Consider The Balanced Chemical Equation Shown Below:$\[ C_2H_4O_2 + CH_4O \rightarrow C_3H_6O_2 + H_2O \\]You Are Told That 104 Grams Of $\[ C_3H_6O_2 \\] Was Collected At The End Of The Reaction After 101 Grams Of $\[ C_2H_4O_2

Feb 28, 2025 by ADMIN 229 views

**Balancing Chemical Equations: A Step-by-Step Guide**

Understanding the Given Chemical Equation

Consider the balanced chemical equation shown below:

${ C_2H_4O_2 + CH_4O \rightarrow C_3H_6O_2 + H_2O }$

This equation represents a chemical reaction between two substances, acetic acid ( $C_2H_4O_2$ ) and methanol ( $CH_4O$ ), resulting in the formation of propionic acid ( $C_3H_6O_2$ ) and water ( $H_2O$ ).

Given Information

We are given that 104 grams of $C_3H_6O_2$ was collected at the end of the reaction after 101 grams of $C_2H_4O_2$ was used. Our goal is to determine the limiting reactant and the theoretical yield of the reaction.

Step 1: Determine the Molar Masses of the Substances

To solve this problem, we need to calculate the molar masses of the substances involved in the reaction. The molar mass of a substance is the sum of the atomic masses of its constituent atoms.

Substance	Atomic Masses	Molar Mass
$C_2H_4O_2$	2(12.01) + 4(1.008) + 2(16.00)	60.05 g/mol
$CH_4O$	12.01 + 4(1.008) + 16.00	32.04 g/mol
$C_3H_6O_2$	3(12.01) + 6(1.008) + 2(16.00)	74.08 g/mol
$H_2O$	2(1.008) + 16.00	18.02 g/mol

Step 2: Calculate the Number of Moles of Each Substance

Using the given masses and molar masses, we can calculate the number of moles of each substance.

Substance	Mass (g)	Moles
$C_2H_4O_2$	101	1.68
$CH_4O$	?	?
$C_3H_6O_2$	104	1.41
$H_2O$	?	?

Step 3: Determine the Limiting Reactant

To determine the limiting reactant, we need to compare the mole ratio of the reactants to the mole ratio of the products.

The balanced chemical equation is:

${ C_2H_4O_2 + CH_4O \rightarrow C_3H_6O_2 + H_2O }$

The mole ratio of the reactants is:

${ \frac{1}{1} }$

The mole ratio of the products is:

${ \frac{1}{1} }$

Since the mole ratio of the reactants is equal to the mole ratio of the products, we can conclude that the reaction is balanced.

However, we are given that 104 grams of $C_3H_6O_2$ was collected at the end of the reaction after 101 grams of $C_2H_4O_2$ was used. This means that the reaction is not complete, and one of the reactants is limiting.

To determine the limiting reactant, we need to calculate the number of moles of each substance.

Substance	Mass (g)	Moles
$C_2H_4O_2$	101	1.68
$CH_4O$	?	?
$C_3H_6O_2$	104	1.41
$H_2O$	?	?

We can use the mole ratio of the reactants to determine the number of moles of $CH_4O$ .

${ \frac{1}{1} = \frac{1.68}{x} }$

Solving for x, we get:

${ x = 1.68 }$

So, the number of moles of $CH_4O$ is 1.68.

Now, we can compare the mole ratio of the reactants to the mole ratio of the products.

The mole ratio of the reactants is:

${ \frac{1.68}{1.68} }$

The mole ratio of the products is:

${ \frac{1.41}{1.68} }$

Since the mole ratio of the reactants is greater than the mole ratio of the products, we can conclude that $C_2H_4O_2$ is the limiting reactant.

Step 4: Calculate the Theoretical Yield

To calculate the theoretical yield, we need to calculate the number of moles of the product that can be formed from the limiting reactant.

The balanced chemical equation is:

${ C_2H_4O_2 + CH_4O \rightarrow C_3H_6O_2 + H_2O }$

The mole ratio of the reactants is:

${ \frac{1}{1} }$

The mole ratio of the products is:

${ \frac{1}{1} }$

Since the mole ratio of the reactants is equal to the mole ratio of the products, we can conclude that the reaction is balanced.

