`aMnO_(4)^(-)+bI^(-)+cH^(+)rarrdMn^(2+)+eI_(2)+fH_(2)O`
In above balance reaction, value of `((c)/(d))` will be :

Options

A. 1.3
B. 1.2
C. 8
D. 5

Answer

To balance the given redox reaction and find the value of \(\frac{c}{d}\), we will follow these steps:

### Step 1: Identify the oxidation and reduction half-reactions.
In the reaction:
\[ \text{MnO}_4^{-} + \text{I}^{-} + \text{H}^{+} \rightarrow \text{Mn}^{2+} + \text{I}_2 + \text{H}_2\text{O} \]
- The manganese in \(\text{MnO}_4^{-}\) is reduced from +7 to +2.
- The iodide ion (\(\text{I}^{-}\)) is oxidized to iodine (\(\text{I}_2\)), changing from -1 to 0.

### Step 2: Write the reduction half-reaction.
The reduction half-reaction for manganese is:
\[ \text{MnO}_4^{-} + 8 \text{H}^{+} + 5 e^{-} \rightarrow \text{Mn}^{2+} + 4 \text{H}_2\text{O} \]
- Here, we added 8 \(\text{H}^{+}\) to balance the hydrogen and 4 \(\text{H}_2\text{O}\) to balance the oxygen.

### Step 3: Write the oxidation half-reaction.
The oxidation half-reaction for iodide is:
\[ 2 \text{I}^{-} \rightarrow \text{I}_2 + 2 e^{-} \]
- Here, we balanced the iodine by adding a coefficient of 2 in front of \(\text{I}^{-}\).

### Step 4: Equalize the number of electrons transferred.
To combine the half-reactions, we need to equalize the number of electrons. The reduction half-reaction involves 5 electrons, while the oxidation half-reaction involves 2 electrons. The least common multiple of 5 and 2 is 10. Thus, we multiply the oxidation half-reaction by 5:
\[ 5 (2 \text{I}^{-} \rightarrow \text{I}_2 + 2 e^{-}) \implies 10 \text{I}^{-} \rightarrow 5 \text{I}_2 + 10 e^{-} \]

### Step 5: Combine the half-reactions.
Now, we can add the balanced half-reactions:
\[ \text{MnO}_4^{-} + 8 \text{H}^{+} + 10 \text{I}^{-} \rightarrow \text{Mn}^{2+} + 4 \text{H}_2\text{O} + 5 \text{I}_2 \]

### Step 6: Identify coefficients \(c\) and \(d\).
In the balanced equation:
- Coefficient \(c\) (for \(\text{H}^{+}\)) is 8.
- Coefficient \(d\) (for \(\text{Mn}^{2+}\)) is 1.

### Step 7: Calculate \(\frac{c}{d}\).
Now we can find the value of \(\frac{c}{d}\):
\[ \frac{c}{d} = \frac{8}{1} = 8 \]

### Final Answer:
The value of \(\frac{c}{d}\) is \(8\).

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