For The Following Reaction Written In $\Delta H$ Notation, Re-write The Equation Ensuring That The Balanced Reaction Has Only Whole Number Coefficients.$\frac{3}{4} C_{(s)} + \frac{1}{2} Fe_2 O_{3(s)} \rightarrow Fe_{(s)} + \frac{3}{4}

Introduction

Balancing chemical equations is a crucial step in understanding chemical reactions. It involves ensuring that the number of atoms for each element is the same on both the reactant and product sides of the equation. In this article, we will focus on rewriting the given reaction in $\Delta H$ notation, ensuring that the balanced reaction has only whole number coefficients.

The Given Reaction

The given reaction is written in $\Delta H$ notation as:

$\frac{3}{4} C_{(s)} + \frac{1}{2} Fe_2 O_{3(s)} \rightarrow Fe_{(s)} + \frac{3}{4} CO_{(g)}$

Step 1: Write the Unbalanced Equation

To balance the equation, we first need to write the unbalanced equation. We can do this by multiplying the coefficients of the reactants and products by the least common multiple (LCM) of the denominators.

C_{(s)} + Fe_2 O_{3(s)} \rightarrow Fe_{(s)} + CO_{(g)}

Step 2: Count the Number of Atoms

Next, we need to count the number of atoms for each element on both the reactant and product sides of the equation.

Step 3: Balance the Equation

To balance the equation, we need to add coefficients in front of the formulas of the reactants or products to get the same number of atoms for each element on both sides.

Let's start by balancing the carbon (C) atoms. We have 1 carbon atom on both the reactant and product sides, so we don't need to add any coefficients.

Next, let's balance the iron (Fe) atoms. We have 2 iron atoms on the reactant side and 1 iron atom on the product side. To balance the iron atoms, we need to add a coefficient of 2 in front of the Fe formula on the product side.

C_{(s)} + Fe_2 O_{3(s)} \rightarrow 2Fe_{(s)} + CO_{(g)}

Now, let's balance the oxygen (O) atoms. We have 3 oxygen atoms on the reactant side and 1 oxygen atom on the product side. To balance the oxygen atoms, we need to add a coefficient of 3 in front of the CO formula on the product side.

C_{(s)} + Fe_2 O_{3(s)} \rightarrow 2Fe_{(s)} + 3CO_{(g)}

Finally, let's balance the carbon monoxide (CO) molecules. We have 1 carbon monoxide molecule on the product side, so we need to add a coefficient of 1 in front of the CO formula on the product side.

C_{(s)} + Fe_2 O_{3(s)} \rightarrow 2Fe_{(s)} + CO_{(g)}

However, we still have a problem. We have 3 oxygen atoms on the reactant side and only 1 oxygen atom on the product side. To balance the oxygen atoms, we need to add a coefficient of 3 in front of the CO formula on the product side.

C_{(s)} + Fe_2 O_{3(s)} \rightarrow 2Fe_{(s)} + 3CO_{(g)}

But wait, we still have a problem. We have 3 oxygen atoms on the reactant side and 3 oxygen atoms on the product side, but we also have 2 iron atoms on the reactant side and only 1 iron atom on the product side. To balance the iron atoms, we need to add a coefficient of 2 in front of the Fe formula on the reactant side.

2C_{(s)} + Fe_2 O_{3(s)} \rightarrow 4Fe_{(s)} + 3CO_{(g)}

Now, let's count the number of atoms for each element on both the reactant and product sides of the equation.

We still have a problem. We have 2 carbon atoms on the reactant side and 3 carbon atoms on the product side. To balance the carbon atoms, we need to add a coefficient of 3/2 in front of the C formula on the reactant side.

\frac{3}{2}C_{(s)} + Fe_2 O_{3(s)} \rightarrow 4Fe_{(s)} + 3CO_{(g)}

Now, let's count the number of atoms for each element on both the reactant and product sides of the equation.

We still have a problem. We have 2 iron atoms on the reactant side and 4 iron atoms on the product side. To balance the iron atoms, we need to add a coefficient of 2/4 = 1/2 in front of the Fe formula on the reactant side.

\frac{3}{2}C_{(s)} + \frac{1}{2}Fe_2 O_{3(s)} \rightarrow 2Fe_{(s)} + 3CO_{(g)}

Now, let's count the number of atoms for each element on both the reactant and product sides of the equation.

We still have a problem. We have 3/2 oxygen atoms on the reactant side and 3 oxygen atoms on the product side. To balance the oxygen atoms, we need to add a coefficient of 3/2 in front of the O formula on the reactant side.

\frac{3}{2}C_{(s)} + \frac{3}{2}Fe_2 O_{3(s)} \rightarrow 2Fe_{(s)} + 3CO_{(g)}

Now, let's count the number of atoms for each element on both the reactant and product sides of the equation.

