Calculate the oxidation numbers of `Cr` in `K_(3)CrO_(8)`:

Explanation

To calculate the oxidation number of Chromium (Cr) in the compound \( K_3CrO_8 \), we can follow these steps:

### Step 1: Identify the oxidation states of known elements
- Potassium (K) is an alkali metal and has an oxidation state of +1.
- Oxygen (O) typically has an oxidation state of -2, but in the case of peroxides, it can be -1.

### Step 2: Determine the structure of \( K_3CrO_8 \)
- The compound \( K_3CrO_8 \) contains 8 oxygen atoms. In this case, we need to recognize that there are peroxide linkages present in the compound. Each of these peroxides contributes an oxidation state of -1 for each oxygen.

### Step 3: Set up the equation for the oxidation states
- The total charge of the compound is neutral (0).
- The contribution from potassium is \( 3 \times (+1) = +3 \).
- If we assume that there are 4 peroxide linkages, then the contribution from the oxygen atoms would be \( 4 \times (-1) \) for the peroxides and \( 4 \times (-2) \) for the remaining oxygen atoms.

### Step 4: Write the equation
The equation can be set up as follows:
\[ 3(+1) + x + 8(-1) = 0 \]
Where \( x \) is the oxidation state of Chromium.

### Step 5: Simplify the equation
Substituting the known values into the equation:
\[ 3 + x - 8 = 0 \]
\[ x - 5 = 0 \]
\[ x = +5 \]

### Conclusion
The oxidation number of Chromium (Cr) in \( K_3CrO_8 \) is +5.

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