Question

\(\mathrm{KMnO}_{4}+\mathrm{H}_{2} \mathrm{SO}_{4}+\mathrm{FeSO}_{4} \rightarrow \mathrm{K}_{2} \mathrm{SO}_{4}+\mathrm{MnSO}_{4}+\) \(\mathrm{Fe}_{2}\left(\mathrm{SO}_{4}\right)_{3}+\mathrm{H}_{2} \mathrm{O}\) Coefficients of sulphuric acid and ferric sulphate in the balanced equation of above reaction are respectively (a) 8,4 (b) 5,8 (c) 4,3 (d) 8,5

Short answer

Answer: H₂SO₄ has a coefficient of 8 and Fe₂(SO₄)₃ has a coefficient of 2.

Step-by-step solution

Write the unbalanced chemical equation

First, write down the unbalanced chemical equation given in the problem. \(\mathrm{KMnO}_{4}+\mathrm{H}_{2} \mathrm{SO}_{4}+\mathrm{FeSO}_{4} \rightarrow \mathrm{K}_{2} \mathrm{SO}_{4}+\mathrm{MnSO}_{4}+\mathrm{Fe}_{2}\left(\mathrm{SO}_{4}\right)_{3}+\mathrm{H}_{2} \mathrm{O}\)

Balance the atoms that appear in the most complex compounds

In this case, let's balance Mn and K atoms. They appear only once on both sides of the equation. \(\mathrm{\textbf{1}KMnO}_{4}+\mathrm{H}_{2} \mathrm{SO}_{4}+\mathrm{FeSO}_{4} \rightarrow \mathrm{\textbf{2}K}_{2} \mathrm{SO}_{4}+\mathrm{\textbf{1}MnSO}_{4}+\mathrm{Fe}_{2}\left(\mathrm{SO}_{4}\right)_{3}+\mathrm{H}_{2} \mathrm{O}\)

Balance the O atoms

Now balance the O atoms, which are not part of water: \(1\mathrm{KMnO}_{4}+\mathrm{H}_{2} \mathrm{SO}_{4}+\mathrm{FeSO}_{4} \rightarrow 2\mathrm{K}_{2} \mathrm{SO}_{4}+1\mathrm{MnSO}_{4}+\mathrm{Fe}_{2}\left(\mathrm{SO}_{4}\right)_{3}+\mathrm{\textbf{4}H}_{2} \mathrm{O}\)

Balance the H; atoms

Balance the hydrogen atoms in the equation. \(1\mathrm{KMnO}_{4}+\textbf{8}\mathrm{H}_{2} \mathrm{SO}_{4}+\mathrm{FeSO}_{4} \rightarrow 2\mathrm{K}_{2} \mathrm{SO}_{4}+1\mathrm{MnSO}_{4}+\mathrm{Fe}_{2}\left(\mathrm{SO}_{4}\right)_{3}+4\mathrm{H}_{2} \mathrm{O}\)

Balance the Fe atoms

Finally, balance the iron (Fe) atoms in the equation. \(1\mathrm{KMnO}_{4}+8\mathrm{H}_{2} \mathrm{SO}_{4}+\textbf{6}\mathrm{FeSO}_{4} \rightarrow 2\mathrm{K}_{2} \mathrm{SO}_{4}+1\mathrm{MnSO}_{4}+\textbf{2}\mathrm{Fe}_{2}\left(\mathrm{SO}_{4}\right)_{3}+4\mathrm{H}_{2} \mathrm{O}\) Now the equation is balanced: \(\mathrm{KMnO}_{4}+8\mathrm{H}_{2} \mathrm{SO}_{4}+6\mathrm{FeSO}_{4} \rightarrow 2\mathrm{K}_{2} \mathrm{SO}_{4}+\mathrm{MnSO}_{4}+2\mathrm{Fe}_{2}\left(\mathrm{SO}_{4}\right)_{3}+4\mathrm{H}_{2} \mathrm{O}\) The coefficients of sulphuric acid (H₂SO₄) and ferric sulphate (Fe₂(SO₄)₃) in the balanced equation are 8 and 2, respectively. Therefore, the correct answer is not listed in the given options.

