Among the following, what is the total number of compounds having zero oxidation state of the underlined elements?
a. `ul(S)O_(3)^(2-)`
b. `H_(2)ul(C )O`
c. `ul(C )H_(2)Cl_(2)`
d. `Na_(2)ul(cl_(2))`

Explanation

To determine the total number of compounds having zero oxidation state for the underlined elements in the given compounds, we will analyze each compound one by one.

### Step 1: Analyze `ul(S)O_(3)^(2-)`
- The compound is `SO3^(2-)`.
- Let the oxidation state of sulfur (S) be \( x \).
- The oxidation state of oxygen (O) is \(-2\).
- The overall charge of the ion is \(-2\).

The equation can be set up as follows:
\[ x + 3(-2) = -2 \]
\[ x - 6 = -2 \]
\[ x = +4 \]

**Conclusion**: The oxidation state of sulfur in this compound is \( +4 \). Therefore, it does not have a zero oxidation state.

### Step 2: Analyze `H_(2)ul(C)O`
- The compound is `H2CO`.
- Let the oxidation state of carbon (C) be \( x \).
- The oxidation state of hydrogen (H) is \( +1\) and for oxygen (O) is \(-2\).

The equation can be set up as follows:
\[ 2(+1) + x + (-2) = 0 \]
\[ 2 + x - 2 = 0 \]
\[ x = 0 \]

**Conclusion**: The oxidation state of carbon in this compound is \( 0 \). Therefore, it has a zero oxidation state.

### Step 3: Analyze `ul(C)H_(2)Cl_(2)`
- The compound is `CH2Cl2`.
- Let the oxidation state of carbon (C) be \( x \).
- The oxidation state of hydrogen (H) is \( +1\) and for chlorine (Cl) is \(-1\).

The equation can be set up as follows:
\[ x + 2(+1) + 2(-1) = 0 \]
\[ x + 2 - 2 = 0 \]
\[ x = 0 \]

**Conclusion**: The oxidation state of carbon in this compound is \( 0 \). Therefore, it has a zero oxidation state.

### Step 4: Analyze `Na_(2)ul(Cl_(2))`
- The compound is `Na2Cl2`.
- Let the oxidation state of chlorine (Cl) be \( x \).
- The oxidation state of sodium (Na) is \( +1\).

The equation can be set up as follows:
\[ 2(+1) + 2x = 0 \]
\[ 2 + 2x = 0 \]
\[ 2x = -2 \]
\[ x = -1 \]

**Conclusion**: The oxidation state of chlorine in this compound is \( -1 \). Therefore, it does not have a zero oxidation state.

### Final Count of Compounds with Zero Oxidation State
From the analysis:
- `SO3^(2-)`: Not zero
- `H2CO`: Zero
- `CH2Cl2`: Zero
- `Na2Cl2`: Not zero

**Total number of compounds with zero oxidation state**: 2 (from `H2CO` and `CH2Cl2`).

### Final Answer
The total number of compounds having zero oxidation state of the underlined elements is **2**.

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