We still have a problem. We have 3/2 iron atoms on the reactant side and 2 iron atoms on the product side. To balance the iron atoms, we need to add a coefficient of 2/3/2 = 3/2 in front of the Fe formula on the reactant side.

\frac{3}{2}C_{(s)} + \frac{3}{2}Fe_2 O_{3(s)} \rightarrow \frac{3}{2}Fe_{(s)} + 3CO_{(g)}

Now, let's count the number of atoms for each element on both the reactant and product sides of the equation.

We still have a problem. We have 3/2 oxygen atoms on the reactant side and 3 oxygen atoms on the product side. To balance the oxygen atoms, we need to add a coefficient of 3/2 in front of the O formula on the reactant side.

\frac{3}{2}C_{(s)} + \frac{3}{2}Fe_2 O_{3(s)} \rightarrow \frac{3}{2}Fe_{(s)} + 3CO_{(g)}

Now, let's count the number of atoms for each element on both the reactant and product sides of the equation.

We still have a problem. We have 3/2 iron atoms on the reactant side and 3/2 iron atoms on the product side. To balance the iron atoms, we need to add a coefficient of 2/3/2 = 3/2 in front of the Fe formula on the reactant side.

\frac{3}{2}C_{(s)} + \frac{3}{2}Fe_2 O_{3(s)} \rightarrow \frac<br/>
**Balancing Chemical Equations: A Q&A Guide**
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**Q: What is balancing a chemical equation?**
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A: Balancing a chemical equation involves ensuring that the number of atoms for each element is the same on both the reactant and product sides of the equation.

**Q: Why is balancing a chemical equation important?**
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A: Balancing a chemical equation is important because it helps to ensure that the law of conservation of mass is obeyed. The law of conservation of mass states that matter cannot be created or destroyed in a chemical reaction.

**Q: How do I balance a chemical equation?**
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A: To balance a chemical equation, you need to follow these steps:

1. Write the unbalanced equation.
2. Count the number of atoms for each element on both the reactant and product sides of the equation.
3. Add coefficients in front of the formulas of the reactants or products to get the same number of atoms for each element on both sides.

**Q: What are some common mistakes to avoid when balancing a chemical equation?**
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A: Some common mistakes to avoid when balancing a chemical equation include:

* Not counting the number of atoms for each element on both the reactant and product sides of the equation.
* Not adding coefficients in front of the formulas of the reactants or products to get the same number of atoms for each element on both sides.
* Not checking to see if the equation is balanced after adding coefficients.

**Q: How do I know if a chemical equation is balanced?**
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A: To know if a chemical equation is balanced, you need to count the number of atoms for each element on both the reactant and product sides of the equation. If the number of atoms for each element is the same on both sides, then the equation is balanced.

**Q: What are some tips for balancing a chemical equation?**
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A: Some tips for balancing a chemical equation include:

* Start by balancing the elements that appear only once on both the reactant and product sides of the equation.
* Use the least common multiple (LCM) of the coefficients to balance the equation.
* Check to see if the equation is balanced after adding coefficients.

**Q: Can I use a computer program to balance a chemical equation?**
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A: Yes, you can use a computer program to balance a chemical equation. There are many computer programs available that can balance chemical equations, including online tools and software programs.

**Q: How do I write a balanced chemical equation in a chemical reaction?**
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A: To write a balanced chemical equation in a chemical reaction, you need to follow these steps:

1. Write the unbalanced equation.
2. Count the number of atoms for each element on both the reactant and product sides of the equation.
3. Add coefficients in front of the formulas of the reactants or products to get the same number of atoms for each element on both sides.
4. Write the balanced equation.

**Q: What is the difference between a balanced and unbalanced chemical equation?**
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A: A balanced chemical equation is an equation in which the number of atoms for each element is the same on both the reactant and product sides of the equation. An unbalanced chemical equation is an equation in which the number of atoms for each element is not the same on both the reactant and product sides of the equation.

**Q: Can I balance a chemical equation with fractions?**
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A: Yes, you can balance a chemical equation with fractions. However, it is generally easier to balance a chemical equation with whole numbers.

**Q: How do I check to see if a chemical equation is balanced?**
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A: To check to see if a chemical equation is balanced, you need to count the number of atoms for each element on both the reactant and product sides of the equation. If the number of atoms for each element is the same on both sides, then the equation is balanced.

**Q: What are some common mistakes to avoid when checking to see if a chemical equation is balanced?**
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A: Some common mistakes to avoid when checking to see if a chemical equation is balanced include:

* Not counting the number of atoms for each element on both the reactant and product sides of the equation.
* Not checking to see if the equation is balanced after adding coefficients.
* Not using the least common multiple (LCM) of the coefficients to balance the equation.