Key concepts

Redox Reactions

Understanding redox (reduction-oxidation) reactions is a crucial aspect of balancing complex chemical equations. In these reactions, the transfer of electrons occurs between two chemical species, changing their oxidation states. Redox reactions can be broken down into two half-reactions:- **Reduction:** Gain of electrons, resulting in a decrease in oxidation state.- **Oxidation:** Loss of electrons, leading to an increase in oxidation state.A good strategy for identifying redox reactions is to look for changes in oxidation numbers of different elements from reactants to products. This helps pinpoint which species are undergoing reduction and which are being oxidized. For example, in the unbalanced form of reaction given \[ \mathrm{KMnO}_{4} + \mathrm{H}_{2} \mathrm{SO}_{4} + \mathrm{FeSO}_{4} \rightarrow \mathrm{K}_{2} \mathrm{SO}_{4} + \mathrm{MnSO}_{4} + \mathrm{Fe}_{2}\left(\mathrm{SO}_{4}\right)_{3} + \mathrm{H}_{2} \mathrm{O}, \] manganese is likely being reduced, and iron is getting oxidized. Recognizing this helps in properly balancing the equation.Balancing redox reactions involves adjusting coefficients so that both mass and charge are conserved, which is critical for achieving an accurate chemical equation.

Stoichiometry

Stoichiometry is a fundamental concept in chemistry that enables us to understand the quantitative relationships in a chemical reaction. It involves using the balanced chemical equation to determine the relationships between the reactants and products in a reaction.When you balance a chemical equation, you alter the coefficients in front of compounds to ensure that the number of atoms for each element is equal on both sides of the equation. This way, you conserve the mass, adhering to the Law of Conservation of Mass. For instance, emphasizing this in the given reaction allows you to deduce the necessary amounts of each substance:\[ \mathrm{KMnO}_{4} + 8\mathrm{H}_{2} \mathrm{SO}_{4} + 6\mathrm{FeSO}_{4} \rightarrow 2\mathrm{K}_{2} \mathrm{SO}_{4} + \mathrm{MnSO}_{4} + 2\mathrm{Fe}_{2}\left(\mathrm{SO}_{4}\right)_{3} + 4\mathrm{H}_{2} \mathrm{O}. \]The coefficients in the balanced equation indicate the mole ratios of reactants and products. They tell you, for example, that two moles of iron(II) sulfate react with one mole of potassium permanganate in the presence of sulfuric acid, highlighting the interplay of stoichiometry and chemical reaction balancing.

Oxidation States

Oxidation states are a vital tool for tracking how electrons are transferred in redox reactions. An oxidation state is an imaginary charge that an atom would have if all its bonds were completely ionic. To assign oxidation states, follow these simple rules:- Pure elements have an oxidation state of 0 (e.g., N₂, O₂).- For ions, the oxidation state is the same as the charge of the ion.- In compounds, Group 1 metals generally have an oxidation state of +1, and Group 2 metals have +2.- Oxygen typically has an oxidation state of -2, while hydrogen is usually +1, except in hydrides where it is -1.Applying these guidelines to the reaction:- In \(\mathrm{KMnO}_{4}\), manganese has an oxidation state of +7, which reduces to +2 in \(\mathrm{MnSO}_{4}\), signifying reduction.- In \(\mathrm{FeSO}_{4}\), iron is in a +2 state, and in \(\mathrm{Fe}_{2}\left(\mathrm{SO}_{4}\right)_{3}\), it is in a +3 state, indicating oxidation.Understanding oxidation states provides clarity on electron transfers and facilitates the process of correctly balancing redox reactions.