1. Balance the redox equation: K_(1)Fe(CN)_(6)+H_(2)SO_(4)+H_(2)O=K_(2)SO_(4)+FeSO_(4)+(NH_(3))_(2)SO_(4)+CO_(4)

To balance the redox equation, we need to follow these steps:<br /><br />1. Identify the oxidation states of each element in the equation.<br />2. Determine which elements are being oxidized and reduced.<br />3. Balance the atoms of the elements that are being oxidized and reduced.<br />4. Balance the charge by adding electrons to the appropriate side of the equation.<br />5. Balance the remaining atoms in the equation.<br /><br />Let's start by identifying the oxidation states of each element in the equation:<br /><br />$K_{1}Fe(CN)_{6}+H_{2}SO_{4}+H_{2}O=K_{2}SO_{4}+FeSO_{4}+(NH_{3})_{2}SO_{4}+CO_{4}$<br /><br />In this equation, the oxidation states are as follows:<br /><br />K: +1<br />Fe: +2<br />C: +4<br />N: -3<br />H: +1<br />S: +6<br />O: -2<br /><br />Now, let's determine which elements are being oxidized and reduced:<br /><br />Fe is being reduced from an oxidation state of +2 to +2 in FeSO4.<br />C is being oxidized from an oxidation state of +4 in K1Fe(CN)6 to +4 in CO4.<br /><br />Next, we balance the atoms of the elements that are being oxidized and reduced:<br /><br />Fe: 1 atom on both sides<br />C: 6 atoms on the left side and 1 atom on the right side<br /><br />To balance the charge, we add electrons to the appropriate side of the equation:<br /><br />$K_{1}Fe(CN)_{6}+H_{2}SO_{4}+H_{2}O=K_{2}SO_{4}+FeSO_{4}+(NH_{3})_{2}SO_{4}+CO_{4}+6e^{-}$<br /><br />Finally, we balance the remaining atoms in the equation:<br /><br />K: 2 atoms on the right side<br />H: 8 atoms on the left side and 8 atoms on the right side<br />S: 1 atom on the left side and 1 atom on the right side<br />O: 12 atoms on the left side and 12 atoms on the right side<br /><br />The balanced redox equation is:<br /><br />$K_{1}Fe(CN)_{6}+H_{2}SO_{4}+H_{2}O=K_{2}SO_{4}+FeSO_{4}+(NH_{3})_{2}SO_{4}+CO_{4}+6e^{-}$