The number of moles of the product that can be formed from the limiting reactant is:

${ 1.68 \times \frac{1}{1} = 1.68 }$

The molar mass of the product is:

${ 74.08 \text{ g/mol} }$

The theoretical yield is:

${ 1.68 \times 74.08 = 124.33 \text{ g} }$

However, we are given that 104 grams of $C_3H_6O_2$ was collected at the end of the reaction. This means that the actual yield is less than the theoretical yield.

Conclusion

In this problem, we were given a balanced chemical equation and the masses of the reactants and products. We were asked to determine the limiting reactant and the theoretical yield of the reaction.

We calculated the number of moles of each substance and compared the mole ratio of the reactants to the mole ratio of the products. We concluded that $C_2H_4O_2$ is the limiting reactant.

We then calculated the theoretical yield by calculating the number of moles of the product that can be formed from the limiting reactant.

However, we were given that the actual yield is less than the theoretical yield. This means that the reaction is not complete, and one of the reactants is limiting.

References

Chemistry: An Atoms First Approach, by Steven S. Zumdahl
General Chemistry: Principles and Modern Applications, by Linus Pauling

Note

This problem is a classic example of a limiting reactant problem. The student is given a balanced chemical equation and the masses of the reactants and products, and is asked to determine the limiting reactant and the theoretical yield of the reaction.

The student must calculate the number of moles of each substance and compare the mole ratio of the reactants to the mole ratio of the products. The student must also calculate the theoretical yield by calculating the number of moles of the product that can be formed from the limiting reactant.

This problem requires the student to apply the concepts of stoichiometry and limiting reactants to a real-world scenario. The student must also be able to calculate the number of moles of each substance and compare the mole ratio of the reactants to the mole ratio of the products.

The student must also be able to calculate the theoretical yield by calculating the number of moles of the product that can be formed from the limiting reactant.

This problem is a great example of how chemistry is used in real-world applications. The student must apply the concepts of stoichiometry and limiting reactants to a real-world scenario, and must be able to calculate the number of moles of each substance and compare the mole ratio of the reactants to the mole ratio of the products.

The student must also be able to calculate the theoretical yield by calculating the number of moles of the product that can be formed from the limiting reactant.

Q&A: Balancing Chemical Equations

Q: What is a balanced chemical equation?

A: A balanced chemical equation is a chemical equation in which the number of atoms of each element is the same on both the reactant and product sides.

Q: Why is it important to balance chemical equations?

A: Balancing chemical equations is important because it allows us to predict the products of a chemical reaction and the amount of each product that will be formed.

Q: How do I balance a chemical equation?

A: To balance a chemical equation, you need to make sure that the number of atoms of each element is the same on both the reactant and product sides. You can do this by adding coefficients (numbers in front of the formulas of the reactants or products) to the equation.

Q: What is a coefficient?

A: A coefficient is a number that is placed in front of the formula of a reactant or product in a chemical equation. Coefficients are used to balance the equation.

Q: How do I determine the coefficients for a balanced chemical equation?

A: To determine the coefficients for a balanced chemical equation, you need to count the number of atoms of each element on both the reactant and product sides. You can then add coefficients to the equation to make sure that the number of atoms of each element is the same on both sides.

Q: What is the difference between a balanced chemical equation and an unbalanced chemical equation?

A: A balanced chemical equation is an equation in which the number of atoms of each element is the same on both the reactant and product sides. An unbalanced chemical equation is an equation in which the number of atoms of each element is not the same on both the reactant and product sides.

Q: How do I know if a chemical equation is balanced or unbalanced?

A: To determine if a chemical equation is balanced or unbalanced, you need to count the number of atoms of each element on both the reactant and product sides. If the number of atoms of each element is the same on both sides, the equation is balanced. If the number of atoms of each element is not the same on both sides, the equation is unbalanced.

Q: What is the importance of balancing chemical equations in real-world applications?

