\(\mathrm{KMnO}_{4}+\mathrm{H}_{2} \mathrm{SO}_{4}+\mathrm{FeSO}_{4} \rightarrow \mathrm{K}_{2} \mathrm{SO}_{4}+\mathrm{MnSO}_{4}+\) \(\mathrm{Fe}_{2}\left(\mathrm{SO}_{4}\right)_{3}+\mathrm{H}_{2} \mathrm{O}\) 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

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

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

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

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.