Consider the following chemical reaction: aFe 2O 3(s) + bCO(g) → cFe (s) + dCO 2
1, 3, 2, 3
Balancing Chemical Equations: The \(\text{Fe}_2\text{O}_3\) and \(\text{CO}\) Reaction
Balancing a chemical equation ensures that the law of conservation of mass is obeyed. This means the number of atoms of each element must be the same on both the reactant side and the product side of the equation. We are given the unbalanced equation:
\(\text{aFe}_2\text{O}_3\text{(s)} + \text{bCO(g)} \rightarrow \text{cFe (s)} + \text{dCO}_2\text{(g)}\)
Here, a, b, c, and d are the stoichiometric coefficients we need to find to balance the equation.
Steps to Balance the Chemical Equation
Let's count the number of atoms of each element on both sides of the equation:
- Reactant Side:
- Iron (Fe): 2 atoms in \(\text{Fe}_2\text{O}_3\), multiplied by coefficient a. Total Fe atoms: \(2a\).
- Oxygen (O): 3 atoms in \(\text{Fe}_2\text{O}_3\) (multiplied by a) plus 1 atom in CO (multiplied by b). Total O atoms: \(3a + b\).
- Carbon (C): 1 atom in CO, multiplied by coefficient b. Total C atoms: \(b\).
- Product Side:
- Iron (Fe): 1 atom in Fe, multiplied by coefficient c. Total Fe atoms: \(c\).
- Oxygen (O): 2 atoms in \(\text{CO}_2\), multiplied by coefficient d. Total O atoms: \(2d\).
- Carbon (C): 1 atom in \(\text{CO}_2\), multiplied by coefficient d. Total C atoms: \(d\).
Setting Up Equations
To balance the equation, the number of atoms of each element must be equal on both sides:
- For Iron (Fe): \(2a = c\)
- For Oxygen (O): \(3a + b = 2d\)
- For Carbon (C): \(b = d\)
Solving for the Coefficients (a, b, c, d)
We have a system of equations. Let's use the simplest relationship first, which is \(b = d\).
Now substitute \(d\) with \(b\) in the oxygen equation:
\(3a + b = 2(b)\)
\(3a + b = 2b\)
Subtract \(b\) from both sides:
\(3a = 2b - b\)
\(3a = b\)
So, we have the relationships: \(b = 3a\) and \(c = 2a\), and \(d = b\). Since \(b=3a\), we also have \(d=3a\).
To find the smallest whole number coefficients, we can choose a simple value for one variable. Let's assume \(a=1\).
- If \(a=1\):
- \(b = 3a = 3 \times 1 = 3\)
- \(c = 2a = 2 \times 1 = 2\)
- \(d = b = 3\)
So, the coefficients are \(a=1\), \(b=3\), \(c=2\), and \(d=3\).
Verifying the Balanced Equation
Let's plug these values back into the equation:
\(1\text{Fe}_2\text{O}_3\text{(s)} + 3\text{CO(g)} \rightarrow 2\text{Fe (s)} + 3\text{CO}_2\text{(g)}\)
Let's check the atom counts:
| Element | Atoms on Reactant Side | Atoms on Product Side | Balanced? |
|---|---|---|---|
| Fe | \(1 \times 2 = 2\) | \(2 \times 1 = 2\) | Yes |
| O | \((1 \times 3) + (3 \times 1) = 3 + 3 = 6\) | \(3 \times 2 = 6\) | Yes |
| C | \(3 \times 1 = 3\) | \(3 \times 1 = 3\) | Yes |
All elements are balanced. The coefficients a, b, c, and d are 1, 3, 2, and 3 respectively.
Coefficients of the Balanced Equation
The values for a, b, c, and d are 1, 3, 2, and 3.
Revision Table: Key Concepts in Balancing Equations
| Concept | Explanation |
|---|---|
| Law of Conservation of Mass | States that mass in an isolated system is neither created nor destroyed by chemical reactions or physical transformations. In chemical equations, this means the total mass of reactants equals the total mass of products, which translates to having the same number of each type of atom on both sides. |
| Stoichiometric Coefficients | The numbers placed in front of the chemical formulas in a balanced chemical equation. They represent the relative number of molecules or moles of each reactant and product involved in the reaction. |
| Subscripts vs. Coefficients | Subscripts in a chemical formula (like the '2' in \(\text{Fe}_2\)) indicate the number of atoms of an element in a molecule. Coefficients (like the 'a' in \(\text{aFe}_2\text{O}_3\)) are placed in front of the formula and can be changed to balance the equation. Changing a subscript changes the substance itself. |
Additional Information: Chemical Reactions
The reaction between iron(III) oxide (\(\text{Fe}_2\text{O}_3\)) and carbon monoxide (\(\text{CO}\)) is a common example of a redox (reduction-oxidation) reaction, specifically a reduction reaction used in the production of iron from its ore in a blast furnace. \(\text{Fe}_2\text{O}_3\) is reduced to Fe, and \(\text{CO}\) is oxidized to \(\text{CO}_2\). Understanding how to balance these chemical equations is fundamental to calculating quantities of reactants and products in chemistry, a topic known as stoichiometry.
The state symbols (s) for solid and (g) for gas indicate the physical state of the substances under the reaction conditions. Including these symbols makes the chemical equation more informative.
Similar Questions
The handle of pressure cookers is made of plastic because it should be made non-conductor of heat. The plastic used here is the first man-made plastic, which is:
Match List-I with List-II and select the correct answer using the code given below the Lists:
List-I
(Compound/Molecule)
List-II
(Shape of Molecule)
A. CH 3F
1. Trigonal planar
B. HCHO
2. Tetrahedral
C. HCN
3. Trigonal pyramidal
D. NH 3
4. Linear
In which of the following, functional group isomerism in not possible?
The x/monomers used for the synthesis of Nylon 6 is/are _________.
Which one of the following polymers does not contain glucose units?
Which one of the following is not an allotrope of carbon?
The PCl 5 molecule has trigonal bipyramidal structure. Therefore, the hybridization of p orbitals should be __________.
Consider the following statements :
1. Concentrated \(H_2SO_4\) is used as a dehydrating agent in esterification reaction.
2. The hydrophilic part of soap is oil and it dissolves in water.
3. Nickel is used as a catalyst in converting vegetable oil into fat.
Which of the statements given above are correct ?- Which one of the following statements is not correct for benzene ?
The correct order of octane number of butane, pentane, hexane and cyclohexane is
Important Questions from Organic Chemistry
Silica is -
The catalyst used in the manufacture of methyl alcohol from water gas is
A carbon compound when heated in excess of concentrated sulphuric acid at 443K gives ethene. The compound is an________.
The manmade fiber obtained by chemical treatment of wood pulp is _____.
The IUPAC name of the compound CH 3CH 2CH 3is-