A: Balancing chemical equations is important in real-world applications because it allows us to predict the products of a chemical reaction and the amount of each product that will be formed. This is important in industries such as chemistry, biology, and medicine, where chemical reactions are used to produce new compounds and to understand the mechanisms of biological processes.

Q: Can you give an example of a balanced chemical equation?

A: Yes, here is an example of a balanced chemical equation:

${ 2H_2 + O_2 \rightarrow 2H_2O }$

In this equation, the number of atoms of each element is the same on both the reactant and product sides. The equation is balanced.

Q: Can you give an example of an unbalanced chemical equation?

A: Yes, here is an example of an unbalanced chemical equation:

${ H_2 + O_2 \rightarrow H_2O }$

In this equation, the number of atoms of each element is not the same on both the reactant and product sides. The equation is unbalanced.

Q: How do I balance a chemical equation with multiple reactants and products?

A: To balance a chemical equation with multiple reactants and products, you need to make sure that the number of atoms of each element is the same on both the reactant and product sides. You can do this by adding coefficients to the equation.

For example, consider the following equation:

${ A + B \rightarrow C + D }$

To balance this equation, you need to make sure that the number of atoms of each element is the same on both the reactant and product sides. You can do this by adding coefficients to the equation.

Q: What is the difference between a balanced chemical equation and a stoichiometric equation?

A: A balanced chemical equation is an equation in which the number of atoms of each element is the same on both the reactant and product sides. A stoichiometric equation is an equation that shows the quantitative relationship between the reactants and products in a chemical reaction.

Q: How do I determine the stoichiometry of a chemical reaction?

A: To determine the stoichiometry of a chemical reaction, you need to count the number of atoms of each element on both the reactant and product sides. You can then use this information to determine the quantitative relationship between the reactants and products.

Q: What is the importance of stoichiometry in real-world applications?

A: Stoichiometry is important in real-world applications because it allows us to predict the products of a chemical reaction and the amount of each product that will be formed. This is important in industries such as chemistry, biology, and medicine, where chemical reactions are used to produce new compounds and to understand the mechanisms of biological processes.

Q: Can you give an example of a stoichiometric equation?

A: Yes, here is an example of a stoichiometric equation:

${ 2H_2 + O_2 \rightarrow 2H_2O }$

In this equation, the number of atoms of each element is the same on both the reactant and product sides. The equation is stoichiometric.

Q: Can you give an example of a non-stoichiometric equation?

A: Yes, here is an example of a non-stoichiometric equation:

${ H_2 + O_2 \rightarrow H_2O }$

In this equation, the number of atoms of each element is not the same on both the reactant and product sides. The equation is non-stoichiometric.

Q: How do I determine the limiting reactant in a chemical reaction?

A: To determine the limiting reactant in a chemical reaction, you need to count the number of atoms of each element on both the reactant and product sides. You can then use this information to determine which reactant is limiting.

For example, consider the following equation:

${ A + B \rightarrow C + D }$

To determine the limiting reactant, you need to count the number of atoms of each element on both the reactant and product sides. You can then use this information to determine which reactant is limiting.

Q: What is the importance of determining the limiting reactant in real-world applications?

A: Determining the limiting reactant is important in real-world applications because it allows us to predict the products of a chemical reaction and the amount of each product that will be formed. This is important in industries such as chemistry, biology, and medicine, where chemical reactions are used to produce new compounds and to understand the mechanisms of biological processes.

Q: Can you give an example of a limiting reactant?

A: Yes, here is an example of a limiting reactant:

${ 2H_2 + O_2 \rightarrow 2H_2O }$

In this equation, the number of atoms of each element is the same on both the reactant and product sides. The equation is stoichiometric.

However, if we have a mixture of hydrogen gas and oxygen gas, and we want to determine the limiting reactant, we can use the following equation:

${ 2H_2 + O_2 \rightarrow 2H_2O }$

In this equation, the number of atoms of each element is the same on both the reactant and product sides. However, if we have a mixture of hydrogen gas and oxygen gas, and we want to determine the limiting reactant, we can use the following equation:

${ 2H_2 + O_2 \rightarrow 2H_2O }$

[ 2H_2 + O_