Arrange the following in increasing order of oxidation state of Ni.
`K_(2)[Ni(CN)_(4)],K_(2)[NiF_(6)],Ni(CO)_(4)`

Options

A. `Ni(CO)_(4), K_(2)[Ni(CN)_(4)], K_(2)[NiF_(6)]`
B. `K_(2)[Ni(CN)_(4)], Ni(CO)_(4), K_(2)[NiF_(6)]`
C. `Ni(CO)_(4), K_(2)[NiF_(6)], K_(2)[Ni(CN)_(4)]`
D. `K_(2)[NiF_(6)], K_(2)[Ni(CN)_(4)], Ni(CO)_(4)`

Explanation

To determine the increasing order of oxidation states of Nickel (Ni) in the given compounds, we will calculate the oxidation state of Ni in each compound step by step.

### Step 1: Calculate the oxidation state of Ni in K2[Ni(CN)4]

1. **Assign variables**: Let the oxidation state of Ni be \( X \).
2. **Identify oxidation states of other elements**:
- Potassium (K) has an oxidation state of +1.
- Cyanide (CN) has an oxidation state of -1.
3. **Set up the equation** based on the overall charge of the compound being zero:
\[ 2(+1) + X + 4(-1) = 0 \]
This simplifies to:
\[ 2 + X - 4 = 0 \]
\[ X - 2 = 0 \]
\[ X = +2 \]

### Step 2: Calculate the oxidation state of Ni in K2[NiF6]

1. **Assign variables**: Let the oxidation state of Ni be \( X \).
2. **Identify oxidation states of other elements**:
- Potassium (K) has an oxidation state of +1.
- Fluorine (F) has an oxidation state of -1.
3. **Set up the equation** based on the overall charge of the compound being zero:
\[ 2(+1) + X + 6(-1) = 0 \]
This simplifies to:
\[ 2 + X - 6 = 0 \]
\[ X - 4 = 0 \]
\[ X = +4 \]

### Step 3: Calculate the oxidation state of Ni in Ni(CO)4

1. **Assign variables**: Let the oxidation state of Ni be \( X \).
2. **Identify oxidation states of other elements**:
- Carbon monoxide (CO) has an oxidation state of 0.
3. **Set up the equation** based on the overall charge of the compound being zero:
\[ X + 4(0) = 0 \]
This simplifies to:
\[ X = 0 \]

### Step 4: Arrange the oxidation states in increasing order

Now that we have calculated the oxidation states of Ni in each compound:
- In K2[Ni(CN)4], the oxidation state of Ni is +2.
- In K2[NiF6], the oxidation state of Ni is +4.
- In Ni(CO)4, the oxidation state of Ni is 0.

Arranging these in increasing order:
1. Ni(CO)4: 0
2. K2[Ni(CN)4]: +2
3. K2[NiF6]: +4

### Final Answer:

The increasing order of oxidation states of Ni in the given compounds is:
\[ \text{Ni(CO)4} < \text{K2[Ni(CN)4]} < \text{K2[NiF6]} \]

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