_7$ × (3 moles $CO_2$ / 1 mole $H_3C_6H_5O_7$) = 0.2031 moles $CO_2$

Therefore, 0.0677 moles of citric acid will produce 0.2031 moles of carbon dioxide. The stoichiometric ratio is a powerful tool in chemistry, allowing us to predict the amounts of products formed from given amounts of reactants.

Step 3: Converting Moles of Carbon Dioxide to Grams

The final step is to convert the moles of carbon dioxide (0.2031 moles) into grams. To do this, we need the molar mass of carbon dioxide ($CO_2$). The molar mass is calculated by summing the atomic masses of carbon and oxygen:

• Carbon (C): 12.01 g/mol
• Oxygen (O): 16.00 g/mol

Molar mass of $CO_2$ = 12.01 g/mol + (2 × 16.00 g/mol) = 44.01 g/mol

Now, we can convert the moles of carbon dioxide to grams using the formula:

Mass = Moles × Molar mass

Mass of $CO_2$ = 0.2031 moles × 44.01 g/mol = 8.938 g

Therefore, the theoretical yield of carbon dioxide is 8.938 grams. This value represents the maximum amount of carbon dioxide that can be produced from the given amount of citric acid, assuming a perfect reaction and no losses during the process. It's important to remember that the actual yield in a real-world experiment may be less than the theoretical yield due to various factors, such as incomplete reactions or loss of product during handling.

Conclusion: The Significance of Theoretical Yield

In conclusion, the theoretical yield of carbon dioxide ($CO_2$) produced from the reaction of 13.00 g of citric acid ($H_3C_6H_5O_7$) with excess baking soda ($NaHCO_3$) is calculated to be 8.938 grams. This calculation involved several key steps:

1. Converting the mass of citric acid to moles using its molar mass.
2. Using the stoichiometric ratio from the balanced chemical equation to determine the moles of carbon dioxide produced.
3. Converting the moles of carbon dioxide to grams using its molar mass.

Understanding how to calculate theoretical yield is crucial in chemistry for several reasons. First, it allows us to predict the maximum amount of product that can be obtained from a given reaction, which is essential for planning experiments and optimizing chemical processes. Second, comparing the theoretical yield to the actual yield obtained in an experiment helps us assess the efficiency of the reaction and identify potential sources of error or loss of product. Finally, the concept of theoretical yield is fundamental to many other stoichiometric calculations, such as calculating percent yield and determining limiting reactants.

By mastering the steps involved in calculating theoretical yield, students and chemists alike can gain a deeper understanding of the quantitative aspects of chemical reactions and make accurate predictions about the outcomes of chemical processes. This knowledge is not only valuable in the laboratory but also in various industrial applications where precise control over chemical reactions is essential.